NAME ____________________________________________ DATE _____________________________ PERIOD _____________

Chapter 2 Study guide - Percents Lesson 1: Decimals and Fractions Decimals like 0.58, 0.12, and 0.08 can be written as fractions.

To write a decimal as a fraction, you can follow these steps.

1. Identify the place value of the last decimal place.

2. Write the decimal as a fraction using the place value as the denominator, and simplify. Example 1 - Write 0.35 as a fraction in simplest form. 0.35= !"

!""!"!""

0.35 means 35 hundredths. 7

= !"!""

!"!""

Simplify. Divide the numerator and denominator by the GCF, 5. 20

= !!" So, in simplest form, 0.35 is !

!".

Example 2 - Write 𝟑

𝟓 as a decimal.

Since 5 is a factor of 10, write an equivalent fraction with a denominator of 10. × 2

!!

= !!"

= 0.6

× 2

Write each decimal as a fraction or mixed number in simplest form.

1. 0.9 2. 0.27 3. 0.008

Write each fraction or mixed number as a decimal.

4.1!! 5.4 !

!"

NAME ____________________________________________ DATE _____________________________ PERIOD _____________

Lesson 2: Percent and Fractions

Write each percent as a fraction in simplest form.

6. 20% 7. 32%

Write each fraction as a percent. 8. !

! 9. !

!"

NAME ____________________________________________ DATE _____________________________ PERIOD _____________

Lesson 3: Percents and Decimals To write a percent as a decimal first rewrite the percent as a fraction with a denominator of 100. Then write the fraction as a decimal by dividing by 100 (move decimal 2 places left).

Write 23% as a decimal.

23% = !"!""

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

= 0.23 Write 23 hundredths as a decimal. To write a decimal as a percent first write the decimal as a fraction with a denominator of 100. Then write the fraction as a percent by multiplying by 100 (move decimal 2 places right).

Write 0.65 as a percent.

0.65 = !"!""

Write 65 hundredths as a fraction.

= 65% Write the fraction as a percent.

Write each percent as a decimal.

10. 39% 11. 4%

Write each decimal as a percent.

12. 0.86 13. 0.2

NAME ____________________________________________ DATE _____________________________ PERIOD _____________

Lesson 4: Percents Greater Than 100% and Percents Less Than 1% A percent greater than 100% equals a number greater than 1. A percent less than 1% equals a number less than 0.01 or !

!"".

Examples Write each percent as a decimal and as a mixed number or fraction in simplest form.

Examples Write each decimal as a percent.

Write each percent as a decimal and as a mixed number or fraction in simplest form.

14. 200% 15. 750% 16. 0.3% 17. 0.48%

Write each decimal as a percent.

18. 2.6

19. 0.008

1. 280%

280% = !"#!""

Definition of percent

= 2.8 or 2 !!

2. 0.12%

0.12% = !.!"!""

Definition of percent

= 0.0012 or !!,!""

3. 2.17

2.17 = 217. Multiply by 100.

= 217%

4. 0.0034

0.0034 = 000.34 Multiply by 100. = 0.34%

NAME ____________________________________________ DATE _____________________________ PERIOD _____________

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Lesson 5: Compare and Order Fractions, Decimals, and Percents

To compare two fractions.

• Find the least common denominator (LCD) of the fractions; that is, find the least common multiple of the denominators.

• Write an equivalent fraction for each fraction using the LCD.

• Compare the numerators.

Example 1 Replace with <, >, or = to make 𝟏

𝟑 𝟓

𝟏𝟐 true.

The LCM of 3 and 12 is 12. So, the LCD is 12.

Rewrite each fraction with a denominator of 12. !! =

!", so !

! = !

!". !

!" = !

!"

Now compare. Since 4 < 5, !

!" < !

!" . So, !

! < !

!" .

Example 2 Order 𝟏

𝟔, 𝟐𝟑, 𝟏𝟒, and 𝟑

𝟖 from least to greatest.

The LCD of the fractions is 24. So, rewrite each fraction with a denominator of 24. !

!

!", so !

! = !

!". !

!

!", so !

! = !"

!".

!

!

!", so !

! = !

!". !

!

!", so !

! = !

!".

The order of the fractions from least to greatest is !!, !!, !!, !!.

Complete by using <, >, or = to make a true statement. 20. !

!" !

! 21. 3 !

! 3 !

!

Order the fractions from least to greatest.

22. 1 !!, 1 !

!, 1 !

!, 1 !

!"

1

2

NAME ____________________________________________ DATE _____________________________ PERIOD _____________

Lesson 6: Estimate with Percents Usementalmathnotestohelpyousolveproblemmentally.Thispartwillbeonyourtestfirst,andyoumaynotuseacalculatorforit.

1. Changeeachproblem(writingdownwhatyouchangeitto)soyoucansolveusingoneofthementalmathrules.2. MentalMathTips:

• 50%àDivideby2• 25%àDivideby4• 75%àDivideby4,thenmultiplyby3(since75is3x25)• 10%àDivideby10• Multipleof10àDivideby10,thenmultiplybyotherfactorofnumber.• 5%àDivideby10,thenDivideby2• 1%àDivideby100

Examples

1.20%of58 2.76%of21.Changeto20%of60 Changeto75%of2060÷10=6,then6x2=12 20÷4=5,then5x3=15Estimate:12 Estimate:15

Estimateeachpercent.

23.49%of8 24.24%of27 25.19%of46

NAME ____________________________________________ DATE _____________________________ PERIOD _____________

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Lesson 7: Percent of a Number Find 25% of 260.

Method 1: Method 2:

Write 25% as a fraction in simplest form. Write 25% as a decimal. Use the fraction in a multiplication problem. Then write a multiplication problem.

25% = !"!"

or !! 25% = 0.25

25% of 260 = !!

× 260 25% of 260 = 0.25 × 260

= 65 = 65 Find the percent of each number.

26. 48% of 50 27. 0.3% of 460

28. 350% of 60 29. 2.7% of 110

Lesson 8:Solve Percent Problems

In a percent proportion, one ratio compares a part to the whole. The other ratio is the equivalent

percent written as a fraction with a denominator of 100. part →

whole →𝑝𝑤=

𝑛100

percent

Example 1 What percent of 25 is 18? !"!"= !

!"" Write the proportion.

!"!"

!!""

Since 25 × 4 = 100, multiply 18 by 4. 72 = n So, 18 is 72% of 25

Write a proportion and solve each problem.

30. What number is 25% of 20? 31. What percent of 50 is 30? 32. 30 is 60% of what number? 33. 12 is what percent of 25?