Fraction, Decimal, & Percent

Equivalencies

Fraction, Decimal, & Percent

EquivalenciesCoach Lesson 4

Also see textbook pages 108 – 110, & 202 – 205.Jeff Rhodus

6th Grade

Elsanor Elementary

Coach Lesson 4Also see textbook pages 108 – 110, & 202 – 205.

Jeff Rhodus

6th Grade

Elsanor Elementary

Getting the Idea!

Fractions, decimals, and percents can all be used to show parts of a whole.

The word percent means “of 100.”

That is why percents can be written as fractions with denominators of 100.

The symbol for percent is %.

This chart shows some common fraction-decimal-percent equivalencies.

Fraction Decimal Percent Fraction Decimal Percent

1

1001

10

1815

0.01

0.1

0.125

0.2

1%

10%

12.5%

20%

141

234

11

or 1

0.25

0.5

0.75

1.0

25%

50%

75%

100%

To convert a fraction or mixed number to a decimal, find an equivalent fraction or improper fraction that has a denominator of 10 or 100, then write the decimal.

Example 1: Convert the fraction 3/5 to a decimal.Strategy: Find the equivalent fraction with a denominator of 10.Step 1: Multiply the numerator and denominator by 2 to find the equivalent fraction with a denominator of 10.

Step 2: Write the decimal.

Solution: The decimal equivalent of 3/5 is 0.6

35

=3 x 55 x 2

=6

10

610

=0.6

Example 2: Convert the decimal 1.44 to a mixed number.Strategy: Write the decimal as an improper with a denominator of 100, then simplify.Step 1: Since the decimal goes to the hundredths place, remove the decimal point and write the digits as the numerator and 100 as the denominator.

Step 2: Change the improper fraction to a mixed number. Then simply the fraction part by dividing the numerator and denominator by 4.

Solution: The mixed number equivalent of 1.44 is 11125

1.44 =144100

144100

=144100

44 : 4100 : 4

11=25

144100

=11125

Example 3: Write 23/100 as a percent.

Strategy: Look at the denominator of the fraction. It is 100.

Since the denominator of 23/100 is 100, the percent is the same as the numerator.

Solution: 23/100 = 23%

Example 4: Convert the fraction 9/20 to a percent.Strategy: Find an equivalent fraction with a denominator of 100, then write the percent.Step 1: Multiply the numerator and denominator by 5 to find the equivalent fraction with a denominator of 100.

Step 2: Change the fraction to a percent. Since the denominator is 100, the percent is the same as the numerator.

Solution: 9/20 = 45%

To convert a percent to a fraction, first convert the percent to a decimal. Then convert the decimal to a fraction. Remember that percents over 100% will be written as mixed numbers since they are greater than a whole.

920

= 9 x 520 x 5

= 45100

45100

=45%

Example 5: Convert 140% to a mixed number.Strategy: Write the percent as an improper fraction with a denominator of 100, then simplify.Step 1: Remove the percent symbol and write the digits as the numerator and 100 as the denominator.

Step 2: Change the improper fraction to a mixed number. Then simply the fraction part by dividing the numerator and denominator by 20.

Solution: 140% = 125

140 =140

100

140100= 140

10040 : 20

100 : 20=

25

140100

=125

To convert a decimal to a percent, move the decimal point two places to the right and insert a percent symbol(%) after the number. Insert zeros as placeholders when necessary.

Example 6: Convert the decimal 0.7 to a percent.

Strategy: Move the decimal point two places to the right.

Step 1: Think of place value.

0.7 = 0.70

Move the decimal point in 0.70 two places to the right.

0.70.

Step 2: Insert a percent symbol at the end of the number.

70%

Solution: 0.7 = 70%