warm up evaluate. 1.2. 3.4

Relating Decimals, Fractions, and Percents6-1Warm UpEvaluate.

1. 2.

3. 4.

13

13+

14

215

315 –7

123

12

4 5

7 2

123 1

445214

5 or

Relating Decimals, Fractions, and Percents6-1

Learn to compare and order decimals, fractions, and percents.

Relating Decimals, Fractions, and Percents6-1

Percent: Ratio that compares a number to 100.

Relating Decimals, Fractions, and Percents6-1

Fraction3/4

Decimal0.75

Percent75%

Read It (3 ÷ 4)Write It 4 3Solve It .75

Move the decimal 2 times to the left.

Move the decimal 2 times to the right.

Write the percent as a fraction over 100. Then simplify.

Relating Decimals, Fractions, and Percents6-1Change the fraction to a decimal:

1.

3.

5.

Continue…….

41 2.

4.

6.

65

131134

10987

623

325

0.25 0.83

5.67 3.33

87.9 34.85

Relating Decimals, Fractions, and Percents6-1Change decimals to percents

Continue…….

Relating Decimals, Fractions, and Percents6-1

Change percents to decimals.

Continue…….

Relating Decimals, Fractions, and Percents6-1Change percents to fractions.

Continue…….

Relating Decimals, Fractions, and Percents6-1

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

Additional Example 1: Finding Equivalent Ratios and Percents

110a: 10% = 10

100=

Relating Decimals, Fractions, and Percents6-1

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

Additional Example 1 Continued

b: 0.25 =14

= 25%

Relating Decimals, Fractions, and Percents6-1

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

Additional Example 1 Continued

c: 40% = 40100= 2

5410

=

Relating Decimals, Fractions, and Percents6-1

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

Additional Example 1 Continued

d: 0.60 =35

= 60%

Relating Decimals, Fractions, and Percents6-1

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

Additional Example 1 Continued

e: 23 % =66 0.666 = 2

3

Relating Decimals, Fractions, and Percents6-1

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

Additional Example 1 Continued

f: 12 % =87 0.875 = 7

88751000=

Relating Decimals, Fractions, and Percents6-1

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

Additional Example 1 Continued

g: 125% = 125 100 = 5

4= 1

41

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 1

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

a: 12 % =12 0.125 = 1

81251000=

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 1 Continued

b: 25% = 25100= 1

4

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

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 1 Continued

c: 0.375 =38

= 37 %12

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

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 1 Continued

d: 50% = 50100= 1

2

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

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 1 Continued

e: 0.625 =58

= 62 %12

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

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 1 Continued

f: 75% = 75100= 3

4

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

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 1 Continued

g: 1 = 100 100 = 100%

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

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Relating Decimals, Fractions, and Percents6-1Additional Example 2A: Comparing Fractions, Decimals,

and PercentsCompare. Write <, >, or =.

40%1414 = 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!

Relating Decimals, Fractions, and Percents6-1Additional Example 2B: Comparing Fractions, Decimals,

and PercentsCompare. Write <, >, or =.

0.893 50%

0.893 = 89.3%

89.3% > 50%

Write as a percent.

Compare.

0.893 > 50%

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 2A

Compare. Write <, >, or =.

65%3434 = 0.75 = 75%

75% > 65%

Write as a percent.

Compare.34 > 65%

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 2B

Compare. Write <, >, or =.

0.136 20%

0.136 = 13.6%

13.6% < 20%

Write as a percent.

Compare.

0.136 < 20%

Relating Decimals, Fractions, and Percents6-1Additional Example 3: Ordering Fractions, Decimals, and

PercentsWrite 0.075%, , 0.41, and 100% in order from least to greatest.

34

34 = 0.75 = 75%

0.41 = 41%

Write as percents.

Compare.

34

0.075% < 41% < 75% < 100%

0.075%, 0.41, , 100%

Relating Decimals, Fractions, and Percents6-1Check It Out: Example 3

Write 35%, 0.25, , and 200% in order from least to greatest.

12

12 = 0.50 = 50%

0.25 = 25%

Write as percents.

Compare.

12

25% < 35% < 50% < 200%

0.25, 35%, , 200%

Relating Decimals, Fractions, and Percents6-1

Gold that is 24 karat is 100% pure gold. Gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper, zinc, silver, or nickel. What percent of 14 karat gold is pure gold?

Additional Example 4: Physical Science Application

Set up a ratio and reduce.

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.

Relating Decimals, Fractions, and Percents6-1

A baker’s dozen is 13. When a shopper purchases a dozen items at the bakery they get 12. It is said that the baker eats 1 item from every batch. What percent of the food does the baker eat?

Check It Out: Example 4

Set up a ratio and reduce.

items eatentotal items

113

113 = 1 13 Find the percent.0.077 7.7%

The baker eats about 7.7% of the items they bake.

Relating Decimals, Fractions, and Percents6-1

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Relating Decimals, Fractions, and Percents6-1Lesson Quiz: Part I

Find each equivalent value.

1. as a percent2. 20% as a fraction3. as a decimal

Compare. Write <, >, or =.

4. 30%

5. 0.650 97% <

37.5%

0.625

>

38

711

15

58

Relating Decimals, Fractions, and Percents6-1Lesson Quiz: 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

Relating Decimals, Fractions, and Percents6-1

1. Identify the equivalent value of as a percent.

A. 45.3%

B. 55.5%

C. 78.3%

D. 86.5%

Lesson Quiz for Student Response Systems59

Relating Decimals, Fractions, and Percents6-1

2. Identify the equivalent value of 45% as a fraction.

A.

B.

C.

D.

Lesson Quiz for Student Response Systems

Relating Decimals, Fractions, and Percents6-1

3. Identify the equivalent value of as a decimal.

A. 0.252

B. 0.375

C. 0.456

D. 0.698

Lesson Quiz for Student Response Systems38

Relating Decimals, Fractions, and Percents6-1

4. Identify the correct symbol to compare.0.430___50%

A. >

B. <

C. =

D. >

Lesson Quiz for Student Response Systems