Pre-Algebra 8-1 Relating Decimals, Fractions, and Percents Pre-Algebra Homework Page 402-403 #1-16 &...
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Transcript of Pre-Algebra 8-1 Relating Decimals, Fractions, and Percents Pre-Algebra Homework Page 402-403 #1-16 &...
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Pre-Algebra Homework
Page 402-403
#1-16
& Spiral Review
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Our Learning GoalStudents will be able to determine and construct fractions, decimals, and percents by understanding their relationships, solving for the unknown, solving increase and decrease, solving sales tax/total cost contextual problems and compute simple interest.
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Our Learning Goal Assignments
• Learn to relate decimals, fractions, & percents (8-1)
• Learn to find percents (8-2)
• Learn to find a number when the percent is known (8-3)
• Learn to find percent increase and decrease (8-4)
• Learn to estimate with percents (8-5)
• Learn to find commission, sales tax, and withholding tax (8-6)
• Learn to compute simple interest (8-7)
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Learning Goal ScaleStudents are able to determine & construct fractions, decimals, & percents:
4 3 2 1 0
• Clear understanding their relationships
• Able to solve for the unknown
• Understands how to solve for increase & decrease
• Calculating solving sales tax/total cost contextual problems
• Computing simple interest
• Understands their relationships
• Some solving for the unknown
• Difficulty solving for increase & decrease
• Understands their relationships
• Difficulty solving for the unknown
• Some understanding their relationships
• Even with help, no understanding or skill demonstrated
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents8-1 Relating Decimals, Fractions, and
Percents
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
8-1 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
45
2145
or
Pre-Algebra
8-1 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Today’s Learning Goal Assignment
Learn to relate decimals, fractions, and percents.
Pre-Algebra
8-1 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%
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Think of the % symbol as meaning /100.
0.75 = 75% = 75/100
Reading Math
Pre-Algebra
8-1 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%
Pre-Algebra
8-1 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
=
Pre-Algebra
8-1 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
b: 0.25 =14
= 25%
Pre-Algebra
8-1 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
c: 40% =40100
=2
5
4
10=
Pre-Algebra
8-1 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
d: 0.60 =35
= 60%
Pre-Algebra
8-1 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
e: 23
% =66 0.666 = 23
Pre-Algebra
8-1 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
f: 12
% =87 0.875 = 78
8751000
=
Pre-Algebra
8-1 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
g: 125% =125 100
=5
4=
1
41
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: Example 1
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
a: 12
% =12 0.125 = 18
1251000
=
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: 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
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Find the equivalent fraction, decimal, or percent for each value given on the circle graph.
Additional Example 2: Finding Equivalent Fractions, Decimals, and Percents
0.15(100) = 15%
720
= 0.35
Fraction Decimal Percent
0.15
35%
38%
320
15100
=
720
35100
=
1950
38100
= 1950 = 0.38
325 = 0.12 0.12(100) = 12%
325
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
You can use information in each column to make three equivalent circle graphs. One shows the breakdown by fractions, one shows the breakdown by decimals, and one shows the breakdown by percents.
Additional Example 2 Continued
The sum of the fractions should be 1.
The sum of the decimals should be 1.
The sum of the percents should be 100%.
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Try This: Example 2
Fill in the missing pieces on the chart below.
Fraction Decimal Percent
0.1
45%
110 0.1(100) = 10%
0.2(100) = 20%
45100
=0.45
1 5
15
=0.2525100
1 4
45100
920=
0.25(100) = 25%
= 0.2
Pre-Algebra
8-1 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 3: 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.
Pre-Algebra
8-1 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. So, what percentage of the food the baker cooks is eaten without being sold?
Try This: Example 3
Set up a ratio and reduce. items eatentotal items
113
113
= 1 13 = Find the percent.0.077 = 7.7%
So the baker, eats 7.7% of the items they bake.
Pre-Algebra
8-1 Relating Decimals, Fractions, and Percents
Lesson Quiz
Find each equivalent value.
1. as a percent
2. 20% as a fraction
3. as a decimal
4. as a percent
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%
37.5%
0.625
56%
38
1425
15
58