Relating Decimals, Fractions, and Percents 6-1 Warm Up Evaluate. 1.2. 3.4. 1 3 1 3 + 14 2 15 3 – 7...

Relating Decimals, Fractions, and Percents6-1

Warm UpEvaluate.

1. 2.

3. 4.

13

1

3+

14

215

315

–7

123

12

4 5

7 2

123 1

44

5214

5or


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


Percent: Ratio that compares a number to 100.


Fraction

3/4

Decimal

0.75

Percent

75%

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.


Change the fraction to a decimal:

1.

3.

5.

Continue…….

4

1 2.

4.

6.

6

5

13

1134

10

987

6

23

3

25

0.25 0.83

5.67 3.33

87.9 34.85


Change decimals to percents

Continue…….


Change percents to decimals.

Continue…….


Change percents to fractions.

Continue…….


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

Additional Example 1: Finding Equivalent Ratios and Percents

1

10a: 10% =

10100

=



Additional Example 1 Continued

b: 0.25 =14

= 25%




c: 40% =40100

=2

5

4

10=




d: 0.60 =35

= 60%




e: 23

% =66 0.666 = 23




f: 12

% =87 0.875 = 78

8751000

=




g: 125% =125 100

=5

4=

1

41


Check It Out: Example 1


a: 12

% =12 0.125 = 18

1251000

=

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Check It Out: Example 1 Continued

b: 25% =25100

=1

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1



c: 0.375 =38

= 37 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1



d: 50% =50100

=1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1



e: 0.625 =58

= 62 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1



f: 75% =75100

=3

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1



g: 1 =100 100

= 100%


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


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!


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


0.893 50%

0.893 = 89.3%

89.3% > 50%

Write as a percent.

Compare.

0.893 > 50%


Check It Out: Example 2A


65%34

34

= 0.75 = 75%

75% > 65%

Write as a percent.

Compare.

34

> 65%


Check It Out: Example 2B


0.136 20%

0.136 = 13.6%

13.6% < 20%

Write as a percent.

Compare.

0.136 < 20%


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 as percents.

Compare.

34

0.075% < 41% < 75% < 100%

0.075%, 0.41, , 100%



Write 35%, 0.25, , and 200% in order


12

12

= 0.50 = 50%

0.25 = 25%

Write as percents.

Compare.

12

25% < 35% < 50% < 200%

0.25, 35%, , 200%


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.


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?


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.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

Find each equivalent value.

1. as a percent

2. 20% as a fraction

3. as a decimal


4. 30%

5. 0.650 97% <

37.5%

0.625

>

38

711

15

58


Lesson Quiz: Part II

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


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


1. Identify the equivalent value of as a percent.

A. 45.3%

B. 55.5%

C. 78.3%

D. 86.5%


59


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

A.

B.

C.

D.



3. Identify the equivalent value of as a decimal.

A. 0.252

B. 0.375

C. 0.456

D. 0.698


38


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

A. >

B. <

C. =

D. >


Relating Decimals, Fractions, and Percents 6-1 Warm Up Evaluate. 1.2. 3.4. 1 3 1 3 + 14 2 15 3 – 7...

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