6-1 Relating Fractions, Decimals, and Percents

Warm UpEvaluate.

1. 2.

3. 4.

13

1

3+

14

215

315

–712

312

4 5

7 2

123

1 4

45

2145

or

6-1 Relating Fractions, Decimals, and Percents

Vocabulary

percent

6-1 Relating Fractions, Decimals, and Percents

Percents are ratios that compare a number to 100.

Ratio Decimal Percent

     

   

   

30%

50%

75%

310

30100=

12

50100=

34

75100=

0.30

0.50

0.75

6-1 Relating Fractions, Decimals, and Percents

Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75

Reading Math

6-1 Relating Fractions, Decimals, and Percents

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

18 = 1 ÷ 8 = 0.125

To convert a decimal to a percent, multiply by 100 and insert the percent symbol.

0.125 100 12.5%

6-1 Relating Fractions, Decimals, and Percents

Find the missing fraction or percent equivalent for each letter a–g on the number line.

Additional Example 1: Finding Equivalent Fractions and Percents

1

10a: 10% =

10100

=

6-1 Relating Fractions, Decimals, and Percents

Additional Example 1 Continued

b: 0.25 =14

= 25%

Find the missing fraction or percent equivalent for each letter a–g on the number line.

6-1 Relating Fractions, Decimals, and Percents

Additional Example 1 Continued

c: 40% =40100

=2

5

4

10=

Find the missing fraction or percent equivalent for each letter a–g on the number line.

6-1 Relating Fractions, Decimals, and Percents

Additional Example 1 Continued

d: 0.60 =35

= 60%

Find the missing fraction or percent equivalent for each letter a–g on the number line.

6-1 Relating Fractions, Decimals, and Percents

Additional Example 1 Continued

e: 23

% =66 0.666 = 23

Find the missing fraction or percent equivalent for each letter a–g on the number line.

6-1 Relating Fractions, Decimals, and Percents

Additional Example 1 Continued

f: 12

% =87 0.875 = 78

8751000

=

Find the missing fraction or percent equivalent for each letter a–g on the number line.

6-1 Relating Fractions, Decimals, and Percents

Additional Example 1 Continued

g: 125% =125 100

=5

4=

1

41

Find the missing fraction or percent equivalent for each letter a–g on the number line.

6-1 Relating Fractions, Decimals, and Percents

Additional Example 2A: Comparing Fractions, Decimals, and Percents

Compare. Write <, >, or =.

40%14

14

= 0.25 = 25%

25% < 40%

Write as a percent.

Compare.

14

< 40%When multiplying a decimal by 100, simply move the decimal point two spaces to the right.

Remember!

6-1 Relating Fractions, Decimals, and Percents

Additional Example 2B: Comparing Fractions, Decimals, and Percents

Compare. Write <, >, or =.

0.893 50%

0.893 = 89.3%

89.3% > 50%

Write as a percent.

Compare.

0.893 > 50%

6-1 Relating Fractions, Decimals, and Percents

Additional Example 3: Ordering Fractions, Decimals, and Percents

Write 0.075%, , 0.41, and 100% in order

from least to greatest.

34

34

= 0.75 = 75%

0.41 = 41%

Write the numbers in the same form.

Compare.

34

0.075% < 41% < 75% < 100%

0.075%, 0.41, , 100%

6-1 Relating Fractions, Decimals, and Percents

Gold that is 24 karat is 100% pure gold. Gold that is 14 karat is 14 parts pure gold and 10 parts another metal. What percent of 14 karat gold is pure gold?

Additional Example 4: Physical Science Application

Set up a ratio and simplify.

parts pure goldtotal parts

1424

712

=

712

= 7 12 = Find the percent.0.583 = 58.3%

13So 14-karat gold is 58.3%, or 58 % pure gold.

6-1 Relating Fractions, Decimals, and Percents

Lesson Review: Part I

Find each equivalent value.

1. as a percent

2. 20% as a fraction

3. as a decimal

Compare. Write <, >, or =.

4. 30%

5. 0.650 97% <

37.5%

0.625

>

38

711

15

58

6-1 Relating Fractions, Decimals, and Percents

Lesson Review: Part II

6. Write 245%, , 0.133, and 66.6% in order

from least to greatest.

5. About 342,000 km2 of Greenland’s total area (2,175,000 km2) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice?

16%

0.133, , 66.6%, 245%

15

15