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Math Revision Sheet

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11/10/2020 eAlpha - 5.1. Understand and Model Percents

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Chapter 5: Percents

Lesson 1: Understand and Model Percents 1 / 21 / 2

Lesson 1: Understand and Model Percents

Remember …A percent is a ratio that compares a quantity out of 100. Percentsare expressed using the symbol %.

76 out of 100 squares are shaded. This means or 76% of the 76

100

Shade the hundredths grid to model each ratio. Type each ratio as a fraction. Thentype the percent.1. 38 out of 100 2. 9 out of 100

To write an equivalent ratio in simplest form, divide the numerator and

denominator by the greatest common factor:

We can also find percents by expressing them as a fraction over 100.3 out of 5 people prefer a certain brand of toothpaste.

÷ = .76

100

4

4

19

25

Write the ratio as a fraction. = = 60% The numerator tells us the value 3

5

60

100 of the percent.

Write an equivalentfraction over 100.

; ;

squares are shaded.

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11/10/2020 eAlpha - 5.2. Relate Fractions, Decimals, and Percents

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Chapter 5: Percents

Lesson 2: Relate Fractions, Decimals, and Percents 1 / 21 / 2

Lesson 2: Relate Fractions, Decimals, and Percents

Remember …To convert a percent to a decimal, use the definition of percent to write a fraction. Then writethe fraction as a decimal.Example:

Type each percent as a decimal and a fraction in simplest form.1. 22% 2. 90%

To convert a decimal to a percent, write the decimal as a fraction with a denominator of 100.Then use the definition of percent to write the fraction as a percent.

32% means 32 out of 100 or . is thirty-two hundredths or 0.32.32

100

32

100

Example:0.67 is sixty-seven hundredths, or , which is 67%.67

100

To convert a fraction to a percent, use an equivalent ratio with 100 in the denominator.

Example: ; × = , or 25%1

4

1

4

25

25

25

100

To convert a percent to a fraction, write the percent as a rate per 100. Then simplify.

Example:85% means 85 out of 100 or . = 85

100

85

100

17

20

To convert a decimal to a fraction, use place value.

Example:0.75 is read as “seventy-five hundredths.” The place value is hundredths, which

is the denominator. So, 0.75 = = .75

100

3

4

To convert a fraction to a decimal, divide the numerator by the denominator.

Example: = 1 ÷ 2 and 1÷ 2 = 0.5 , so = 0.5.1

2

1

2

3. 56%

4. 57% 5. 86% 6. 73%

; ; ;

; ; ;

=

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11 22

Chapter 5: Percents

Lesson 2: Relate Fractions, Decimals, and Percents 2 / 22 / 2

Multiple-Choice Practice

19. Which is NOT modeledby the grid?

A.

1.5625%A. B.

C. D.

B.

C. D.

15%

3

20

0.15

3

100

Type each decimal as a percent and a fraction in simplest form.7. 0.6 8. 0.05 9. 0.28

10. 0.95 11. 0.01 12. 0.64

; ; ;

; ; ;

Type each fraction as a decimal and a percent.13. 1

5

14. 13

25

15. 41

50

16. 77

100

17. 5

16

18. 13

18

; ; ;

; ; ;

20. Which shows 74% as a fraction?

A. B.

C. D.

1

74

37

100

37

50

74

21. Which shows as a percent?5

32

15.625%

156.25% 1,562.5%

0.275A. B.

C. D.

22. Which shows 27.5% as a decimal?

2.75

275 2,750

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Chapter 5: Percents

Lesson 3: Percents Greater Than 100 or Less Than 1 1 / 21 / 2

Lesson 3: Percents Greater Than 100 or Less Than 1

Remember …Percents greater than 100 or less than 1 can be modeled as fractions and decimals.

Type each percent as a decimal and a mixed number in simplest form or wholenumber in simplest form.1. 120% 2. 225%

Example

As a decimal: 136% = 1.00 + 0.36 = 1.36

136% = + = = 1 = 1 100

100

36

100

136

100

36

100

9

25

ExampleWrite 0.25% as a decimal and as a fraction in simplest form.

0.25% = 0.25

100

3. 350%

4. 426% 5. 1200% 6. 3275%

;

Use the same process of converting percents to fractions or decimals for percentsgreater than 100 or less than 1.

For percents greater than 100, the equivalent fraction can be written as an improper fractionor mixed number.

Write 136% as a decimal and as a mixed number insimplest form.

As a mixed number:

× = 0.25

100

100

100

25

10, 000

As a decimal: = 0.0025.25

10, 000

As a fraction, you can simplify ÷ = .25

10, 000

25

25

1

400

Write the percent as a fraction with a denominator of 100.

To eliminate the decimal in the numerator, multiply the numerator and denominator by 100.

; ;

; ; ;

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Chapter 5: Percents

Lesson 3: Percents Greater Than 100 or Less Than 1 2 / 22 / 2

Multiple-Choice Practice

19. Which is NOT modeled by the grid?

A.

0.5%A.

B.

C.

D.

C.

B. D.

0.13

113%

113

100

1.13

Type each percent as a decimal and a fraction in simplest form.7. 0.03% 8. 0.11% 9. 270%

10. 0.025% 11. 4,900% 12. 2,280%

;

Type each mixed number as a decimal and a percent.

13. 2 4

5

14. 15.

16. 17. 18.

; ; ;

; ; ;

20. Which percent is equivalent to ?1

200, 000

21. Which decimal is equivalent to 0.009%?

0.005%

0.05% 0.0005%

; ;

; ; ;

6 7

2510

1

10

4 2

53

3

162 2

3

0.00009A.

B.

C.

D.

0.09

0.009 0.9

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22. A savings account has an annual interest rate of 0.4%. What is this value as a decimal and afraction in simplest form?

Chapter 5: Percents

Lesson 4: Compare and Order Rational Numbers 1 / 21 / 2

Lesson 4: Compare and Order Rational Numbers

Remember …A rational number is a number that can be written as a fraction , where a and b are

a

b

Compare. Use the symbols <, >, or =.

1. 2.

Example

Convert all numbers to decimals to compare:

3. 4.

3

10

2% 0.2

integers and b does not equal 0. Terminating decimals, repeating decimals, mixed numbersand fractions are all examples of rational numbers.

To compare and order rational numbers, write the numbers in the same form. Then you canuse place value or a number line to compare and order the numbers.

Write the following numbers from least to greatest. , 110%, 2.8, 1 , 15%, 0.585

8

3

8

0.25

0.625, 1.1, 2.8, 1.375, 0.15, 0.58

From least to greatest, the decimal values are:

0.15, 0.58, 0.625, 1.1, 1.375, 2.8,

From least to greatest, the original values are:

15%, 0.58, , 110%, 1 , 2.85

8

3

8

2

5

42% 0.5 9%

Type the numbers in order from least to greatest.

5. 0.11, 10%, , 0.15, 25%1

5

6. 85%, 0.9, , , 70%3

4

4

5

7. 0.5, 49%, , 0.55, 2

3

5

6

8. 7%, 0.77, , 87%, 0.787

10

, , , , , , , ,

, , , , , , , ,

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11/10/2020 Lesson 1

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UNIT 1

Name: Date:

Lesson 1Understand Ratios and Unit Rates

1. For the given situation, write the ratio 3 ways.

4 daisies for every 7 carnations

a. Word form 4 to 7

b. Colon form 4 : 7

c. Fraction form 4

7

2. For the given situation, write the ratio 3 ways.

65 students for every 3 buses

a. Word form 65 to 3

b. Colon form 65 : 3

c. Fraction form 65

3

3. A fruit bowl contains 11 apples and 6 oranges. What is the ratio of oranges to apples inthe fruit bowl?

a. 11 : 6 b. 6 : 11 c. 11 : 17 d. 6 : 17

11/10/2020 Lesson 1

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4. There are 19 students in Lucy’s class who take the bus to school. The rest of the studentsin her class walk to school. If there are 24 students in Lucy’s class, what is the ratio ofstudents who take the bus to students who walk?

a. 19 : 5 b. 5 : 19 c. 19 : 24 d. 5 : 24

5. Last week, Sheila walked 10 miles in 4 hours. Brenda walked 8 miles in 5 hours.

Write a ratio 3 ways that represents the miles walked to hours for each girl.

Sheila:

a. Word form 10 to 4

b. Colon form 10 : 4

c. Fraction form

Part A

10

4

Brenda:

a. Word form 8 to 5

b. Colon form 8 : 5

c. Fraction form 8

5

Express each girl’s ratio as a unit rate.

Sheila: miles per hour

Brenda: miles per hour

Part B

10

4

8

5

11/10/2020 Lesson 1

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Chuck walked 5 miles last week.

If Chuck’s unit rate was the same as Sheila’s unit rate, how many hours did he walk?

2 hours

Part C

Grade 6 Copyright © by William H. Sadlier, Inc. All rights reserved.

Explain your reasoning.

Possible answer:Chuck walked half the distance as Sheila at the same unit rate, so it tookhim half as many hours.

Progress Mathematics

11/10/2020 Lesson 4

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UNIT 1

Name: Date:

Lesson 4Solve Unit Rate Problems

1. Bruce travels 120 miles in 3 hours. What is his average speed?

40 miles per hour

2. At a store, 4 sweaters cost $84. What is the unit cost?

$ 21 per sweater

3. Tim works 26 hours in 4 days. Paul works 32 hours in 5 days.

How many hours does Tim work per day? Write your answer as a decimal.

6.5 hours per day

Part A

How many hours does Paul work per day? Write your answer as a decimal.

6.4 hours per day

Part B

Who works more hours per day?

works more hours per day.

Part C

Tim

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Explain your answer.

Possible answer:Tim works 6.5 hours per day, and Paul works 6.4 hours per day. If Isubtract their total work hours per day, 6.5 – 6.4 = 0.1, the difference isone tenth hour. That means Tim works 0.1 or more hour per day thanPaul.

1

10

4. Yesterday, Mr. Lopez drove his car 270 miles in 6 hours. Today, Mr. Lopez drove his car200 miles in 4 hours. Compare his average speed for those two days.

Possible answer:

Yesterday: 

Today: 

Today Mr. Lopez drove 5 miles per hour faster.

270 miles

6 hours= 45

miles

hours

200 miles

4 hours= 50

miles

hours

Grade 6 Copyright © by William H. Sadlier, Inc. All rights reserved.

5. A package of 8 pens costs $4. What is the unit cost?

a. $0.40 per pen b. $0.50 per pen c. $2.00 per pen d. $4.00 per pen

Progress Mathematics

11/10/2020 Lesson 7

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UNIT 1

Name: Date:

Lesson 7Convert Measurement Units

1. Convert the measurement.

820 milliliters = 0.82 liter

2. Convert the measurement.

6 pounds = 96 ounces

3. Yesterday, Carlos drove 280 kilometers in 4 hours. Today, Carlos drove 40 kilometers in30 minutes. Compare his unit rate for each day. Which statement is true?

a. Today, Carlos drove 10 kilometers per hour faster than yesterday.

b. Today, Carlos drove 40 kilometers per hour faster than yesterday.

c. Today, Carlos drove 70 kilometers per hour faster than yesterday.

d. Today, Carlos drove 80 kilometers per hour faster than yesterday.

4. Naomi bought 7 quarts of milk for a morning meeting. She will put a pitcher of milk oneach table. Each pitcher holds 2 cups of milk. What is the greatest number of full pitchersthat Naomi can fill?

Naomi can fill 14 pitchers.

11/10/2020 Lesson 7

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5. Sanjay runs at a rate of 6 miles per hour.

What is Sanjay’s rate in feet per hour?

Sanjay’s rate is 31,680 feet per hour.

Part A

Show your work.

1 mi = 5,280 ft; 6 mi = 6 × (5,280 ft) = 31,680 ft

What is Sanjay’s rate in feet per minute?

Sanjay’s rate is 528 feet per minute.

Part B

Show your work.

1 hour 60 min; = = 528 ft

31,680

60

What is Sanjay’s rate in feet per second?

Sanjay’s rate is 8.8 feet per second.

Part C

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Show your work.

1 min 60 sec; = = 8.8 ft

528

60

Grade 6 Copyright © by William H. Sadlier, Inc. All rights reserved.

Is there a way to find Sanjay’s rate in feet per second in fewer steps? If so, show how.

Part D

Yes. 1 hour ; = 60 min × = 3, 600 sec60 sec

1 min= 8.8 ft/sec

31,680

3,600

Progress Mathematics