course 1 8-8 percents, decimals, and fractions 6 th grade math homework page 424 #1-26 answers!
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Course 1
8-9 Percent Problems
6th Grade Math HOMEWORK
Page 428
#1-14
Our Learning Goal for Chapter 8Students will understand ratios, proportions, and percents by being able to write ratios, find unit rates, solve proportions, identify similar figures, find unknown measures, make scale drawings, understand relationships, and solve problems including those involving discounts, tips, sales tax, and simple interest.
Our Learning Goal Assignments• Learn to write ratios and rates and to find unit rates (8-1)• Learn to write and solve proportions (8-2)• Learn to use proportions to make conversions within the
customary system (8-3)• Learn to use ratios to identify similar figures (8-4)• Learn to use proportions and similar figures to find unknown
measures (8-5)• Learn to read and use map scale and scale drawings (8-6)• Learn to write percents as decimals and as fractions (8-7)• Learn to write decimals and fractions as percents (8-8)• Learn to find the missing value in a percent problem (8-9)• Learn to solve percent problems that involve discounts, tips,
and sales tax (8-10)
8-9 Percent Problems
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Warm UpWarm Up
Lesson PresentationLesson Presentation
Warm UpWrite each decimal as a percent and fraction.
1. 0.38
2. 0.06
3. 0.2
38%,
6%,
20%,
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8-9 Percent Problems
1950
__
350
__
1 5
__
Today’s Learning Goal Assignment
Learn to find the missing value in a percent problem.
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8-9 Percent Problems
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8-9 Percent Problems
To find the percent of one number is of another, use this proportion:
% 100
= is of
If you are looking for 45% of 420, 45 replaces the percent sign and 420 replaces “of.” The first denominator, 100, always stays the same. The “is” part is what you have been asked to find.
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8-9 Percent Problems
Additional Example 1: Application
First estimate your answer. Think: 35% = ,
which is close to , and 560 is close to 600. So
about of the students participate in after-school sports.
35100
___
1 3
__
1 3
__
1 3
__ This is the estimate.• 600 = 200
Think: “35 out of 100 is how many out of 560?”
Helpful Hint
There are 560 students in Ella’s school. If 35% of the students participate in after-school sports, how many students participate in after-school sports?
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8-9 Percent Problems
Additional Example 1 ContinuedNow solve:
s 560
___ 35 100
___ =
100 • s = 35 • 560
100s = 19,600
100s 100
____ 19,600 100
_____ =
s = 196
Let s represent the number of students who participate in after-school sports.
The cross products are equal.
s is multiplied by 100.
Divide both sides of the equation by 100 to undo multiplication.
Since 196 is close to your estimate of 200, 196 is a reasonable answer.
196 students participate in after-school sports.
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8-9 Percent Problems
Try This: Example 1
There are 480 students in Tisha’s school. If 70% of the students participated in the fundraising program, how many students participated in the fundraising program?
First estimate your answer. Think: 70% = ,
which is close to , and 480 is close to 500. So
about of the students participated in the
fundraising program.
70100
___
3 4
__
3 4
__
This is the estimate. 3 4
__ • 500 = 375
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8-9 Percent Problems
Try This: Example 1 ContinuedNow solve:
s 480
___ 70 100
___ =
100 • s = 70 • 480
100s = 33,600
100s 100
____ 33,600 100
_____ =
s = 336
Let s represent the number of students who participated in the fundraising program.
The cross products are equal.
s is multiplied by 100.
Divide both sides of the equation by 100 to undo multiplication.
Since 336 is close to your estimate of 375, 336 is a reasonable answer.
336 students participated in the fundraising program.
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8-9 Percent Problems
Additional Example 2: Application
Johan is 25% of the way through his exercises. If he has exercised for 20 minutes so far, how much longer does he have to work out?
is of
__ % 100
___ =
100 • 20 = 25 • m
25% of the exercises are completed, so 20 minutes is 25% of the total time needed.
The cross products are equal.
20 m
__ 25 100
___ = Set up a proportion. The “of” part is what you have been asked to find.
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8-9 Percent Problems
Additional Example 2 Continued
2,000 = 25m
2,000 25
_____ 25m 25
____ =
80 = m
m is multiplied by 25.
Divide both sides by 25 to undo multiplication.
The time needed for the exercises is 80 min. So far, the exercises have taken 20 min. Because 80 – 20 = 60, Johan will be finished in 60 min.
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8-9 Percent Problems
Try This: Example 2
Phil is 30% of the way through his homework. If he has worked for 15 minutes so far, how much longer does he have to work?
is of
__ % 100
___ =
100 • 15 = 30 • m
30% of the exercises are completed, so 15 minutes is 30% of the total time needed.
The cross products are equal.
15 m
__ 30 100
___ = Set up a proportion. The “of” part is what you have been asked to find.
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8-9 Percent Problems
Try This: Example 2 Continued
1,500 = 30m
1,500 30
_____ 30m 30
____ =
50 = m
m is multiplied by 30.
Divide both sides by 30 to undo multiplication.
The time needed for the homework is 50 min. So far, the homework has taken 15 min. Because 50 – 15 = 35, Phil will be finished in 35 min.
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8-9 Percent Problems
Instead of using proportions, you can also multiply to find a percent of a number.
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8-9 Percent Problems
Additional Example 3: Multiplying to Find a Percent of a Number
36% = 0.36
0.36 • 50
Write the percent as a decimal.
Multiply using the decimal.
18So 18 is 36% of 50.
17% = 0.17
0.17 • 95
Write the percent as a decimal.
Multiply using the decimal.
16.15
So 16.15 is 17% of 95.
A. Find 36% of 50.
B. Find 17% of 95.
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8-9 Percent Problems
Try This: Example 3
20% = 0.20
0.20 • 70
Write the percent as a decimal.
Multiply using the decimal.
14So 14 is 20% of 70.
12% = 0.12
0.12 • 83
Write the percent as a decimal.
Multiply using the decimal.
9.96
So 9.96 is 12% of 83.
A. Find 20% of 70.
B. Find 12% of 83.
Lesson Quiz
1. Find 28% of 310.
2. Find 70% of 542.
3. Martha is taking a 100-question test. She has completed 60% of the test in 45 minutes. How much longer will it take her to finish the test?
4. Crystal has a collection of 72 pennies. If 25% of them are Canadian, how many Canadian pennies does she have?
379.4
86.8
Insert Lesson Title Here
30 min
18
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8-9 Percent Problems