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**Lesson 1: Investigate • Thousandths**

**Lesson 2: Place Value of Decimals**

**Lesson 3: Compare and Order Decimals**

**Lesson 4: Round Decimals**

**Lesson 5: Investigate • Decimal Addition**

**Lesson 6: Investigate • Decimal Subtraction**

**Mid-Chapter Checkpoint**

**Lesson 7: Estimate Decimal Sums and Differences**

- Estimate Decimal Sums and Differences – Page No. 137
- Estimate Decimal Sums and Differences Lesson Check – Page No. 138

**Lesson 8: Add Decimals**

- Add Decimals – Page No. 140
- Add Decimals Lesson Check – Page No. 141
- Add Decimals Lesson Check 1 – Page No. 142

**Lesson 9: Subtract Decimals**

- Subtract Decimals – Page No. 144
- Subtract Decimals Lesson Check – Page No. 145
- Unlock the Problem – Page No. 146

**Lesson 10: Algebra • Patterns with Decimals**

**Lesson 11: Problem Solving • Add and Subtract Money**

**Lesson 12: Choose a Method**

- Choose a Method – Page No. 156
- Choose a Method Lesson Check – Page No. 157
- Choose a Method Lesson Check 1 – Page No. 158

**Review/Test**

- Review/Test – Page No. 159
- Review/Test – Page No. 160
- Review/Test – Page No. 161
- Review/Test – Page No. 162
- Review/Test – Page No. 163
- Review/Test – Page No. 164

**Write the decimal shown by the shaded parts of each model.**

Question 1.

______

Answer:

0.665

Explanation:

The given picture shows

6 hundredths, 6 tenths, and 5 thousandths are shaded

665/1000 = 0.665

Question 2.

______

Answer:

0.398

Explanation:

The given picture shows

3 hundredths, 9 tenths, and 8 thousandths are shaded

398/1000 = 0.398

Question 3.

______

Answer:

0.181

Explanation:

The given picture shows

1 hundredth, 8 tenths, and 1 thousandth are shaded

181/1000 = 0.181

Question 4.

______

Answer:

0.990

Explanation:

The given picture shows

9 hundredth, 9 tenths, and 0 thousandths are shaded

990/1000 = 0.990

**Complete the sentence.**

Question 5.

0.6 is 10 times as much as ______ .

______

Answer:

\(\frac{6}{100}\) = 0.06

Explanation:

Let the unknown number is S

0.6 = 10S

S = 0.6/10 = \(\frac{6}{10}\) x \(\frac{1}{10}\)

S = \(\frac{6}{100}\) = 0.06

Question 6.

0.007 is \(\frac{1}{10}\) of _______ .

______

Answer:

0.07

Explanation:

Let the unknown number is S

0.007 = \(\frac{1}{10}\)S

S = 0.007 x 10 = 0.07

Question 7.

0.008 is \(\frac{1}{10}\) of ________ .

______

Answer:

0.08

Explanation:

Let the unknown number is S

0.008 = \(\frac{1}{10}\)S

S = 0.008 x 10 = 0.08

Question 8.

0.5 is 10 times as much as ______ .

______

Answer:

0.05

Explanation:

Let the unknown number is S

0.5 = 10S

S = 0.5/10 = \(\frac{5}{10}\) x \(\frac{1}{10}\)

S = \(\frac{5}{100}\) = 0.05

**Use place-value patterns to complete the table.**

Question 9.

Type below:

_________

Answer:

Explanation:

0.2 is 10 times as much as

Let the unknown number is S

0.2 = 10S

S = 0.2/10 = 0.02

0.2 is 1/10 of

0.2 = S/10

S = 0.2 x 10 = 2

0.07 is 10 times as much as

Let the unknown number is S

0.07 = 10S

S = 0.07/10 = 0.007

0.07 is 1/10 of

0.07 = S/10

S = 0.07 x 10 = 0.7

0.05 is 10 times as much as

Let the unknown number is S

0.05 = 10S

S = 0.05/10 = 0.005

0.05 is 1/10 of

0.05 = S/10

S = 0.05 x 10 = 0.5

0.4 is 10 times as much as

Let the unknown number is S

0.4 = 10S

S = 0.4/10 = 0.04

0.4 is 1/10 of

0.4 = S/10

S = 0.4 x 10 = 4

Question 10.

Type below:

_________

Answer:

Explanation:

0.06 is 10 times as much as

Let the unknown number is S

0.06 = 10S

S = 0.06/10 = 0.006

0.06 is 1/10 of

0.06 = S/10

S = 0.06 x 10 = 0.6

0.9 is 10 times as much as

Let the unknown number is S

0.9 = 10S

S = 0.9/10 = 0.09

0.9 is 1/10 of

0.9 = S/10

S = 0.9 x 10 = 9

0.3 is 10 times as much as

Let the unknown number is S

0.3 = 10S

S = 0.3/10 = 0.03

0.3 is 1/10 of

0.3 = S/10

S = 0.3 x 10 = 3

0.08 is 10 times as much as

Let the unknown number is S

0.08 = 10S

S = 0.08/10 = 0.006

0.08 is 1/10 of

0.08 = S/10

S = 0.08 x 10 = 0.8

**Use the table for 17 and 20.**

Question 17.

A science teacher showed an image of a carpenter bee on a wall. The image is 10 times as large as the actual bee. Then he showed another image of the bee that is 10 times as large as the first image. What is the length of the bee in the second image?

______ meters

Answer:

2.5 meters

Explanation:

A science teacher showed an image of a carpenter bee on a wall. The image is 10 times as large as the actual bee.

carpenter bee = 0.025

The first image = 0.025 x 10 = 0.25

The second image = 10 times as large as the first image = 0.25 x 10 = 2.5

Question 18.

Math Explain how you can use place value to describe how 0.05 and 0.005 compare.

Type below:

_________

Answer:

Both numbers have 0 ones. So, we cannot compare these two numbers.

Look at the tenths. Both numbers have 0 tenths. So, we cannot compare these numbers.

Look at the hundredths.

The first number has 5 hundredths. The second number has 0 hundredths.

So, 0.05 > 0.005

Question 19.

Use Repeated Reasoning Terry, Sasha, and Harry each chose a number. Terry’s number is ten times as much as Sasha’s. Harry’s number is \(\frac{1}{10}\) of Sasha’s. Sasha’s number is 0.4. What number did each person choose?

Terry’s number: ______

Harry’s number: ______

Answer:

Terry’s number: 4

Harry’s number: 0.04

Explanation:

Sasha’s number is 0.4

Terry’s number is ten times as much as Sasha’s.

Terry’s number = 10 x 0.4 = 10 x \(\frac{4}{10}\) = 4

Harry’s number is \(\frac{1}{10}\) of Sasha’s.

Harry’s number = \(\frac{1}{10}\) x 0.4 = \(\frac{1}{10}\) x \(\frac{4}{10}\) = \(\frac{4}{100}\) = 0.04

Sasha’s number is 0.4

Terry’s number is 4

Harry’s number is 0.04

Question 20.

An atlas beetle is about 0.14 of a meter long. How does the length of the atlas beetle compare to the length of a leafcutting bee?

Type below:

_________

Answer:

An atlas beetle is about 0.14 of a meter long.

length of a leafcutting bee = 0.014

1 tenth is greater than 0 tenths.

So, 0.14 > 0.014

So, atlas beetle length is greater than the length of a leafcutting bee

Question 21.

Choose the numbers that make the statement true.

0.65 is 10 times as much as and \(\frac{1}{10}\) of

Type below:

_________

Answer:

0.65 is 10 times as much as 0.065

0.65 is \(\frac{1}{10}\) of 6.5

Explanation:

0.65 is 10 times as much as

0.65 = 10S

S = 0.65/10 = 0.065

0.65 is \(\frac{1}{10}\) of

0.65 x 10 = 6.5

So, 0.65 is 10 times as much as 0.065

0.65 is \(\frac{1}{10}\) of 6.5

Question 1.

Complete the place-value chart to find the value of each digit.

Type below:

_________

Answer:

Explanation:

3 x 1 = 3

5 Tenths = 5 x 1/10 = 0.5

2 hundredths = 2 x 1/100 = 0.02

3 thousandths = 3 x 1/1000 = 0.003

**Write the value of the underlined digit.**

Question 2.

0.543

Type below:

_________

Answer:

0.04

Explanation:

(0 x 1) + (5 x \(\frac{1}{10}\)) + (4 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))

4 x \(\frac{1}{100}\) = 4 hundredths = 0.04

Question 3.

6.234

Type below:

_________

Answer:

0.2

Explanation:

(6 x 1) + (2 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))

2 x \(\frac{1}{10}\) = 2 tenths = 0.2

Question 4.

3.954

Type below:

_________

Answer:

0.004

Explanation:

(3 x 1) + (9 x \(\frac{1}{10}\)) + (5 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))

4 x \(\frac{1}{1000}\) = 4 thousandths = 0.004

**Write the number in two other forms.**

Question 5.

0.253

Type below:

_________

Answer:

Word Form: two hundred fifty-three thousandths

Expanded Form: (0 x 1) + (2 x \(\frac{1}{10}\)) + (5 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))

Question 6.

7.632

Type below:

_________

Answer:

Word Form: seven and six hundred thirty-two thousandths

Expanded Form: (7 x 1) + (6 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))

**On Your Own**

**Write the value of the underlined digit.**

Question 7.

0.496

Type below:

_________

Answer:

0.09

Explanation:

(0 x 1) + (4 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))

9 x \(\frac{1}{100}\) = 9 hundredths = 0.09

Question 8.

2.726

Type below:

_________

Answer:

0.7

Explanation:

(2 x 1) + (7 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))

7 x \(\frac{1}{10}\) = 0.7

Question 9.

1.066

Type below:

_________

Answer:

0.006

Explanation:

(1 x 1) + (0 x \(\frac{1}{10}\)) + (6 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))

6 x \(\frac{1}{1000}\) = 0.006

Question 10.

6.399

Type below:

_________

Answer:

0.3

Explanation:

(6 x 1) + (3 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))

3 x \(\frac{1}{10}\) = 0.3

Question 11.

0.002

Type below:

_________

Answer:

0.002

Explanation:

(0 x 1) + (0 x \(\frac{1}{10}\)) + (0 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))

2 x \(\frac{1}{1000}\) = 0.002

Question 12.

4.371

Type below:

_________

Answer:

0.001

Explanation:

(4 x 1) + (3 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (1 x \(\frac{1}{1000}\))

1 x \(\frac{1}{1000}\) = 0.001

**Write the number in two other forms.**

Question 13.

0.489

Type below:

_________

Answer:

Word Form: four hundred eighty-nine thousandths

Expanded Form: (0 x 1) + (4 x \(\frac{1}{10}\)) + (8 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))

Question 14.

5.916

Type below:

_________

Answer:

Word Form: five and nine hundred sixteen thousandths

Expanded Form: (5 x 1) + (9 x \(\frac{1}{10}\)) + (1 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))

**Use the table for 15–16.**

Question 15.

What is the value of the digit 7 in New Mexico’s average annual rainfall?

Type below:

_________

Answer:

0.07

Explanation:

New Mexico’s average annual rainfall = 0.372

(0 x 1) + (3 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))

7 x \(\frac{1}{100}\) = 0.07

Question 16.

Which of the states has an average annual rainfall with the least number in the thousandths place? What is another way to write the total annual rainfall in this state?

_________

Answer:

Wisconsin

(0 x 1) + (8 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (0 x \(\frac{1}{1000}\))

Explanation:

California = 0.564

New Mexico = 0.372

New York = 1.041

Wisconsin = 0.820

Maine = 1.074

The state that has an average annual rainfall with the least number in the thousandths place

0 < 1 < 2 < 4. So, the state is Wisconsin.

Another way to write the total annual rainfall in Wisconsin state is (0 x 1) + (8 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (0 x \(\frac{1}{1000}\))

Question 17.

Verify the Reasoning of Others Damian wrote the number four and twenty-three thousandths as 4.23. Describe and correct his error.

Type below:

_________

Answer:

four and twenty-three thousandths = 4 ones and 0 tenths, 2 hundredths, three thousandths = 4.023.

He has written 4.23 which is wrong.

Question 18.

Dan used a meter stick to measure some seedlings in his garden. One day, a corn stalk was 0.85 m tall. A tomato plant was 0.850 m. A carrot top was 0.085 m. Which plant was shortest?

_________

Answer:

the carrot top is the shortest plant

Explanation:

Dan used a meter stick to measure some seedlings in his garden. One day, a corn stalk was 0.85 m tall. A tomato plant was 0.850 m. A carrot top was 0.085 m. 0 tenths are less than the 8 tenths. So, 0.085 is less than 0.85 or 0.850. So, the carrot top is the shortest plant.

Question 19.

Math Explain how you know that the digit 6 does not have the same value in the numbers 3.675 and 3.756.

Type below:

_________

Answer:

In 3.675, the digit of 6 is in the tenths place. So, its value is 6 x 1/10 or 0.6.

In 3.756, the digit of 6 is in the thousandths place, so its value is 6 x 1/1000 or 0.006.

Question 20.

What is the value of the underlined digit? Mark all that apply.

0.589

Options:

a. 0.8

b. 0.08

c. eight tenths

d. eight hundredths

e. 8 × (\(\frac{1}{10}\))

Answer:

b. 0.08

d. eight hundredths

Explanation:

(0 x 1) + (5 x \(\frac{1}{10}\)) + (8 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))

8 x \(\frac{1}{100}\) = 8 hundredths = 0.08

Question 1.

Use the place-value chart to compare the two numbers. What is the greatest place-value position where the digits differ?

Type below:

_________

Answer:

3.472 > 3.445

They differ in hundredths position

Explanation:

Compare the ones; 3 = 3

Compare the tenths; 4 = 4

Compare the hundredths; 7 > 4

So, 3.472 > 3.445

**Compare. Write <, >, or =.**

Question 2.

4.563 ______ 4.536

Answer:

4.563 > 4.536

Explanation:

Compare the ones; 4 = 4

Compare the tenths; 5 = 5

Compare the hundredths; 6 > 3

So, 4.563 > 4.536

Question 3.

5.640 ______ 5.64

Answer:

5.640 = 5.64

Explanation:

Compare the ones; 5 = 5

Compare the tenths; 6 = 6

Compare the hundredths; 4 = 4

Compare the thousandths; 0 = 0

So, 5.640 = 5.64

Question 4.

8.673 ______ 8.637

Answer:

8.673 > 8.637

Explanation:

Compare the ones; 8 = 8

Compare the tenths; 6 = 6

Compare the hundredths; 7 > 3

So, 8.673 > 8.637

**Name the greatest place-value position where the digits differ.**

**Name the greater number.**

Question 5.

3.579; 3.564

______

Answer:

3.579 > 3.564

The greatest place-value position where the digits differ are hundredths

Explanation:

Compare the ones; 3 = 3

Compare the tenths; 5 = 5

Compare the hundredths; 7 > 6

So, 3.579 > 3.564

The greatest place-value position where the digits differ are hundredths

Question 6.

9.572; 9.637

______

Answer:

9.572 < 9.637

The greatest place-value position where the digits differ are tenths

Explanation:

Compare the ones; 9 = 9

Compare the tenths; 5 < 6

So, 9.572 < 9.637

The greatest place-value position where the digits differ are tenths

Question 7.

4.159; 4.152

______

Answer:

4.159 > 4.152

The greatest place-value position where the digits differ are thousandths

Explanation:

Compare the ones; 4 = 4

Compare the tenths; 1 = 1

Compare the hundredths; 5 = 5

Compare the thousandths; 9 > 2

So, 4.159 > 4.152

The greatest place-value position where the digits differ are thousandths

**Order from least to greatest.**

Question 8.

4.08; 4.3; 4.803; 4.038

Answer:

4.038, 4.08, 4.3, 4.803

Explanation:

Compare the ones; All are equal

Compare the tenths; 0 < 3 < 8.

So, 4.08, 4.038, 4.3, 4.803

Compare the hundredths of 4.08 and 4.038; 8 > 3

So, 4.038, 4.08, 4.3, 4.803

Question 9.

1.703; 1.037; 1.37; 1.073

Answer:

1.037, 1.073, 1.37, 1.703

Explanation:

Compare the ones; All are equal

Compare the tenths; 0 < 3 < 7.

So, 1.037; 1.073; 1.37; 1.703

Compare the hundredths of 1.037 and 1.073; 3 < 7

So, 1.037, 1.073, 1.37, 1.703

**On Your Own**

**Compare. Write <, >, or =.**

Question 10.

8.72 ______ 8.720

Answer:

8.72 = 8.720

Explanation:

Compare the ones; 8 = 8

Compare the tenths; 7 = 7

Compare the hundredths; 2 = 2

Compare the thousands; 0 = 0

So, 8.72 = 8.720

Question 11.

5.4 ______ 5.243

Answer:

5.4 > 5.243

Explanation:

Compare the ones; 5 = 5

Compare the tenths; 4 > 2

So, 5.4 > 5.243

Question 12.

1.036 ______ 1.306

Answer:

1.036 < 1.306

Explanation:

Compare the ones; 1 = 1

Compare the tenths; 0 < 3

So, 1.036 < 1.306

Question 13.

2.573 ______ 2.753

Answer:

2.573 < 2.753

Explanation:

Compare the ones; 2 = 2

Compare the tenths; 5 < 7

So, 2.573 < 2.753

Question 14.

9.300 ______ 9.3

Answer:

9.300 = 9.3

Explanation:

Compare the ones; 9 = 9

Compare the tenths; 3 = 3

Compare the hundredths; 0 = 0

Compare the thousands; 0 = 0

So, 9.300 = 9.3

Question 15.

6.76 ______ 6.759

Answer:

6.76 > 6.759

Explanation:

Compare the ones; 6 = 6

Compare the tenths; 7 = 7

Compare the hundredths; 6 > 5

So, 6.76 > 6.759

**Order from greatest to least.**

Question 16.

2.007; 2.714; 2.09; 2.97

______ ; ______ ; ______ ; ______

Answer:

2.97; 2.714; 2.09; 2.007

Explanation:

Compare the ones; All are equal

Compare the tenths; 0 < 7 < 9.

So, 2.007; 2.09; 2.714; 2.97

Compare the hundredths of 2.007 and 2.09; 0 < 9

So, 2.007; 2.09; 2.714; 2.97

Order from greatest to least = 2.97; 2.714; 2.09; 2.007

Question 17.

0.386; 0.3; 0.683; 0.836

______ ; ______ ; ______ ; ______

Answer:

0.836; 0.683; 0.386; 0.3

Explanation:

Compare the ones; All are equal

Compare the tenths; 0 < 3 < 6 < 8.

So, 0.386; 0.3; 0.683; 0.836

Compare the hundredths of 0.386 and 0.3; 8 > 0

So, 0.3; 0.386; 0.683; 0.836

Order from greatest to least = 0.836; 0.683; 0.386; 0.3

Question 18.

5.249; 5.43; 5.340; 5.209

______ ; ______ ; ______ ; ______

Answer:

5.43; 5.340; 5.249; 5.209

Explanation:

Compare the ones; All are equal

Compare the tenths; 2 < 3 < 4.

So, 5.249; 5.209; 5.340; 5.43

Compare the hundredths of 5.249 and 5.209; 4 > 0

So, 5.209; 5.249; 5.340; 5.43

Order from greatest to least = 5.43; 5.340; 5.249; 5.209

Question 19.

0.678; 1.678; 0.587; 0.687

______ ; ______ ; ______ ; ______

Answer:

1.678; 0.687; 0.678; 0.587

Explanation:

Compare the ones; 0 < 1

So, 0.678; 0.587; 0.687; 1.678

Compare the tenths of 0.678; 0.587; 0.687; 5 < 6.

So, 0.587; 0.678; 0.687; 1.678

Compare the hundredths of 0.678 and 0.687; 7 < 8

So, 0.587; 0.678; 0.687; 1.678

Order from greatest to least = 1.678; 0.687; 0.678; 0.587

**Use Reasoning Algebra Find the unknown digit to make each statement true.**

Question 20.

3.59 > 3.5 ______ 1 > 3.572

Answer:

3.59 > 3.581 > 3.572

Explanation:

The possible values are

3.573; 3.574; 3.575; 3.578; 3.579; 3.580; 3.581; 3.582; 3.583; 3.584; 3.585; 3.586; 3.587; 3.588; 3.589;

The digit that ends with 1 is 3.581.

So, the unknown digit is 3.581

Question 21.

6.837 > 6.83 ______ > 6.835

Answer:

6.837 > 6.836 > 6.835

Explanation:

The value must be 6.836. Because 6 is the only digit between 5 and 7.

So, the unknown digit is 6.836

Question 22.

2.45 < 2 ______ 6 < 2.461

Answer:

2.45 < 2.456 < 2.461

Explanation:

2.451; 2.452; 2.453; 2.454; 2.455; 2.456; 2.457; 2.458; 2.459; 2.460; 2.461

The digit that ends with 6 is 2.456.

So, the unknown digit is 2.456

**Use the table for 23–26.**

Question 23.

In comparing the height of the mountains, which is the greatest place value where the digits differ?

_________

Answer:

The greatest place value where the digits differ is hundredths

Explanation:

3.104; 3.134; 3.152

0 hundredths < 3 hundredths < 5 hundredths

3.152; Mount Steele, Yukon is the greatest mountain.

The greatest place value where the digits differ is hundredths.

Question 24.

Use Math Vocabulary How does the height of Mount Steele compare to the height of Mount Blackburn? Compare the heights using words.

Type below:

_________

Answer:

The Height of Mount Steele is greater than Height of Mount Blackburn.

Explanation:

Height of Mount Steele = 3.152

Height of Mount Blackburn = 3.104

3.152 > 3.104

The Height of Mount Steele is greater than Height of Mount Blackburn.

Question 25.

Explain how to order the heights of the mountains from greatest to least.

Type below:

_________

Answer:

3.152 > 3.134 > 3.104

Explanation:

3.104; 3.134; 3.152

0 hundredths < 3 hundredths < 5 hundredths

3.152 > 3.134 > 3.104

Question 26.

What if the height of Mount Blackburn were 0.05 mile greater? Would it then be the mountain with the greatest height? Explain.

______

Answer:

Height of Mount Blackburn = 3.104 + 0.05 = 3.154

3.154 > 3.152 > 3.134.

Yes, Mount Blackburn would have the greatest height if it has 0.05 mile greater.

Question 27.

Orlando kept a record of the total rainfall each month for 5 months.

Order the months from the least amount of rainfall to the greatest amount of rainfall.

Least ______ ______ ______ ______ ______ Greatest

Answer:

Least: 3.09; 3.75; 4.04; 4.09; 4.42 Greatest

Explanation:

3.75; 4.42; 4.09; 3.09; 4.04

3 < 4

3.75; 3.09; 4.42; 4.09; 4.04

Compare tenths of 3.75 and 3.09; 0 < 7

3.09; 3.75; 4.42; 4.09; 4.04

Compare tenths of 4.42; 4.09; 4.04; 0 <4

3.09; 3.75; 4.09; 4.04; 4.42

Compare hundredths of 4.09 and 4.04; 4 < 9

So, 3.09; 3.75; 4.04; 4.09; 4.42

**Write the place value of the underlined digit. Round each number to the place of the underlined digit.**

Question 1.

0.673

Place value: ________

Round: ________

Answer:

Place value: 7 hundredths = 0.07

Round: 0.670

Explanation:

0.673

(0 x 1) + (6 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))

Place Value: 7 x \(\frac{1}{100}\) = 7 hundredths = 0.07

0.673

3 < 5

0.670

Question 2.

4.282

Place value: ________

Round: ________

Answer:

Place value: 2 tenths = 0.2

Round: 4.300

Explanation:

4.282

(4 x 1) + (2 x \(\frac{1}{10}\)) + (8 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))

Place Value: 2 x \(\frac{1}{10}\) = 2 tenths = 0.2

4.282

8 > 5

4.300

Question 3.

12.917

Place value: ________

Round: ________

Answer:

Place value: 2 ones = 2

Round: 13

Explanation:

12.917

(1 x 10) + (2 x 1) + (9 x \(\frac{1}{10}\)) + (1 x \(\frac{1}{100}\)) + (7 x \(\frac{1}{1000}\))

Place Value: 2 x 1 = 2 ones = 2

12.917

9 > 5

13

**Name the place value to which each number was rounded.**

Question 4.

0.982 to 0.98

________

Answer:

The hundredths

Explanation:

As 2 < 5, We round 0.982 to 0.98.

The place value of the digit 8 is hundredths.

The hundredths

Question 5.

3.695 to 4

________

Answer:

The ones

Explanation:

As 6 > 5, We round 3.695 to 4.

The place value of the digit 3 is ones.

The ones

Question 6.

7.486 to 7.5

________

Answer:

The tenths

Explanation:

As 8 > 5, We round 7.486 to 7.5.

The place value of the digit 4 is tenths.

The tenths

**On Your Own**

**Write the place value of the underlined digit. Round each number to the place of the underlined digit.**

Question 7.

0.592

Place value: ________

Round: ________

Answer:

Place value: 5 tenths = 0.5

Round: 0.6

Explanation:

0.592

(0 x 1) + (5 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))

Place Value: 5 x \(\frac{1}{10}\) = 5 tenths = 0.5

0.592

9 > 5

0.6

Question 8.

6.518

Place value: ________

Round: ________

Answer:

Place value: 6 ones = 6

Round: 7

Explanation:

6.518

(6 x 1) + (5 x \(\frac{1}{10}\)) + (1 x \(\frac{1}{100}\)) + (8 x \(\frac{1}{1000}\))

Place Value: 6 x 1 = 6 ones = 6

6.518

5 = 5

7

Question 9.

0.809

Place value: ________

Round: ________

Answer:

Place value: 0 hundredths = 0

Round: 0.8

Explanation:

0.809

(0 x 1) + (8 x \(\frac{1}{10}\)) + (0 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))

Place Value: 0 x \(\frac{1}{100}\) = 0 hundredths = 0

0.809

0 < 5

0.800

Question 10.

3.334

Place value: ________

Round: ________

Answer:

Place value: 7 tenths = 0.7

Round: 3

Explanation:

3.334

(3 x 1) + (3 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))

Place Value: 3 x \(\frac{1}{10}\) = 7 tenths = 0.7

3.334

3 < 5

3.000

Question 11.

12.074

Place value: ________

Round: ________

Answer:

Place value: 0 tenths = 0

Round: 12.1

Explanation:

12.074

(1 x 10) + (2 x 1) + (0 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))

Place Value: 0 x \(\frac{1}{10}\) = 0 tenths = 0

12.074

7 > 5

12.1

Question 12.

4.494

Place value: ________

Round: ________

Answer:

Place value: 9 hundredths = 0.09

Round: 4.49

Explanation:

4.494

(4 x 1) + (4 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))

Place Value: 9 x \(\frac{1}{100}\) = 9 hundredths = 0.09

4.494

4 < 5

4.49

**Name the place value to which each number was rounded.**

Question 13.

0.328 to 0.33

________

Answer:

The hundredths

Explanation:

As 8 > 5, We round 0.328 to 0.33.

The place value of the digit 2 is hundredths.

The hundredths

Question 14.

2.607 to 2.61

________

Answer:

The hundredths

Explanation:

As 7 > 5, We round 2.607 to 2.61.

The place value of the digit 0 is hundredths.

The hundredths

Question 15.

12.583 to 13

________

Answer:

The ones

Explanation:

As 5 = 5, We round 12.583 to 13.

The place value of the digit 2 is ones.

The ones

**Round 16.748 to the place named.**

Question 16.

tenths: ______

Answer:

16.7

Explanation:

Round 16.748 to the nearest tenths

The tenth digit is 7. So, 4 < 5

16.7

Question 17.

hundredths: ______

Answer:

16.75

Explanation:

Round 16.748 to the nearest hundredths

The hundredth digit is 4. So, 8 > 5

16.75

Question 18.

ones: ______

Answer:

17

Explanation:

Round 16.748 to the nearest ones

The ones digit is 6. So, 7 > 5

17

Question 19.

Explain what happens when you round 4.999 to the nearest tenth.

Type below:

_________

Answer:

5

Explanation:

round 4.999 to the nearest tenth

The tenth digit is 9. So, 9 > 5

5

**Use the table for 20–22.**

Question 20.

The speeds of two insects when rounded to the nearest whole number are the same. Which two insects are they?

_________

_________

Answer:

Bumblebee

Honeybee

Explanation:

Dragonfly = 6.974 meters; nearest whole number = 7

Horsefly = 3.934 meters; nearest whole number = 4

Bumblebee = 2.861 meters; nearest whole number = 3

Honeybee = 2.548 meters; nearest whole number = 3

Housefly = 1.967 meters; nearest whole number = 2

Bumblebee and Honeybee speeds are the same if their rounded to the nearest whole number.

Question 21.

What is the speed of the housefly rounded to the nearest hundredth?

______ meters per second

Answer:

3.93 meters per second

Explanation:

Horsefly = 3.934 meters rounded to the nearest hundredth

The hundredth digit is 3. So, 4 < 5

3.93

Question 22.

What’s the Error? Mark said that the speed of a dragonfly rounded to the nearest tenth was 6.9 meters per second. Is he correct? If not, what is his error?

Type below:

_________

Answer:

Dragonfly = 6.974 meters rounded to the nearest tenth.

The tenth digit is 9. So, 7 > 5

7.

So, Mark said is wrong.

Question 23.

A rounded number for the speed of an insect is 5.67 meters per second. What are the fastest and slowest speeds to the thousandths that could round to 5.67 meters per second? Explain.

Type below:

_________

Answer:

The slowest speed to the thousandths that could round to 5.67 meters per second is 5.671

The fastest speed to the thousandths that could round to 5.67 meters per second is 5.674

Explanation:

To find the slowest speed to the thousandths that could round to 5.67 meters per second we need to find the lowest digit which will not affect the digit in the hundredths place, and that is 1. So, the slowest speed to the thousandths that could round to 5.67 meters per second is 5.671.

To find the fastest speed to the thousandths that could round to 5.67 meters per second we need to find the greatest digit which will not affect the digit in the hundredths place, and that is 4. So, the fastest speed to the thousandths that could round to 5.67 meters per second is 5.674.

Question 24.

The price of a certain box of cereal at the grocery store is $0.258 per ounce. For numbers 24a–24c, select True or False for each statement.

a. Rounded to the nearest whole number, the price is $1 per ounce.

i. yes

ii. no

Answer:

ii. no

Explanation:

$0.258

2 < 5.

So, if we rounded to the nearest whole number, the value becomes 0.

Question 24.

b. Rounded to the nearest tenth, the price is $0.3 per ounce.

i. yes

ii. no

Answer:

i. yes

Explanation:

$0.258

5 = 5

So, $3 is the answer.

Question 24.

c. Rounded to the nearest hundredth, the price is $0.26 per ounce.

i. yes

ii. no

Answer:

i. yes

Explanation:

$0.258

8 > 5

$0.26

**Complete the quick picture**

Question 1.

1.37 + 1.85 =

______

Answer:

Explanation:

1.37 + 1.85 = 3. 22

Add hundredths; 7 + 5 = 12; Regroup

Add tenths; 3 + 8 + 1 = 12; Regroup

Add tens; 1 + 1 + 1 = 3

**Add. Draw a quick picture.**

Question 2.

0.9 + 0.7 =

______

Answer:

0.9 + 0.7 = 1.6

Explanation:

0.9 + 0.7 =

Add tenths 9 + 7 = 16; Regroup

Add ones 0 + 0 + 1 = 1

0.9 + 0.7 = 1.6

Question 3.

0.65 + 0.73 =

______

Answer:

0.65 + 0.73 = 1.38

Explanation:

0.65 + 0.73 = 1.38

Add hundredths 5 + 3 = 8;

Add tenths 6 + 7 = 13; Regroup

Add ones 0 + 0 + 1 = 1

0.65 + 0.73 = 1.38

Question 4.

1.3 + 0.7 =

______

Answer:

1.3 + 0.7 = = 2

Explanation:

Add tenths 3 + 7 = 10; Regroup

Add ones 1 + 1 = 2

1.3 + 0.7 = = 2

Question 5.

2.72 + 0.51 =

______

Answer:

2.72 + 0.51 = 3.23

Explanation:

Add hundredths 2 + 1 = 3

Add tenths 5 + 7 = 12; Regroup

Add ones 2 + 0 + 1 = 3

2.72 + 0.51 = 3.23

**Problem Solving Applications**

Question 6.

Carissa bought 2.35 pounds of chicken and 2.7 pounds of turkey for lunches this week. She used a quick picture to and the amount of lunch meat. Does Carissa’s work make sense? Explain.

______

Answer:

Yes; Because she bought 2.35 pounds of chicken and 2.7 pounds

2.35 + 2.7 = 5.05 pounds.

there is 5 ones and 5 hundredths.

Question 7.

Robyn and Jim used quick pictures to model 1.85 + 2.73.

Robyn’s Work

1.85 + 2.73 = 3.158

Does Robyn’s work make sense?

Explain your reasoning.

Type below:

_________

Answer:

Robyn’s work doesn’t make sense. Because 7 + 8 = 15. So, he needs to regroup and then add 1 to the one’s digits.

1 + 2 + 1 = 4

1.85 + 2.73 = 4.58 is the correct answer.

Jim’s Work

1.85 + 2.73 = 4.58

Does Jim’s work make sense?

Explain your reasoning.

Answer:

Jim’s work makes sense.

Add: 1.85 + 2.73 = 4.58.

4 ones, 5 tenths, and 8 hundredths.

Question 8.

Make Arguments Explain how you would help Robyn understand that regrouping is important when adding decimals.

Type below:

_________

Answer:

Regrouping is important when adding decimals. When you add two digits, if their addition is more than 10 then we need to regroup the values to find the correct answer.

Question 9.

Write a decimal addition problem that requires regrouping the hundredths. Explain how you know you will need to regroup.

Type below:

_________

Answer:

Let’s add 1.47 and 1.35 As we have more than 9 hundredths we have to regroup and mid the tenths.

So, now we have 8 tenths and two-hundredths left.

Also, as we have less than 9 tenths we do not have to regroup and add the ones.

The answer is 2.82.

As we have more than 9 hundredths we have to regroup and mid the tenths.

**Complete the quick picture to find the difference.**

Question 1.

0.62 − 0.18 =

______

Answer:

Explanation:

0.62 − 0.18

Subtract hundredths: 2 – 8;

There are not enough hundredths. So, regroup

12 – 8 = 4

Subtract tenths: 5 – 1 = 4

Subtract ones: 0 – 0 = 0

So, 0.62 − 0.18 = 0.44

**Subtract. Draw a quick picture.**

Question 2.

3.41 − 1.74 =

______

Answer:

Explanation:

3.41 − 1.74

Subtract hundredths: 1 – 4;

There are not enough hundredths. So, regroup

11 – 4 = 7

Subtract tenths: 3 – 7

There are not enough tenths. So, regroup

13 – 7 = 6

Subtract ones: 2 – 1 = 1

So, 3.41 − 1.74 = 1.67

Question 3.

0.84 − 0.57 =

______

Answer:

Explanation:

0.84 − 0.57

Subtract hundredths: 4 – 7;

There are not enough hundredths. So, regroup

14 – 7 = 7

Subtract tenths: 7 – 5 = 2

Subtract ones: 0 – 0 = 0

So, 0.84 − 0.57 = 0.27

Question 4.

4.05 − 1.61 =

______

Answer:

Explanation:

4.05 − 1.61

Subtract hundredths: 5 – 1 = 4;

Subtract tenths: 0 – 6

There are not enough hundredths. So, regroup

10 – 6 = 4

Subtract ones: 3 – 1 = 2

So, 4.05 − 1.61 = 2.44

**Problem Solving Applications**

Question 6.

Write a decimal subtraction equation that requires regrouping from the tenths. Explain how you know you will need to regroup.

Type below:

__________

Answer:

Subtract 0.32 and 0.05

Subtract hundredths. As there are not enough hundredths we have to regroup. So, we have 10 more hundredths and one-tenth I.

Subtract tenths. As there are enough tenths we do not have to regroup.

The answer: 0.27

Question 7.

Antonio left his MathBoard on his desk during lunch. The quick picture below shows the problem he was working on when he left.

Write a word problem that can be solved using the quick picture above.

Pose a problem. Solve your problem.

Type below:

__________

Answer:

From the given picture, he has drawn eight-hundredths and crosses two-hundredths. Then, he has drawn six tenths and crossed four-tenths. When comes to ones. he has taken three ones and crossed two out of them.

there are 7 – 2 = 5 hundredths

6 – 4 = 2 tenths

3 – 2 = 1 ones

1.25

Question 7.

Use Reasoning Describe how you can change the problem by changing the quick picture.

Type below:

__________

Answer:

By changing the quick picture, the value of place value is changed.

Question 8.

The price of a box of markers at a retail store is $4.65. he price of a box of markers at the school bookstore is $3.90. How much more do the markers cost at the retail store? Explain how you can use a quick picture to solve the problem.

$ ______

Answer:

The price of a box of markers at a retail store is $4.65. he price of a box of markers at the school bookstore is $3.90.

$4.65 – $3.90 = $0.75

Question 1.

Explain how you can use base-ten blocks to find 1.54 + 2.37.

Type below:

__________

Answer:

1.54 + 2.37

Add hundredths 4 + 7 = 11; Regroup

Add tenths 5 + 3 + 1 = 9;

Add ones 2 + 1 = 3

1.54 + 2.37 = 3.91

We have to use three square boxes to show three ones, 9 lines to show 9 tenths, and 1 dot to show one hundredth

**Complete the sentence.**

Question 2.

0.04 is \(\frac{1}{10}\) of

Answer:

0.04 is \(\frac{1}{10}\) of 0.4

Explanation:

Let the unknown number is S

0.04 = \(\frac{1}{10}\)S

S = 0.04 x 10 = 0.4

Question 3.

0.06 is 10 times as much as

Answer:

\(\frac{6}{1000}\) = 0.006

Explanation:

Let the unknown number is S

0.06 = 10S

S = 0.06/10

S = \(\frac{6}{100}\) x \(\frac{1}{10}\)

S = \(\frac{6}{1000}\) = 0.006

**Write the value of the underlined digit.**

Question 4.

6.54

Type below:

__________

Answer:

4 hundredths = 0.04

Explanation:

(6 x 1) + (5 x \(\frac{1}{10}\)) + (4 x \(\frac{1}{100}\))

4 x \(\frac{1}{100}\) = 4 hundredths = 0.04

Question 5.

0.837

Type below:

__________

Answer:

8 tenths = 0.8

Explanation:

(0 x 1) + (8 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (7 x \(\frac{1}{1000}\))

8 x \(\frac{1}{10}\) = 8 tenths = 0.8

Question 6.

8.702

Type below:

__________

Answer:

2 thousandths = 0.002

Explanation:

(8 x 1) + (7 x \(\frac{1}{10}\)) + (0 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))

2 x \(\frac{1}{1000}\) = 2 thousandths = 0.002

Question 7.

*9*.173

Type below:

__________

Answer:

9 ones = 9

Explanation:

(9 x 1) + (1 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))

9 x 1 = 9 ones = 9

**Compare. Write <, >, or =.**

Question 8.

6.52 _____ 6.520

Answer:

6.52 = 6.520

Explanation:

Compare the ones; 6 = 6

Compare the tenths; 5 = 5

Compare the hundredths; 2 = 2

Compare the thousandths; 0 = 0

So, 6.52 = 6.520

Question 9.

3.589 _____ 3.598

Answer:

3.589 < 3.598

Explanation:

Compare the ones; 3 = 3

Compare the tenths; 5 = 5

Compare the hundredths; 8 < 9

So, 3.589 < 3.598

Question 10.

8.483 _____ 8.463

Answer:

8.483 > 8.463

Explanation:

Compare the ones; 8 = 8

Compare the tenths; 4 = 4

Compare the hundredths; 8 > 6

So, 8.483 > 8.463

**Write the place value of the underlined digit. Round each number to the place of the underlined digit.**

Question 11.

0.724

Place value: __________

Round: __________

Answer:

Place value: 7 tenths = 0.7

Round: 0.7

Explanation:

0.724

(0 x 1) + (7 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))

Place Value: 7 x \(\frac{1}{10}\) = 7 tenths = 0.7

0.724

2 < 5

0.7

Question 12.

2.576

Place value: __________

Round: __________

Answer:

Place value: 2 ones = 2

Round: 3

Explanation:

2.576

(2 x 1) + (5 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))

Place Value: 2 x 1 = 2 ones = 2

2.576

5 = 5

3

Question 13.

4.769

Place value: __________

Round: __________

Answer:

Place value: 6 hundredths = 0.06

Round: 4.77

Explanation:

4.769

(4 x 1) + (7 x \(\frac{1}{10}\)) + (6 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))

Place Value: 6 x \(\frac{1}{100}\)) = 6 hundredths = 0.06

4.769

9 > 5

4.77

**Draw a quick picture to find the sum or difference.**

Question 14.

2.46 + 0.78 =

Answer:

Explanation:

2.46 + 0.78 = 3.24

Question 15.

3.27 − 1.84 =

Answer:

Explanation:

3.27 − 1.84 = 1.43

Question 16.

Marco read that a honeybee can fly up to 2.548 meters per second. He rounded the number to 2.55. To which place value did Marco round the speed of a honeybee?

__________

Answer:

Marco read that a honeybee can fly up to 2.548 meters per second. He rounded the number to 2.55.

The speed of a honeybee is 2.548.

Marco has to round this number to the nearest hundredth to get 2.55.

The digit in the hundredths places increases by 1.

The 8 > 5

So, the rounded number is 2.55.

Question 17.

What is the relationship between 0.04 and 0.004?

Type below:

__________

Answer:

Comapre ones; 0 = 0

Compare tenths; 0 = 0

Compare hundredths; 4 > 0

So, 0.04 > 0.004

Question 18.

Jodi drew a quick picture to model the answer for 3.14 − 1.75. Draw what her picture might look like.

Type below:

__________

Answer:

Explanation:

Jodi drew a quick picture to model the answer for 3.14 − 1.75

3.14 – 1.75 = 1.39

Question 19.

The average annual rainfall in California is 0.564 of a meter per year. What is the value of the digit 4 in that number?

Type below:

__________

Answer:

The average annual rainfall in California is 0.564 of a meter per year.

(0 x 1) + (5 x \(\frac{1}{10}\)) + (6 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))

4 x \(\frac{1}{1000}\) = 4 thousandths = 0.004

Question 20.

Jan ran 1.256 miles on Monday, 1.265 miles on Wednesday, and 1.268 miles on Friday. What were her distances from greatest to least?

_____ mi; _____ mi; _____ mi

Answer:

1.268 mi; 1.265 mi; 1.256 mi

Explanation:

Jan ran 1.256 miles on Monday, 1.265 miles on Wednesday, and 1.268 miles on Friday.

Compare hundredths: 6 > 5

So, 1.265; 1.268; 1.256

Compare thousandths in 1.265 and 1.268

8 > 5

1.268 mi; 1.265 mi; 1.256 mi

**Use rounding to estimate.**

Question 1.

2.3 4

1.9

+5.2 3

————

Estimate: _____

Answer:

Estimate: About 9

Explanation:

2.34; 3 < 5; 2

1.9; 9 > 5; 2

5.23; 2 < 5; 5

Add: 2 + 2 + 5 = 9

Question 2.

10.3 9

-4.2 8

————

Estimate: _____

Answer:

Estimate: About 6

Explanation:

10.39; 3 < 5; 10

4.28; 2 < 5; 4

Subtract: 10 – 4 = 6

Question 3.

$ 19.7 5

+$3.9 8

————

Estimate: $ _____

Answer:

Estimate: About $24

Explanation:

19.7 5; 7 > 5; 20

3.98; 9 > 5; 4

20 + 4 = 24

**Use benchmarks to estimate.**

Question 4.

0.3 4

0.1

+0.2 5

————

Estimate: _____

Answer:

Estimate: About 0.55

Explanation:

0.3 4 is closer to 0.35

0.1 is closer to 0

0.25

0.35 + 0 + 0.25 = 0.55

Question 5.

10.3 9

-4.2 8

————

Estimate: _____

Answer:

Estimate: About 6

Explanation:

10.3 9 is closer to 10

4.2 8 is closer to 4

10 – 4 = 6

**On Your Own**

**Use rounding to estimate.**

Question 6.

0.9 3

+0.1 8

————

Estimate: _____

Answer:

Estimate: About 1

Explanation:

0.93; 9 >5; 1

0.18; 1 < 5; 0

1 + 0 = 1

Question 7.

7.4 1

-3.8 8

————

Estimate: _____

Answer:

Estimate: About 3

Explanation:

7.41; 4 < 5; 7

3.88; 8 > 5; 4

7 – 4 = 3

Question 8.

14.6 8

-3.9 3

————

Estimate: _____

Answer:

Estimate: About 11

Explanation:

14.68; 6 > 5; 15

3.93; 9 > 5; 4

15 – 4 = 11

**Use benchmarks to estimate.**

Question 9.

12.4 1

-6.4 7

————

Estimate: _____

Answer:

Estimate: About 6

Explanation:

12.41 is closer to 12

6.47 is closer to 6

12 – 6 = 6

Question 10.

8.1 2

-5.5 2

————

Estimate: _____

Answer:

Estimate: About 2

Explanation:

8.12 is closer to 8

5.52 is closer to 6

8 – 6 = 2

Question 11.

9.7 5

-3.4 7

————

Estimate: _____

Answer:

Estimate: About 7

Explanation:

9.75 is closer to 10

3.47 is closer to 3

10 – 3 = 7

**Practice: Copy and Solve Use rounding or benchmarks to estimate.**

Question 12.

12.83 + 16.24

Estimate: _____

Answer:

Estimate: About 29

Explanation:

12.83; 8 > 5; 13

16.24; 2 <5; 16

13 + 16 = 29

Question 13.

$26.92 − $11.13

Estimate: $ _____

Answer:

Estimate: About $16

Explanation:

26.92; 9 > 5; 27

11.13; 1 < 5; 11

27 – 11 = 16

Question 14.

9.41 + 3.82

Estimate: _____

Answer:

Estimate: About 13

Explanation:

9.41; 4 < 5; 9

3.82; 8 > 5; 4

9 + 4 = 13

**Use Reasoning Estimate to compare. Write < or >.**

Question 15.

2.74 + 4.22 _____ 3.13 + 1.87

Answer:

2.74 + 4.22 > 3.13 + 1.87

Explanation:

2.74; 7 > 5; 3

4.22; 2 < 5 ; 4

3 + 4 = 7

3.13; 1 < 5; 3

1.87; 8 > 5; 2

3 + 2 = 5

So, 7 > 5

2.74 + 4.22 > 3.13 + 1.87

Question 16.

6.25 – 2.39 _____ 9.79 – 3.84

Answer:

6.25 – 2.39 < 9.79 – 3.84

Explanation:

6.25; 2 < 5; 6

2.39; 3 < 5; 2

6 – 2 = 4

9.79; 7 > 5; 10

3.84; 8 >5; 4

10 – 4 = 6

4 < 6

6.25 – 2.39 < 9.79 – 3.84

**Use the table to solve 17–18. Show your work.**

Question 17.

For the week of April 4, 1964, the Beatles had the top four songs. About how long would it take to listen to these four songs?

about _____ minutes

Answer:

about 10 minutes

Explanation:

Can’t Buy Me Love = 2.30 min

She Loves You = 2.50 min

I Want to Hold You Hand = 2.75 min

Please Please Me = 2.00 min

2.30; 3 < 5; 2

2.50; 5 = 5; 3

2.75; 7 > 5; 3

2.00; 2 < 5; 2

2 + 3 + 3 + 2 = 10 min

Question 18.

What’s the Error? Isabelle says she can listen to the first three songs in the table in 6 minutes.

Type below:

_________

Answer:

Can’t Buy Me Love = 2.30 min

She Loves You = 2.50 min

I Want to Hold You Hand = 2.75 min

2.30; 3 < 5; 2

2.50; 5 = 5; 3

2.75; 7 > 5; 3

2 + 3 + 3 = 8 minutes

About 8 minutes

Question 19.

Tracy ran a lap around the school track in 74.2 seconds. Malcolm ran a lap in 65.92 seconds. Estimate the difference in the times in which the students completed the lap.

about _____ seconds

Answer:

about 8 seconds

Explanation:

Tracy ran a lap around the school track in 74.2 seconds.

74.2; 2 < 5; 74

Malcolm ran a lap in 65.92 seconds.

65.92; 9 > 5; 66

74 – 66 = 8

about 8 seconds

**Nutrition**

Your body needs protein to build and repair cells. You should get a new supply of protein each day. The average 10-year-old needs 35 grams of protein daily. You can find protein in foods like meat, vegetables, and dairy products.

**Use estimation to solve.**

Question 20.

Gina had a scrambled egg and a cup of low-fat milk for breakfast. She had an oat bran muffin for a morning snack. About how many more grams of protein did Gina have for breakfast than for a snack?

about _____ grams

Answer:

about 17 grams

Explanation:

Gina had a scrambled egg and a cup of low-fat milk for breakfast. She had an oat bran muffin for a morning snack.

1 scrambled egg = 6.75 grams

1 cup shredded whear cereal = 5.56 grams

1 oat bran muffin = 3.99 grams

1 cup low-fat milk = 8.22 grams

6.75; 7 > 5; 7

8.22; 2 < 5; 8

3.99; 9 > 5; 4

7 + 2 + 9 = 18

The average 10-year-old needs 35 grams of protein daily.

So, 35 – 18 = 17

Gina have 17 more grams of protein for breakfast than for a snack.

Question 21.

Pablo had a cup of shredded wheat cereal, a cup of low-fat milk, and one other item for breakfast. He had about 21 grams of protein. What was the third item Pablo had for breakfast?

_________

Answer:

6 grams

Explanation:

1 cup shredded whear cereal = 5.56 grams

1 cup low-fat milk = 8.22 grams

5.56; 5 = 5; 6

8.22; 2 < 5; 9

6 + 9 = 15

15 + S = 21 grams

S = 21 – 15 = 6 grams

The third item Pablo had 6 grams for breakfast

**Estimate. Then find the sum.**

Question 1.

2.5

+4.6

Estimate: _____

Sum: _____

Answer:

Estimate: 8

Sum: 7.1

Explanation:

2.5 nearest whole number is 3

4.6 nearest whole number is 5

Estimate: 3 + 5 = 8

Sum: 2.5 + 4.6 = 7.1

Question 2.

8.7 5

+6.4 3

Estimate: _____

Sum: _____

Answer:

Estimate: 15

Sum: 15.18

Explanation:

8.75 nearest whole number is 9

6.43 nearest whole number is 6

Estimate: 9 + 6 = 15

Sum: 8.75 + 6.43 = 15.18

Question 3.

2.0 3

+7.8 9

Estimate: _____

Sum: _____

Answer:

Estimate: 10

Sum: 9.92

Explanation:

2.03 nearest whole number is 2

7.89 nearest whole number is 8

Estimate: 2 + 8 = 10

Sum: 2.03 + 7.89 = 9.92

Question 4.

6.34 + 3.8 =

Estimate: _____

Sum: _____

Answer:

Estimate: 10

Sum: 10.14

Explanation:

6.34 nearest whole number is 6

3.8 nearest whole number is 4

Estimate: 6 + 4 = 10

Sum: 6.34 + 3.8 = 10.14

Question 5.

5.63 + 2.6 =

Estimate: _____

Sum: _____

Answer:

Estimate: 9

Sum: 8.23

Explanation:

5.63 nearest whole number is 6

2.6 nearest whole number is 3

Estimate: 6 + 3 = 9

Sum: 5.63 + 2.6 = 8.23

**Connect Symbols and Words Find the sum.**

Question 6.

seven and twenty-five hundredths added to nine and four tenths

Type below:

________

Answer:

7.25 + 9.4 = 16.65

Explanation:

seven and twenty-five hundredths = 7.25

nine and four tenths = 9.4

7.25 + 9.4 = 16.65

Question 7.

twelve and eight hundredths added to four and thirty-five hundredths

Type below:

________

Answer:

12.08 + 4.35 = 16.43

Explanation:

twelve and eight hundredths = 12.08

four and thirty-five hundredths = 4.35

12.08 + 4.35 = 16.43

Question 8.

nineteen and seven tenths added to four and ninety-two hundredths

Type below:

________

Answer:

19.7 + 4.92 = 24.62

Explanation:

nineteen and seven tenths = 19.7

four and ninety-two hundredths = 4.92

19.7 + 4.92 = 24.62

Question 9.

one and eighty-two hundredths added to fifteen and eight tenths

Type below:

________

Answer:

1.82 + 15.8 = 17.62

Explanation:

one and eighty-two hundredths = 1.82

fifteen and eight tenths = 15.8

1.82 + 15.8 = 17.62

**Practice: Copy and Solve Find the sum.**

Question 10.

7.99 + 8.34

_____

Answer:

16.33

Explanation:

7.99 + 8.34

Add hundredths; 9 + 4 = 13; regroup

Add tenths; 9 + 3 + 1 = 13; regroup

Add tens; 7 + 8 + 1 = 16

16.33

Question 11.

15.76 + 8.2

_____

Answer:

23.96

Explanation:

15.76 + 8.2

Add hundredths; 6 + 0 = 6;

Add tenths; 7 + 2 = 9;

Add tens; 5 + 8 = 13; regroup

Add hundreds; 1 + 1 = 2

23.96

Question 12.

9.6 + 5.49

_____

Answer:

15.09

Explanation:

9.6 + 5.49

Add hundredths; 0 + 9 = 9;

Add tenths; 6 + 4 = 10; regroup;

Add tens; 9 + 5 + 1 = 15; regroup

15.09

Question 13.

33.5 + 16.4

_____

Answer:

49.9

Explanation:

33.5 + 16.4

Add tenths; 5 + 4 = 9;

Add tens; 3 + 6 = 9;

Add hundreds; 3 + 1 = 4

49.9

Question 14.

9.84 + 21.52

_____

Answer:

31.36

Explanation:

9.84 + 21.52

Add hundredths; 4 + 2 = 6;

Add tenths; 8 + 5 = 13; regroup

Add tens; 9 + 1 + 1 = 11; regroup

Add hundreds; 0 + 2 + 1 = 3

31.36

Question 15.

3.89 + 4.6

_____

Answer:

8.49

Explanation:

3.89 + 4.6

Add hundredths; 9 + 0 = 9;

Add tenths; 8 + 6 = 14;

Add tens; 3 + 4 + 1 = 8;

8.49

Question 16.

42.19 + 8.8

_____

Answer:

50.99

Explanation:

42.19 + 8.8

Add hundredths; 0 + 9 = 9;

Add tenths; 1 + 8 = 9;

Add tens; 2 + 8 = 10; regroup

Add hundreds; 4 + 1 = 5

50.99

Question 17.

16.74 + 5.34

_____

Answer:

22.08

Explanation:

16.74 + 5.34

Add hundredths; 4 + 4 = 8;

Add tenths; 7 + 3 = 10; regroup

Add tens; 6 + 5 + 1 = 12; regroup

Add hundreds; 1 + 1 = 2

22.08

Question 18.

27.58 + 83.9

_____

Answer:

111.48

Explanation:

27.58 + 83.9

Add hundredths; 8 + 0 = 8;

Add tenths; 5 + 9 = 14; regroup

Add tens; 7 + 3 + 1 = 11; regroup

Add hundreds; 2 + 8 + 1 = 11

111.48

Question 19.

Tania measured the growth of her plant each week. The first week, the plant’s height measured 2.65 decimeters. During the second week, Tania’s plant grew 0.7 decimeter. How tall was Tania’s plant at the end of the second week?

Describe the steps you took to solve the problem.

_____ decimeters

Answer:

3.35 decimeters

Explanation:

Tania measured the growth of her plant each week. The first week, the plant’s height measured 2.65 decimeters. During the second week, Tania’s plant grew 0.7 decimeter.

2.65 + 0.7 = 3.35

Question 20.

Maggie had $35.13. Then her mom gave her $7.50 for watching her younger brother. She was paid $10.35 for her old roller skates. How much money does Maggie have now?

$ _____

Answer:

$52.98

Explanation:

Maggie had $35.13. Then her mom gave her $7.50 for watching her younger brother. She was paid $10.35 for her old roller skates.

35.13 + 7.50 + 10.35 = 52.98

Question 21.

A city receives an average rainfall of 16.99 centimeters in August. One year, during the month of August, it rained 8.33 centimeters by August 15th. Then it rained another 4.65 centimeters through the end of the month. What was the total rainfall in centimeters for the month?

a. What do you need to find?

Type below:

________

Answer:

We need to find out what was the total rainfall in centimeters for the month, so we have to find the sum 8.33+ 4.65.

Explanation:

A city receives an average rainfall of 16.99 centimeters in August. One year, during the month of August, it rained 8.33 centimeters by August 15th. Then it rained another 4.65 centimeters through the end of the month. We need to find out what was the total rainfall in centimeters for the month, so we have to find the sum 8.33+ 4.65.

Question 21.

b. What information are you given?

Type below:

________

Answer:

We know that one year during the month Aug., it rained 8.33 centimeters by Aug. 15th. Then it rained another 4.65 centimeters through the end of the month.

Question 21.

c. How will you use addition to find the total number of centimeters of rain that fell?

Type below:

________

Answer:

We have to add the hundredths first, then the tenths and in the end the ones.

Question 21.

d. Show how you solved the problem.

Type below:

________

Answer:

sum 8.33+ 4.65.

Add the hundredths first. 3 hundredths + 5 hundredths = 8 hundredths.

Add the tenths. 3 tenths + 6 tenths = 9 tenths.

Add the ones. 8 + 4 = 12 tens

Therefore, the sum is 8.33+ 4.65 = 12.98.

Question 21.

e. Complete the sentence. It rained _________ centimeters for the month.

______ centimeters

Answer:

12.98 centimeters

Explanation:

It rained 12.98 centimeters for the month.

Question 22.

Horatio caught a fish that weighed 1.25 pounds. Later he caught another fish that weighed 1.92 pounds. What was the combined weight of both fish? Use the digits on the tiles to solve the problem. Digits may be used more than once or not at all.

______ pounds

Answer:

3.17 pounds

Explanation:

Horatio caught a fish that weighed 1.25 pounds. Later he caught another fish that weighed 1.92 pounds.

1.25 + 1.92 = 3.17 pounds

**Estimate. Then find the difference.**

Question 1.

5.8 3

−2.1 8

———-

Estimate: ______

Difference: ______

Answer:

Estimate: 4

Difference: 3.65

Explanation:

5.83 is closer to 6

2.18 is closer to 2

6 – 2 = 4

5.83 – 2.18 = 3.65

Question 2.

4.4 5

−1.8 6

———–

Estimate: ______

Difference: ______

Answer:

Estimate: 2

Difference: 2.59

Explanation:

4.45 is closer to 4

1.86 is closer to 2

4 – 2 = 2

4.45 – 1.86 = 2.59

Question 3.

4.0 3

−2.2 5

———-

Estimate: ______

Difference: ______

Answer:

Estimate: 2

Difference: 1.78

Explanation:

4.03 is closer to 4

2.25 is closer to 2

4 – 2 = 2

4.03 – 2.25 = 1.78

**Find the difference. Check your answer.**

Question 4.

0.7 0

−0.4 3

———-

______

Answer:

0.27

Explanation:

0.70 − 0.43

Subtract hundredths: 0 – 3;

There are not enough hundredths. So, regroup

10 – 3 = 7

Subtract tenths: 6 – 4 = 2

Subtract ones: 0 – 0 = 0

0.27

**Check:** 0.70 − 0.43 = 0.27

0.27 = 0.27

Question 5.

13.2

−8.0 4

———-

______

Answer:

5.16

Explanation:

13.2 − 8.04

Subtract hundredths: 0 – 4;

There are not enough hundredths. So, regroup

10 – 4 = 6

Subtract tenths: 1 – 0 = 1

Subtract ones: 3 – 8;

There are not enough tens. So, regroup

13 – 8 = 5

Subtract hundreds: 0 – 0 = 0;

5.16

Check: 13.2 − 8.04 = 5.16

5.16 = 5.16

Question 6.

15.8

−9.6 7

———-

______

Answer:

6.13

Explanation:

15.8 − 9.67

Subtract hundredths: 0 – 7;

There are not enough hundredths. So, regroup

10 – 7 = 3

Subtract tenths: 7 – 6 = 1

Subtract ones: 5 – 9;

There are not enough ones. So, regroup

15 – 9 = 6

Subtract hundreds: 0 – 0 = 0;

6.13

Check: 15.8 − 9.67 = 6.13

6.13 = 6.13

**Connect Symbols and Words Find the difference.**

Question 7.

three and seventy-two hundredths subtracted from five and eighty-one hundredths

______

Answer:

three and seventy-two hundredths = 3.72

five and eighty-one hundredths = 5.81

5.81 – 3.72 = 2.09

Question 8.

one and six-hundredths subtracted from eight and thirty-two hundredths

______

Answer:

one and six-hundredths = 1.06

eight and thirty-two hundredths = 8.23

8.23 – 1.06 = 7.17

**Use Reasoning Algebra Write the unknown number for n.**

Question 9.

5.28 − 3.4 = n

n = ______

Answer:

n = 1.88

Explanation:

5.28 − 3.4 = 1.88

Question 10.

n − 6.47 = 4.32

n = ______

Answer:

n = 10.79

Explanation:

n − 6.47 = 4.32

n = 4.32 + 6.47

n = 10.79

Question 11.

11.57 − n = 7.51

n = ______

Answer:

n = 4.06

Explanation:

11.57 − n = 7.51

11.57 = 7.51 + n

n = 11.57 – 7.51

n = 4.06

**Practice: Copy and Solve Find the difference.**

Question 12.

8.42 − 5.14 = ______

Answer:

3.28

Explanation:

8.42 − 5.14

Subtract hundredths: 2 – 4;

There are not enough hundredths. So, regroup

12 – 4 = 8

Subtract tenths: 3 – 1 = 2

Subtract ones: 8 – 5 = 3

3.28

Question 13.

16.46 − 13.87 = ______

Answer:

2.59

Explanation:

16.46 − 13.87

Subtract hundredths: 6 – 7;

There are not enough hundredths. So, regroup

16 – 7 = 9

Subtract tenths: 3 – 8

There are not enough tenths. So, regroup

13 – 8 = 5

Subtract ones: 5 – 3 = 2;

Subtract hundreds: 1 – 1 = 0;

2.59

Question 14.

34.27 − 17.51 = ______

Answer:

16.76

Explanation:

34.27 − 17.51

Subtract hundredths: 7 – 1 = 6;

Subtract tenths: 2 – 5

There are not enough tenths. So, regroup

12 – 5 = 7;

Subtract ones: 3 – 7

There are not enough ones. So, regroup

13 – 7 = 6

Subtract hundreds: 2 – 1 = 1;

16.76

Question 15.

15.83 − 11.45 = ______

Answer:

4.38

Explanation:

15.83 − 11.45

Subtract hundredths: 3 – 5;

There are not enough hundredths. So, regroup

13 – 5 = 8

Subtract tenths: 7 – 4 = 3

Subtract ones: 5 – 1 = 4;

Subtract hundreds: 1 – 1 = 0;

4.38

Question 16.

12.74 − 10.54 = ______

Answer:

2.2

Explanation:

12.74 − 10.54

Subtract hundredths: 4 – 4 = 0;

Subtract tenths: 7 – 5 = 2

Subtract ones: 2 – 0 = 2;

Subtract hundreds: 1 – 1 = 0;

2.20

Question 17.

48.21 − 13.65 = ______

Answer:

34.56

Explanation:

48.21 − 13.65

Subtract hundredths: 1 – 5;

There are not enough hundredths. So, regroup

11 – 5 = 6

Subtract tenths: 1 – 6

There are not enough tenths. So, regroup

11 – 6 = 5

Subtract ones: 7 – 3 = 4;

Subtract hundreds: 4 – 1 = 3;

34.56

Question 18.

Beth finished a race in 3.35 minutes. Ana finished the race in 0.8 minute less than Beth. Fran finished the race in 1.02 minutes less than Ana. What was Fran’s time to finish the race in minutes?

______ minutes

Answer:

1.53 minutes

Explanation:

Beth finished a race in 3.35 minutes. Ana finished the race in 0.8 minute less than Beth.

3.35 – 0.8 = 2.55

Fran finished the race in 1.02 minutes less than Ana.

2.55 – 1.02 = 1.53

Question 19.

Fatima planted sunflower seeds in a flower patch. The tallest sunflower grew 2.65 meters tall. The height of the shortest sunflower was 0.34 meter less than the tallest sunflower. What was the height, in meters, of the shortest sunflower?

______ meters

Answer:

2.31 meters

Explanation:

Fatima planted sunflower seeds in a flower patch. The tallest sunflower grew 2.65 meters tall. The height of the shortest sunflower was 0.34 meter less than the tallest sunflower.

2.65 – 0.34 = 2.31

Question 20.

In peanut butter, how many more grams of protein are there than grams of carbohydrates? Use the label below.

a. What do you need to know?

Type below:

_________

Answer:

We need to find how many more grams of protein are there than grams of carbohydrates?

Question 20.

b. How will you use subtraction to find how many more grams of protein there are than grams of carbohydrates?

Type below:

_________

Answer:

Grams of protein = 8.1 g

grams of carbohydrates = 6.2g

8.1 – 6.2 = 1.9 grams

Question 20.

c. Show how you solved the problem.

Type below:

_________

Answer:

8.1 – 6.2

Subtract tenths: 1 – 2

There are not enough tenths. So, regroup

11 – 2 = 9

Subtract ones:

7 – 6 = 1

1.9 grams

Question 20.

d. Complete each sentence.

The peanut butter has ______ grams of protein.

The peanut butter has ______ grams of carbohydrates.

There are ______ more grams of protein than grams of carbohydrates in the peanut butter.

Type below:

_________

Answer:

The peanut butter has 8.1 grams of protein.

The peanut butter has 6.2 grams of carbohydrates.

There are 1.9 more grams of protein than grams of carbohydrates in the peanut butter.

Question 21.

Kyle is building a block tower. Right now the tower stands 0.89 meter tall. How much higher does the tower need to be to reach a height of 1.74 meters?

______ meters

Answer:

0.85 meters

Explanation:

Kyle is building a block tower. Right now the tower stands 0.89 meter tall.

To reach a height of 1.74, 1.74 – 0.89 = 0.85

Question 22.

Dialyn scored 2.5 points higher than Gina at a gymnastics event. Select the values that could represent each student’s gymnastics score. Mark all that apply.

Options:

a. Dialyn: 18.4 points, Gina: 16.9 points

b. Dialyn: 15.4 points, Gina: 13.35 points

c. Dialyn: 16.2 points, Gina: 13.7 points

d. Dialyn: 19.25 points, Gina: 16.75 points

Answer:

c. Dialyn: 16.2 points, Gina: 13.7 points

d. Dialyn: 19.25 points, Gina: 16.75 points

Explanation:

Dialyn scored 2.5 points higher than Gina at a gymnastics event.

a. 18.4 – 16.9 = 1.5

b. 15.4 – 13.35 = 2.05

c. 16.2 – 13.7 = 2.5

d. 19.25 – 16.75 = 2.5

**Write a rule for the sequence.**

Question 1.

0.5, 1.8, 3.1, 4.4, …

Think: Is the sequence increasing or decreasing?

Rule: _________

Answer:

Add 1.3 to the previous term in the sequence to get the next one.

Explanation:

Compare 0.5, 1.8; 0.5 < 1.8

The sequence is increasing as the second term is greater than the first term.

The operation will use addition.

0.5 + x = 1.8

x = 1.8 – 0.5 = 1.3

1.8 + 1.3 = 3.1

3.1 + 1.3 = 4.4

Add 1.3 to the previous term in the sequence to get the next one.

Question 2.

23.2, 22.1, 21, 19.9, …

Rule: _________

Answer:

Subtract 1.1 to the previous term in the sequence to get the next one.

Explanation:

Compare 23.2 and 22.1; 23.2 > 22.1

The sequence is decreasing as the second term is lesser than the first term.

The operation will use subtraction.

23.2 – 22.1 = 1.1

22.1 – 21 = 1.1

21 – 19.9 = 1.1

Subtract 1.1 to the previous term in the sequence to get the next one.

**Write a rule for the sequence. Then find the unknown term.**

Question 3.

0.3, 1.5, ____ , 3.9, 5.1

Missing value: ______

Rule: ______

Answer:

Missing value: 2.7

Rule: Add 1.2 to the previous term in the sequence to get the next one.

Explanation:

Compare 0.3 and 1.5; 0.3 < 1.5

The sequence is increasing as the second term is greater than the first term.

The operation will use addition.

1.5 – 0.3 = 1.2

0.3 + 1.2 = 1.5

1.5 + 1.2 = 2.7

2.7 + 1.2 = 3.9

3.9 + 1.2 = 5.1

Add 1.2 to the previous term in the sequence to get the next one.

Question 4.

19.5, 18.8, 18.1, 17.4, ______

Missing value: ______

Rule: ______

Answer:

Missing value: 16.7

Rule: Subtract 0.7 to the previous term in the sequence to get the next one.

Explanation:

Compare 19.5 and 18.8; 19.5 > 18.8

The sequence is decreasing as the second term is lesser than the first term.

The operation will use subtraction.

19.5 – 18.8 = 0.7

18.8 – 18.1 = 0.7

18.1 – 17.4 = 0.7

17.4 – 0.7 = 16.7

Subtract 0.7 to the previous term in the sequence to get the next one.

**On Your Own**

**Write the first four terms of the sequence.**

Question 5.

Rule: start at 10.64, subtract 1.45

______ ; ______ ; ______ ; ______

Answer:

9.19; 7.74; 6.29; 4.84

Explanation:

10.64 – 1.45 = 9.19

9.19 – 1.45 = 7.74

7.74 – 1.45 = 6.29

6.29 – 1.45 = 4.84

9.19; 7.74; 6.29; 4.84

Question 6.

Rule: start at 0.87, add 2.15

______ ; ______ ; ______ ; ______

Answer:

3.02; 5.17; 7.32; 9.47

Explanation:

0.87 + 2.15 = 3.02

3.02 + 2.15 = 5.17

5.17 + 2.15 = 7.32

7.32 + 2.15 = 9.47

3.02; 5.17; 7.32; 9.47

Question 7.

Rule: start at 19.3, add 1.8

______ ; ______ ; ______ ; ______

Answer:

21.1; 22.9; 24.7; 26.5

Explanation:

19.3 + 1.8 = 21.1

21.1 + 1.8 = 22.9

22.9 + 1.8 = 24.7

24.7 + 1.8 = 26.5

21.1; 22.9; 24.7; 26.5

Question 8.

Rule: start at 29.7, subtract 0.4

______ ; ______ ; ______ ; ______

Answer:

29.3; 28.9; 28.5; 28.1

Explanation:

29.7 – 0.4 = 29.3

29.3 – 0.4 = 28.9

28.9 – 0.4 = 28.5

28.5 – 0.4 = 28.1

29.3; 28.9; 28.5; 28.1

Question 9.

Marta put $4.87 in her coin bank. Each day she added 1 quarter, 1 nickel, and 3 pennies. How much money was in her coin bank after 6 days? Describe the pattern you used to solve.

$ ______

Answer:

$10.52

Add 1.13 to the previous term in the sequence to get the next one.

Explanation:

Marta put $4.87 in her coin bank. Each day she added 1 quarter, 1 nickel, and 3 pennies.

She added 1.13 each day.

4.87 + 1.13 = 6.00

6.00 + 1.13 = 7.13

7.13 + 1.13 = 8.26

8.26 + 1.13 = 9.39

9.39 + 1.13 = 10.52

Add 1.13 to the previous term in the sequence to get the next one.

Question 10.

Identify Relationships Look at the list below. Do the numbers show a pattern? Explain how you know.

11.23, 10.75, 10.3, 9.82, 9.37, 8.89

Type below:

_________

Answer:

Compare 11.23 and 10.75; 11.23 > 10.75

The sequence is decreasing as the second term is greater than the first term.

The operation will use subtraction.

11.23 – 10.75 = 0.48

10.75 – 10.3 = 0.45

10.3 – 9.82 = 0.48

9.82 – 9.37 = 0.45

9.37 – 8.89 = 0.48

First two terms difference is 0.48

Second and third term difference is 0.45

third and fourth term difference is 0.48

fourth and fifth term difference is 0.45

fifth and sixth term difference is 0.48

**Pose a Problem**

Question 11.

Bren has a deck of cards. As shown below, each card is labeled with a rule describing a pattern in a sequence. Select a card and decide on a starting number. Use the rule to write the first five terms in your sequence.

Sequence: _____ , _____ , _____ , _____ , _____

Write a problem that relates to your sequence and requires the sequence be extended to solve.

Pose a Problem Solve your problem.

Type below:

_________

Answer:

1.6 + 0.33 = 1.93

1.93 + 0.33 = 2.26

2.26 + 0.33 = 2.59

2.59 + 0.33 = 2.92

2.92 + 0.33 = 3.25

Start at 1.6 and write the first five terms of the sequence?

Add 0.3 to the previous term in the sequence to get the next one.

Question 12.

Colleen and Tom are playing a number pattern game. Tom wrote the following sequence.

33.5, 34.6, 35.7, ________, 37.9

What is the unknown term in the sequence?

_____

Answer:

36.8

Explanation:

33.5 < 34.6

34.6 – 33.5 = 1.1

33.5 + 1.1 = 34.6

34.6 + 1.1 = 35.7

35.7 + 1.1 = 36.8

36.8 + 1.1 = 37.9

Question 1.

Sara wants to buy a bottle of apple juice from a vending machine. She needs exactly $2.30. She has the following bills and coins:

Make and complete a table to find all the ways Sara could pay for the juice. First, draw a table with a column for each type of bill or coin. Next, fill in your table with each row showing a different way Sara can make exactly $2.30.

Type below:

_________

Answer:

Sara wants to buy a bottle of apple juice from a vending machine. She needs exactly $2.30.

Question 2.

What if Sara decides to buy a bottle of water that costs $1.85? What are all the different ways she can make exactly $1.85 with the bills and coins she has? Which coin must Sara use?

Type below:

_________

Answer:

If Sara decides to buy a bottle of water that costs $1.85, then

1 bill, 3 quarters, 1 dime; 1 bill, 3 quarters, 2 nickels; quarter

Question 3.

At the end of August, Mr. Diaz had a balance of $441.62. Since then, he has written two checks for $157.34 and $19.74 and made a deposit of $575.00. Mr. Diaz says his balance is $739.54. Find Mr. Diaz’s correct balance.

$ _____

Answer:

At the end of August, Mr. Diaz had a balance of $441.62.

Since then, he has written two checks for $157.34 and $19.74 and made a deposit of $575.00.

Subtract the checks from the initial amount, and add the deposit.

441.85 – (157.34 + 19.74) + 575 = 839.77

So, $839.77

**Use the following information to solve 4–6.**

**At Open Skate Night, admission is $3.75 with a membership card and $5.00 without a membership card. Skate rentals are $3.00.**

Question 4.

Aidan paid the admission for himself and two friends at Open Skate Night. Aidan had a membership card, but his friends did not. Aidan paid with a $20 bill. How much change should Aidan receive?

$ _____

Answer:

$6.25

Explanation:

Aidan had a membership card, but his friends did not.

$3.75 + $5.00 + $5.00 = $13.75

Aidan paid with a $20 bill.

$20 – $13.75 = $6.25

Question 5.

The Moores paid $6 more for skate rentals than the Cotters did. Together, the two families paid $30 for skate rentals. How many pairs of skates did the Moores rent?

_____ pairs of skates

Answer:

6 pairs of skates

Question 6.

Analyze Jennie and 5 of her friends are going to Open Skate Night. Jennie does not have a membership card. Only some of her friends have membership cards. What is the total amount that Jennie and her friends might pay for admission?

Type below:

_________

Answer:

They will pay $27.50 if only 2 of her friends have membership cards.

Question 7.

Marisol bought 5 movie tickets for a show. Each ticket cost $6.25. Complete the table to show the price of 2, 3, 4, and 5 tickets.

Type below:

_________

Answer:

**Find the sum or difference.**

Question 1.

4.19 + 0.58

_____

Answer:

4.77

Explanation:

4.19 + 0.58 = 1.38

Add hundredths 9 + 8 = 17; Regroup;

Add tenths 1 + 5 + 1 = 7;

Add ones 4 + 0 = 4

4.19 + 0.58 = 4.77

Question 2.

9.99 − 4.1

_____

Answer:

5.89

Explanation:

9.99 − 4.1

Subtract hundredths: 9 – 0 = 9;

Subtract tenths: 9 – 1 = 8

Subtract ones: 9 – 4 = 5

So, 9.99 − 4.1 = 5.89

Question 3.

5.7 + 2.25 + 1.3

_____

Answer:

9.25

Explanation:

5.7 + 2.25 + 1.3

Add hundredths 0 + 5 + 0 = 5;

Add tenths 7 + 2 + 3 = 12; Regroup

Add ones 5 + 2 + 1 + 1 = 9

5.7 + 2.25 + 1.3 = 9.25

Question 4.

28.6 − 9.84

_____

Answer:

18.76

Explanation:

28.6 − 9.84

Subtract hundredths: 0 – 4;

There are not enough hundredths. So, regroup

10 – 4 = 6.

Subtract tenths: 5 – 8;

There are not enough tenths. So, regroup

15 – 8 = 7

Subtract ones: 7 – 9;

There are not enough ones. So, regroup

17 – 9 = 8

Subtract hundreds: 1 – 0 = 1;

So, 28.6 − 9.84 = 18.76

Question 5.

$15.79 + $32.81

$ _____

Answer:

$48.6

Explanation:

$15.79 + $32.81

Add hundredths 9 + 1 = 10; Regroup

Add tenths 7 + 8 + 1 = 16; Regroup

Add ones 5 + 2 + 1 = 8

Add hundreds 1 + 3 = 4

$15.79 + $32.81 = $48.60

Question 6.

38.44 − 25.86

_____

Answer:

12.58

Explanation:

38.44 − 25.86

Subtract hundredths: 4 – 6;

There are not enough hundredths. So, regroup

14 – 6 = 8

Subtract tenths: 3 – 8;

There are not enough tenths. So, regroup

13 – 8 = 5

Subtract ones: 7 – 5 = 2;

Subtract hundreds: 3 – 2 = 1;

So, 38.44 − 25.86 = 12.58

**Find the sum or difference.**

Question 7.

$ 18.39

+$7.56

————

$ _____

Answer:

$25.95

Explanation:

$ 18.39 + $7.56

Add hundredths 9 + 6 = 15; Regroup

Add tenths 5 + 3 + 1 = 9;

Add ones 8 + 7 = 15; Regroup

Add hundreds 1 + 0 + 1 = 2

$ 18.39 + $7.56 = $25.95

Question 8.

8.22 − 4.39

_____

Answer:

Explanation:

8.22 − 4.39

Subtract hundredths: 2 – 9;

There are not enough hundredths. So, regroup

12 – 9 = 3

Subtract tenths: 1 – 3;

There are not enough tenths. So, regroup

11 – 3 = 8

Subtract ones: 7 – 4 = 3;

So, 8.22 − 4.39 = 3.83

Question 9.

93.6 − 79.84

_____

Answer:

13.76

Explanation:

93.6 − 79.84

Subtract hundredths: 0 – 4;

There are not enough hundredths. So, regroup

10 – 4 = 6

Subtract tenths: 5 – 8;

There are not enough tenths. So, regroup

15 – 8 = 7

Subtract ones: 2 – 9;

There are not enough ones. So, regroup

12 – 9 = 3

Subtract hundreds: 8 – 7 = 1;

So, 93.6 − 79.84 = 13.76

Question 10.

1.82

2.28

+2.18

————

_____

Answer:

6.28

Explanation:

1.82 + 2.28 + 2.18

Add hundredths 2 + 8 + 8 = 18; Regroup

Add tenths 8 + 2 + 1 + 1 = 12; Regroup

Add ones 1 + 2 + 2 + 1 = 6;

1.82 + 2.28 + 2.18 = 6.28

**Practice: Copy and Solve Find the sum or difference.**

Question 11.

6.3 + 2.98 + 7.7

_____

Answer:

16.98

Explanation:

6.3 + 2.98 + 7.7

Add hundredths 0 + 8 + 0 = 8;

Add tenths 3 + 9 + 7 = 19; Regroup

Add ones 6 + 2 + 7 + 1 = 16;

6.3 + 2.98 + 7.7 = 16.98

Question 12.

27.96 − 16.2

_____

Answer:

11.76

Explanation:

27.96 − 16.2

Subtract hundredths: 6 – 0 = 6;

Subtract tenths: 9 – 2 = 7;

Subtract ones: 7 – 6 = 1;

Subtract hundreds: 2 – 1 = 1;

So, 27.96 − 16.2 = 11.76

Question 13.

12.63 + 15.04

_____

Answer:

27.67

Explanation:

12.63 + 15.04

Add hundredths 3 + 4 = 7;

Add tenths 6 + 0 = 6;

Add ones 2 + 5 = 7;

Add hundreds 1 + 1 = 2

12.63 + 15.04 = 27.67

Question 14.

9.24 − 2.68

_____

Answer:

6.56

Explanation:

9.24 − 2.68

Subtract hundredths: 4 – 8;

There are not enough hundredths. So, regroup

14 – 8 = 6

Subtract tenths: 1 – 6;

There are not enough tenths. So, regroup

11 – 6 = 5

Subtract ones: 8 – 2 = 6;

So, 9.24 − 2.68 = 6.56

Question 15.

$18 − $3.55

$ _____

Answer:

$14.45

Explanation:

$18 − $3.55

Subtract hundredths: 0 – 5;

There are not enough hundredths. So, regroup

10 – 5 = 5

Subtract tenths;

There are not enough tenths. So, regroup

9 – 5 = 4

Subtract ones: 7 – 3 = 4;

Subtract hundreds: 1 – 0 = 0

So, $18 − $3.55 = $14.45

Question 16.

9.73 − 2.52

_____

Answer:

7.21

Explanation:

9.73 − 2.52

Subtract hundredths: 3 – 2 = 1;

Subtract tenths; 7 – 5 = 2

Subtract ones: 9 – 2 = 7;

So, 9.73 − 2.52 = 7.21

Question 17.

$54.78 + $43.62

$ _____

Answer:

$98.4

Explanation:

$54.78 + $43.62

Add hundredths 8 + 2 = 10; Regroup

Add tenths 7 + 6 + 1 = 14; Regroup

Add ones 4 + 3 + 1 = 8;

Add hundreds 5 + 4 = 9

$54.78 + $43.62 = $98.40

Question 18.

7.25 + 0.25 + 1.5

_____

Answer:

9

Explanation:

7.25 + 0.25 + 1.5

Add hundredths 5 + 5 + 0 = 10; Regroup

Add tenths 2 + 2 + 5 + 1 = 10; Regroup

Add ones 7 + 0 + 1 + 1 = 9;

7.25 + 0.25 + 1.5 = 9.00

**Use Reasoning Algebra Find the missing number.**

Question 19.

n − 9.02 = 3.85

n = _____

Answer:

n = 12.87

Explanation:

n − 9.02 = 3.85

n = 3.85 + 9.02

n = 12.87

Question 20.

n + 31.53 = 62.4

n = _____

Answer:

n = 30.87

Explanation:

n + 31.53 = 62.4

n = 62.4 – 31.53 = 30.87

n = 30.87

Question 21.

9.2 + n + 8.4 = 20.8

n = _____

Answer:

n = 3.2

Explanation:

9.2 + n + 8.4 = 20.8

n + 17.6 = 20.8

n = 20.8 – 17.6

n = 3.2

**Problem Solving Applications**

Question 22.

Jake needs 7.58 meters of wood to complete a school project. He buys a 2.25-meter plank of wood and a 3.12-meter plank of wood. How many more meters of wood does Jake need to buy?

_____ meters

Answer:

2.21 meters

Explanation:

Jake needs 7.58 meters of wood to complete a school project. He buys a 2.25-meter plank of wood and a 3.12-meter plank of wood.

2.25 + 3.12 = 5.37

7.58 – 5.37 = 2.21

Question 23.

Lori needs a length of twine 8.5 meters long to mark a row in her garden. Andrew needs a length of twine 7.25 meters long for his row. They have one length of twine that measures 16.27 meters. After they each take the lengths they need, how much twine will be left?

_____ meters

Answer:

0.52 meters

Explanation:

Lori needs a length of twine 8.5 meters long to mark a row in her garden. Andrew needs a length of twine 7.25 meters long for his row. They have one length of twine that measures 16.27 meters.

8.5 + 7.25 = 15.75

16.27 – 15.75 = 0.52

**Use the table to solve 24–26.**

Question 24.

How much farther did the gold medal winner jump than the silver medal winner?

_____ meters

Answer:

0.1 meters

Explanation:

Gold medal = 8.34 meters

Silver medal = 8.24 meters.

8.34 – 8.24 = 0.10 meters

gold medal winner jump 0.1 meters than the silver medal winner

Question 25.

The fourth-place competitor’s jump measured 8.19 meters. If his jump had been 0.10 meter greater, what medal would he have received? Explain how you solved the problem.

_________

Answer:

Explanation:

The fourth-place competitor’s jump measured 8.19 meters. If his jump had been 0.10 meter greater

8.19 + 0.1 = 8.29

He may receive a silver medal. 8.29 is in between 8.24 and 8.34

Question 26.

In the 2004 Olympics, the gold medalist for the men’s long jump had a jump of 8.59 meters. How much farther did the 2004 gold medalist jump compared to the 2008 gold medalist?

_____ meters

Answer:

0.25 meters

Explanation:

In the 2004 Olympics, the gold medalist for the men’s long jump had a jump of 8.59 meters.

In 2008, 8.34 meters

8.59 – 8.34 = 0.25 meters

Question 27.

Alexander and Holly are solving the following word problem.

At the supermarket Carla buys 2.25 pounds of hamburger. She also buys 3.85 pounds of chicken. How many pounds of hamburger and chicken did Carla buy?

Alexander set up his problem as 2.25 + 3.85.

Holly set up her problem as 3.85 + 2.25.

Who is correct? Explain your answer and solve the problem.

Answer:

Alexander and Holly are solving the following word problem.

At the supermarket, Carla buys 2.25 pounds of hamburger. She also buys 3.85 pounds of chicken. She buys 2.25 + 3.85 = 6.10 pounds.

From the commutative property, 2.25 + 3.85 = 3.85 + 2.25

So, both answers are correct

Question 1.

Chaz kept a record of how many gallons of gas he purchased each day last week.

Order the days from least amount of gas Chaz purchased to greatest amount of gas Chaz purchased.

Least: _____ ; _____ ; _____ ; _____ ; _____ Greatest

Answer:

Least: 3.75; 3.9; 4.256; 4.258; 4.5 Greatest

Explanation:

Monday = 4.5 gallons

Tuesday = 3.9 gallons

Wednesday = 4.258 gallons

Thursday = 3.75 gallons

Friday = 4.256 gallons

The days from least amount of gas Chaz purchased to the greatest amount of gas Chaz purchased

4.5; 3.9; 4.258; 3.75; 4.256

3 < 4

3.9; 3.75; 4.5; 4.258; 4.256

9 > 7. So, 3.9; 3.75

5 > 2; 4.5; 4.258; 4.256

8 > 6; 4.258; 4.256

4.5; 4.258; 4.256; 3.9; 3.75

3.75; 3.9; 4.256; 4.258; 4.5

**For 2a–2c, select True or False for each statement**

Question 2.

2a. 16.437 rounded to the nearest whole number is 16.

i. TRUE

ii. FALSE

Answer:

i. TRUE

Explanation:

16.437; 4 < 5.

So, the nearest whole number is 16

Question 2.

2b. 16.437 rounded to the nearest tenth is 16.4.

i. TRUE

ii. FALSE

Answer:

i. TRUE

Explanation:

16.437 rounded to the nearest tenth

3 < 5

16.4

Question 2.

2c. 16.437 rounded to the nearest hundredth is 16.43.

i. TRUE

ii. FALSE

Answer:

ii. FALSE

Explanation:

16.437 rounded to the nearest hundredth is

7 > 5

16.44

Question 3.

Students are selling muffins at a school bake sale. One muffin costs $0.25, 2 muffins cost $0.37, 3 muffins cost $0.49, and 4 muffins cost $0.61. If this pattern continues, how much will 7 muffins cost? Explain how you found your answer.

$ _____

Answer:

$0.97

Explanation:

Students are selling muffins at a school bake sale. One muffin costs $0.25, 2 muffins cost $0.37, 3 muffins cost $0.49, and 4 muffins cost $0.61.

0.37 – 0.25 = 0.12

0.49 – 0.37 = 0.12

0.61 – 0.49 = 0.12

For 5 muffins 0.61 + 0.12 = 0.73

For 6 muffins 0.73 + 0.12 = 0.85

For 7 muffins 0.85 + 0.12 = 0.97

Every muffin cost increases with 0.12.

Question 4.

What is the value of the underlined digit? Mark all that apply. 0.679

Options:

a. 0.6

b. 0.06

c. six tenths

d. six hundredths

e. 6 × \(\frac{1}{10}\)

Answer:

a. 0.6

c. six tenths

e. 6 × \(\frac{1}{10}\)

Explanation:

0.679

(0 x 1) + (6 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))

6 x \(\frac{1}{10}\) = 0.6 = 6 tenths

Question 5.

Rowanda jogged 2.14 kilometers farther than Terrance. Select the values that could represent how far each student jogged. Mark all that apply.

Options:

a. Rowanda: 6.5 km, Terrance: 4.36 km

b. Rowanda: 4.8 km, Terrance: 2.76 km

c. Rowanda: 3.51 km, Terrance: 5.65 km

d. Rowanda: 7.24 km, Terrance: 5.1 km

Answer:

a. Rowanda: 6.5 km, Terrance: 4.36 km

d. Rowanda: 7.24 km, Terrance: 5.1 km

Explanation:

Rowanda jogged 2.14 kilometers farther than Terrance.

a. Rowanda: 6.5 km, Terrance: 4.36 km

6.5 – 4.36 = 2.14

b. Rowanda: 4.8 km, Terrance: 2.76 km

4.8 – 2.76 = 2.04

c. Rowanda: 3.51 km, Terrance: 5.65 km

5.65 – 3.51 = 2.14

d. Rowanda: 7.24 km, Terrance: 5.1 km

7.24 – 5.1 = 2.14

The first and fourth values can represent how far each student jogged.

Question 6.

Shade the model to show the decimal 0.542.

Type below:

_________

Answer:

Explanation:

0.542 = 542/1000

5 hundredths, 4 tenths, 2 thousandths

Question 7.

Benjamin rode his bicycle 3.6 miles on Saturday and 4.85 miles on Sunday. How many miles did he ride Saturday and Sunday combined?

Use the digits on the tiles to solve the problem. Digits may be used more than once or not at all.

_________ miles

Answer:

8.45 miles

Explanation:

Benjamin rode his bicycle 3.6 miles on Saturday and 4.85 miles on Sunday.

3.6 + 4.85 = 8.45

Question 8.

The school is 3.65 miles from Tonya’s house and 1.28 miles from Jamal’s house. How much farther from school is Tonya’s house than Jamal’s house? Explain how you can use a quick picture to solve the problem.

_____ miles

Answer:

2.37 miles

Explanation:

The school is 3.65 miles from Tonya’s house and 1.28 miles from Jamal’s house.

3.65 – 1.28 = 2.37

Question 9.

A vet measured the mass of two birds. The mass of the robin was 76.64 grams. The mass of the blue jay was 81.54 grams. Estimate the difference in the masses of the birds.

≈ _____ grams

Answer:

5 grams

Explanation:

A vet measured the mass of two birds. The mass of the robin was 76.64 grams. The mass of the blue jay was 81.54 grams.

76.64 grams is closer to 77

81.54 grams is closer to 82

82 – 77 = 5

The estimated difference in the masses of the birds is 5 grams.

Question 10.

Rick bought 5 yogurt bars at a snack shop. Each yogurt bar cost $1.75. Complete the table to show the price of 2, 3, 4, and 5 yogurt bars.

Type below:

_________

Answer:

Explanation:

Question 11.

Clayton Road is 2.25 miles long. Wood Pike Road is 1.8 miles long. Kisha used a quick picture to find the combined length of Clayton Road and Wood Pike Road. Does Kisha’s work make sense? Explain why or why not

i. Yes

ii. No

Answer:

i. Yes

Explanation:

Clayton Road is 2.25 miles long. Wood Pike Road is 1.8 miles long.

2.25 + 1.8 = 4.05

4 tens, 0 tenths, 5 hundredths

Question 12.

Bob and Ling are playing a number pattern game. Bob wrote the following sequence.

28.9, 26.8, 24.7, __, 20.5

What is the unknown term in the sequence?

_____

Answer:

26.8

Explanation:

Bob and Ling are playing a number pattern game. Bob wrote the following sequence.

28.9, 26.8, 24.7, __, 20.5

28.9 – 26.8 = 2.1

26.8 – 24.7 = 2.1

Every number is increased by 2.1

So, the unknown number is 24.7 + 2.1 = 26.8

**Rafael bought 2.15 pounds of potato salad and 4.2 pounds of macaroni salad to bring to a picnic. For 13a–13c, select Yes or No to indicate whether each statement is true.**

Question 13.

13a. Rounded to the nearest whole number, Rafael bought 2 pounds of potato salad.

i. Yes

ii. No

Answer:

i. Yes

Explanation:

2.15 pounds of potato salad

1 < 5 ;

So, Rounded to the nearest whole number is 2

Question 13.

13b. Rounded to the nearest whole number, Rafael bought 4 pounds of macaroni salad.

i. Yes

ii. No

Answer:

i. Yes

Explanation:

4.2 pounds of macaroni salad

2 < 5

So, Rounded to the nearest whole number is 4

Question 13.

13c. Rounded to the nearest tenth, Rafael bought 2.1 pounds of potato salad.

i. Yes

ii. No

Answer:

ii. No

Explanation:

2.15 pounds of potato salad

5 = 5 ;

So, Rounded to the nearest whole number is 2.2

Question 14.

The four highest scores on the floor exercise at a gymnastics meet were 9.675, 9.25, 9.325, and 9.5 points. Choose the numbers that make the statement true.

The lowest: _________

The highest: _________

Answer:

The lowest: 9.25

The highest: 9.75

Explanation:

Compare ones; All ones are the same.

Compare tenths; 9.75 has the highest number of tenths and 9.25 has the lowest number of tenths.

The lowest of these four scores was 9.25 points. The highest of these four scores was 9.75 points.

Question 15.

Michelle records the value of one euro in U.S. dollars each day for her social studies project. The table shows the data she has recorded so far.

On which two days was the value of 1 euro the same when rounded to the nearest hundredth of a dollar?

Options:

a. Monday

b. Tuesday

c. Wednesday

d. Thursday

Answer:

a. Monday

c. Wednesday

Explanation:

Monday = 1.448

The digit in the hundredths place is 4. 8 > 5; So, the rounded number is 1.45

Tuesday = 1.443

The digit in the hundredths place is 4. 3 < 5; So, the rounded number is 1.44

Wednesday = 1.452

The digit in the hundredths place is 5. 2 < 5; So, the rounded number is 1.45

Thursday = 1.458

The digit in the hundredths place is 5. 8 > 5; So, the rounded number is 1.46

Question 16.

Miguel has $20. He spends $7.25 on a movie ticket, $3.95 for snacks, and $1.75 for bus fare each way. How much money does Miguel have left?

$ _____

Answer:

$7.05

Explanation:

Miguel has $20. He spends $7.25 on a movie ticket, $3.95 for snacks, and $1.75 for bus fare each way.

$7.25 + $3.95 + $1.75 = $12.95

$20 – $12.95 = $7.05

Question 17.

Yolanda’s sunflower plant was 64.34 centimeters tall in July. During August, the plant grew 18.2 centimeters.

Part A

Estimate the height of Yolanda’s plant at the end of August by rounding each value to the nearest whole number. Will your estimate be less than or greater than the actual height? Explain your reasoning.

_____ cm

Answer:

First, we want to round the number 64.34 to the nearest whole number.

1. We have to round this number to the molest tenth. To round the number to the nearest tenth we need to look at the digit in the hundredths place. So, as 4 < 5, the rounded number is 64.3.

2. We now have to round this number to the nearest one. lb round the number to the nearest one we need to look at the digit in the tenths place. So, as 3 < 5, the rounded number is 64.

Now, we have to round the number 18.2 to the nearest whole number.

1. We have to round this number to the nearest one. To round the number to the nearest one we need to look at the digit in the tenths place. So, as 2 <5, the rounded number is 18.

So, we now have to find the sum of these rounded values: 64 + 18 = 82. Therefore, the estimated height of Volanda’s plant at the and of August is: 82 centimeters.

The estimate is less than the actual height because rounded values are less than the actual values.

Question 17.

Part B

What was the exact height of the plant at the end of August? Was the estimate less than or greater than the exact value?

_____ cm

Answer:

The exact height of the plant is: 64.34 + 18.2

Add the hundredths first.

4 hundre.dths + 0 hundredths = 4 hundredths

Add the tenths.

3 tenths + 2 tenths = 5 tenths Add the ones. Regroup as nee.ded

Add the tens.

6 tens + 1 ten + 1 regrouped ten = 8 tens.

Therefore, the exact height is 64.34+ 18.2 = 82.54.

The estimate is less than the actual height.

Question 18.

Oscar ran the 100-yard dash in 12.41 seconds. Jesiah ran the 100-yard dash in 11.85 seconds. How many seconds faster was Jesiah’s time than Oscar’s time?

_____ second(s)

Answer:

0.56 seconds

Explanation:

Oscar ran the 100-yard dash in 12.41 seconds. Jesiah ran the 100-yard dash in 11.85 seconds.

12.41 – 11.85 = 0.56 seconds.

Jesiah’s time is 0.56 seconds faster than Oscar’s time.

Question 19.

Choose the value that makes the statement true.

Type below:

_________

Answer:

2 hundredths and 5 thousandths

Explanation:

1.025

(1 x 1) + (0 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (5 x \(\frac{1}{1000}\))

2 x \(\frac{1}{100}\) = 2 hundredths

5 x \(\frac{1}{1000}\) = 5 thousandths

In the number 1.025, the value of the digit 2 is 2 hundredths, and the value of the digit 5 is 5 thousandths.

Question 20.

Troy and Lazetta are solving the following word problem. Rosalie’s cat weights 9.8 pounds. Her dog weighs 25.4 pounds. What is the weight of both animals combined. Troy sets up his problem as 9.8 + 25.4. Lazetta sets up her problem as 25.4 + 9.8. Who is correct? Explain your answer and solve the problem.

_________

Answer:

Troy and Lazetta are solving the following word problem. Rosalie’s cat weighs 9.8 pounds. Her dog weighs 25.4 pounds.

9.8 + 25.4

Add tenths 8 + 4 = 12; regroup

Add ones 9 + 5 + 1 regrouped one = 15 ones; regroup

Add tens 0 + 2 + 1 regrouped ten = 3 tens.

35.2

Lazetta: 25.4 + 9.8 = 35.2

Therefore, the answer is 25.4 + 9.8 = 35.2

The weight of both animals combined is 35.2 pounds. So, both were right.

Question 21.

Type below:

_________

Answer:

0.084 and 8.4

Explanation:

0.84 is 10 times as much as

0.84 = 10S

S = 0.84/10 = 0.084

0.84 is 1/10 of

0.84 = 1/10 x S

S = 0.84 x 10 = 8.4

So, from the given answers, 0.84 is 10 times as much as 0.084 and 0.84 is 1/10 of 8.4