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6-1 Relating Fractions, Decimals, and Percents
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson Presentation
PreviewPreview
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
NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
California Standards
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
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
Find the missing fraction or percent equivalent for each letter a–g on the number line.
6-1 Relating Fractions, Decimals, and Percents
Check It Out! Example 1 Continued
b: 25% =25100
=1
4
Find the missing fraction 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
6-1 Relating Fractions, Decimals, and Percents
Check It Out! Example 1 Continued
c: 0.375 =38
= 37 %1
2
Find the missing fraction 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
6-1 Relating Fractions, Decimals, and Percents
Check It Out! Example 1 Continued
d: 50% =50100
=1
2
Find the missing fraction 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
6-1 Relating Fractions, Decimals, and Percents
Check It Out! Example 1 Continued
e: 0.625 =58
= 62 %1
2
Find the missing fraction 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
6-1 Relating Fractions, Decimals, and Percents
Check It Out! Example 1 Continued
f: 75% =75100
=3
4
Find the missing fraction 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
6-1 Relating Fractions, Decimals, and Percents
Check It Out! Example 1 Continued
g: 1 =100 100
= 100%
Find the missing fraction 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
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
Check It Out! Example 2A
Compare. Write <, >, or =.
65%34
34
= 0.75 = 75%
75% > 65%
Write as a percent.
Compare.
34
> 65%
6-1 Relating Fractions, Decimals, and Percents
Check 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%
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
Check 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 the numbers in the same form.
Compare.
12
25% < 35% < 50% < 200%
0.25, 35%, , 200%
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
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 simplify.
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.
6-1 Relating Fractions, Decimals, and Percents
Lesson Quiz: 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 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