Course 3 6-1 Relating Decimals, Fractions, and Percents 6-1 Relating Decimals, Fractions, and...
-
Upload
nelson-lucas -
Category
Documents
-
view
217 -
download
1
Transcript of Course 3 6-1 Relating Decimals, Fractions, and Percents 6-1 Relating Decimals, Fractions, and...
Course 3
6-1 Relating Decimals, Fractions, and Percents6-1 Relating Decimals, Fractions, and
Percents
Course 3
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Course 3
6-1 Relating Decimals, Fractions, 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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
Learn to compare and order decimals, fractions, and percents.
Course 3
6-1 Relating Decimals, Fractions, and Percents
Vocabulary
percent
Course 3
6-1 Relating Decimals, Fractions, and Percents
Percents are ratios that compare a number to 100.
RatioEquivalent Ratio with Denominator of 100 Percent
310
1234
3010050
10075
100
30%
50%
75%
Course 3
6-1 Relating Decimals, Fractions, and Percents
Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75
Reading Math
Course 3
6-1 Relating Decimals, Fractions, 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%
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
=
Course 3
6-1 Relating Decimals, Fractions, and Percents
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%
Course 3
6-1 Relating Decimals, Fractions, and Percents
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=
Course 3
6-1 Relating Decimals, Fractions, and Percents
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%
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
=
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
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
Course 3
6-1 Relating Decimals, Fractions, 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!
Course 3
6-1 Relating Decimals, Fractions, 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%
Course 3
6-1 Relating Decimals, Fractions, 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%
Course 3
6-1 Relating Decimals, Fractions, 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%
Course 3
6-1 Relating Decimals, Fractions, 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 as percents.
Compare.
34
0.075% < 41% < 75% < 100%
0.075%, 0.41, , 100%
Course 3
6-1 Relating Decimals, Fractions, 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 as percents.
Compare.
12
25% < 35% < 50% < 200%
0.25, 35%, , 200%
Course 3
6-1 Relating Decimals, Fractions, 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, 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.
Course 3
6-1 Relating Decimals, Fractions, 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 reduce.
items eatentotal items
113
113
= 1 13 = Find the percent.0.077 = 7.7%
The baker eats 7.7% of the items they bake.
Course 3
6-1 Relating Decimals, Fractions, and Percents
Lesson Quiz: Part 1
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
Course 3
6-1 Relating Decimals, Fractions, and Percents
Lesson Quiz: Part 2
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