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Relating Fractions, Decimals, and Percents6-1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
Relating Fractions, Decimals, and Percents6-1
Warm UpEvaluate.
1. 2.
3. 4.
13
1
3+
14
215
315
–712
312
4 5
7 2
123
1 4
45
2145
or
Relating Fractions, Decimals, and Percents6-1
Problem of the Day
A fast-growing flower grows to a height of 12 inches in 12 weeks by doubling its height every week. If you want your flower to be only 6 inches tall, after how many weeks should you pick it?
11 weeks
Relating Fractions, Decimals, and Percents6-1
Prep for MA.8.A.6.4 Perform operations on real numbers (including…percents…)…Review MA.6.A.5.1Review MA.6.A.5.2
Sunshine State Standards
Relating Fractions, Decimals, and Percents6-1
Vocabulary
percent
Relating Fractions, Decimals, and Percents6-1
Percents are ratios that compare a number to 100.
Relating Fractions, Decimals, and Percents6-1
Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75
Reading Math
Relating Fractions, Decimals, and Percents6-1
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%
Relating Fractions, Decimals, 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
1
10a: 10% =
10100
=
Relating Fractions, Decimals, 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 Fractions, Decimals, 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
5
4
10=
Relating Fractions, Decimals, 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 Fractions, Decimals, 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 = 23
Relating Fractions, Decimals, 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 = 78
8751000
=
Relating Fractions, Decimals, 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 Fractions, Decimals, and Percents6-1
Check 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 = 18
1251000
=
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Fractions, Decimals, and Percents6-1
Check 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 Fractions, Decimals, and Percents6-1
Check It Out: Example 1 Continued
c: 0.375 =38
= 37 %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 Fractions, Decimals, and Percents6-1
Check 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 Fractions, Decimals, and Percents6-1
Check It Out: Example 1 Continued
e: 0.625 =58
= 62 %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 Fractions, Decimals, and Percents6-1
Check 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 Fractions, Decimals, and Percents6-1
Check 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 Fractions, Decimals, and Percents6-1
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!
Relating Fractions, Decimals, and Percents6-1
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%
Relating Fractions, Decimals, and Percents6-1
Check It Out: Example 2A
Compare. Write <, >, or =.
65%34
34
= 0.75 = 75%
75% > 65%
Write as a percent.
Compare.
34
> 65%
Relating Fractions, Decimals, and Percents6-1
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%
Relating Fractions, Decimals, and Percents6-1
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%
Relating Fractions, Decimals, and Percents6-1
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 as percents.
Compare.
12
25% < 35% < 50% < 200%
0.25, 35%, , 200%
Relating Fractions, Decimals, 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 Fractions, Decimals, 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 Fractions, Decimals, and Percents6-1
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
Relating Fractions, Decimals, and Percents6-1
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
Relating Fractions, Decimals, and Percents6-1
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
Relating Fractions, Decimals, 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 Systems
59
Relating Fractions, Decimals, and Percents6-1
2. Identify the equivalent value of 45% as a fraction.
A.
B.
C.
D.
Lesson Quiz for Student Response Systems
Relating Fractions, Decimals, 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 Systems
38
Relating Fractions, Decimals, and Percents6-1
4. Identify the correct symbol to compare.0.430___50%
A. >
B. <
C. =
D. >
Lesson Quiz for Student Response Systems
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