6.3 the percent proportion - edl chapter 6 percents 6.3 lesson what percent of 15 is 12? a — w = p...
TRANSCRIPT
226 Chapter 6 Percents
The Percent Proportion6.3
How can you use models to estimate
percent questions?
The statement “25% of 12 is 3” has three numbers. In real-life problems, any one of these numbers can be unknown.
Which number Question is missing? Type of Question
What is 25% of 12? 3 Find a part of a number.
3 is what percent of 12? 25% Find a percent.
3 is 25% of what? 12 Find the whole.
Work with a partner. Use a model to estimate the answer to each question.
a. What number is 50% of 30?
0 15 30
0% 50% 100%
So, from the model, is 50% of 30.
b. What number is 75% of 30? c. What number is 40% of 30?
d. What number is 6% of 30? e. What number is 65% of 30?
ACTIVITY: Estimating a Part11
Work with a partner. Use a model to estimate the answer to each question.
a. 15 is what percent of 75?
0 75
0% 100%20%
15
40%
30
60%
45
80%
60
So, from the model, 15 is of 75.
b. 5 is what percent of 20? c. 18 is what percent of 40?
d. 50 is what percent of 80? e. 75 is what percent of 50?
ACTIVITY: Estimating a Percent22COMMON CORE
Percent ProportionIn this lesson, you will● use the percent
proportion to fi nd parts, wholes, and percents.
Learning Standard7.RP.3
Section 6.3 The Percent Proportion 227
Work with a partner. Use a model to estimate the answer to each question.
a. 24 is 33 1
— 3
% of what number?
0 72
0% 100%
24 48
33 %13 66 %2
3
So, from the model, 24 is 33 1
— 3
% of .
b. 13 is 25% of what number? c. 110 is 20% of what number?
d. 75 is 75% of what number? e. 81 is 45% of what number?
Work with a partner. Use a ratio table to answer each question. Then compare your answer to the estimate you found using the model.
a. What number is 6% of 30? b. What number is 65% of 30?
Part 6
Whole 100 30
Part 65
Whole 100 30
c. 18 is what percent of 40? d. 81 is 45% of what number?
Part 18
Whole 40 100
Part 45 81
Whole 100
ACTIVITY: Estimating a Whole33
ACTIVITY: Using Ratio Tables44
5. IN YOUR OWN WORDS How can you use models to estimate percent questions? Give examples to support your answer.
6. Complete the proportion below using the given labels.
percent
100
whole
part
=
Use what you learned about estimating percent questions to complete Exercises 5–10 on page 230.
Use a ModelWhat quantities are given? How can you use the model to fi nd the unknown quantity?
Math Practice
1d1d
2c2c
1e1e
3e3e
228 Chapter 6 Percents
Lesson6.3
What percent of 15 is 12?
a
— w
= p —
100 Write the percent proportion.
12
— 15
= p —
100 Substitute 12 for a and 15 for w.
100 ⋅ 12
— 15
= 100 ⋅ p —
100 Multiplication Property of Equality
80 = p Simplify.
So, 80% of 15 is 12.
0
0% 100%20%
3
40%
6
60%
9
80%
12 15
EXAMPLE Finding a Percent11
What number is 36% of 50?
a
— w
= p —
100 Write the percent proportion.
a
— 50
= 36
— 100
Substitute 50 for w and 36 for p.
50 ⋅ a
— 50
= 50 ⋅ 36
— 100
Multiplication Property of Equality
a = 18 Simplify.
So, 18 is 36% of 50.
EXAMPLE Finding a Part22
Lesson Tutorials
The Percent Proportion
Words You can represent “a is p percent of w” with the proportion
a
— w
= p —
100
where a is part of the whole w, and p%, or p —
100 , is the percent.
Numbers 3 out of 4 is 75%.
3
— 4
= 75
— 100
whole
partpercent
Study TipIn percent problems, the word of is usually followed by the whole.
Section 6.3 The Percent Proportion 229
150% of what number is 24?
a
— w
= p —
100 Write the percent proportion.
24
— w
= 150
— 100
Substitute 24 for a and 150 for p.
24 ⋅ 100 = w ⋅ 150 Cross Products Property
2400 = 150w Multiply.
16 = w Divide each side by 150.
So, 150% of 16 is 24.
0
0% 150%50%
8
100%
16 24
Write and solve a proportion to answer the question.
1. What percent of 5 is 3? 2. 25 is what percent of 20?
3. What number is 80% of 60? 4. 10% of 40.5 is what number?
5. 0.1% of what number is 4? 6. 1
— 2
is 25% of what number?
EXAMPLE Finding a Whole33
Exercises 11 –18
The bar graph shows the strengths of tornadoes that occurred in Alabama in 2011. What percent of the tornadoes were EF1s?
The total number of tornadoes, 145, is the whole, and the number of EF1 tornadoes, 58, is the part.
a
— w
= p —
100 Write the percent proportion.
58
— 145
= p —
100 Substitute 58 for a and 145 for w.
100 ⋅ 58
— 145
= 100 ⋅ p —
100 Multiplication Property of Equality
40 = p Simplify.
So, 40% of the tornadoes were EF1s.
7. Twenty percent of the tornadoes occurred in central Alabama on April 27. How many tornadoes does this represent?
EXAMPLE Real-Life Application44
10
20
30
40
50
60
70
0EF0
36
EF1
58
EF2
29
EF3
13
EF4
7
EF5
2
Strength
Nu
mb
er o
f to
rnad
oes
2011 Alabama Tornadoes
Exercises6.3
230 Chapter 6 Percents
1. VOCABULARY Write the percent proportion in words.
2. WRITING Explain how to use a proportion to fi nd 30% of a number.
3. NUMBER SENSE Write and solve the percent
0
0% 100%20% 40% 60% 80%
40proportion represented by the model.
4. WHICH ONE DOESN’T BELONG? Which proportion does not belong with the other three? Explain your reasoning.
15
— w
= 50
— 100
12
— 15
= 40
— n
15
— 25
= p —
100
a
— 20
= 35
— 100
9+(-6)=3
3+(-3)=
4+(-9)=
9+(-1)=
Use a model to estimate the answer to the question. Use a ratio table to check your answer.
5. What number is 24% of 80? 6. 15 is what percent of 40?
7. 15 is 30% of what number? 8. What number is 120% of 70?
9. 20 is what percent of 52? 10. 48 is 75% of what number?
Write and solve a proportion to answer the question.
11. What percent of 25 is 12? 12. 14 is what percent of 56?
13. 25% of what number is 9? 14. 36 is 0.9% of what number?
15. 75% of 124 is what number? 16. 110% of 90 is what number?
17. What number is 0.4% of 40? 18. 72 is what percent of 45?
a —
w = p
— 100
a — 34
= 40 —
100
a = 13.6
✗ 19. ERROR ANALYSIS Describe and correct the error
in using the percent proportion to answer the question below.
“40% of what number is 34?”
20. FITNESS Of 140 seventh-grade students, 15% earn the Presidential Physical Fitness Award. How many students earn the award?
21. COMMISSION A salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?
Help with Homework
11
22
33
Section 6.3 The Percent Proportion 231
Evaluate the expression when a = −15 and b = −5. (Section 1.5)
32. a ÷ b 33. b + 14
— a
34. b 2
— a + 5
35. MULTIPLE CHOICE What is the solution of 9x = −1.8? (Section 3.4)
○A x = −5 ○B x = −0.2 ○C x = 0.2 ○D x = 5
Write and solve a proportion to answer the question.
22. 0.5 is what percent of 20? 23. 14.2 is 35.5% of what number?
24. 3
— 4
is 60% of what number? 25. What number is 25% of 7
— 8
?
26. HOMEWORK You are assigned 32 math exercises for homework. You complete 87.5% of these before dinner. How many do you have left to do after dinner?
27. HOURLY WAGE Your friend earns $10.50 per hour. This is 125% of her hourly wage last year. How much did your friend earn per hour last year?
28. CAMPSITE The bar graph shows the numbers of reserved campsites at a campground for one week. What percent of the reservations were for Friday or Saturday?
29. PROBLEM SOLVING A classmate displays the
0Greg Diego Amber Rashad Chloe
Candidate
Vo
tes
Class President Electionresults of a class president election in the bar graph shown.
a. What is missing from the bar graph?
b. What percent of the votes does the last-place candidate receive? Explain your reasoning.
c. There are 124 votes total. How many votes does Chloe receive?
30. REASONING 20% of a number is x. What is 100% of the number? Assume x > 0.
31. Answer each question. Assume x > 0.
a. What percent of 8x is 5x? b. What is 65% of 80x?
5
10
15
20
25
30
35
0Mon
5
Tue
3
Wed
4
Thu
7
Fri
26
Sat Sun
30
9
Day
Res
erva
tio
ns
Campground
MSCA7PE_0603.indd 231MSCA7PE_0603.indd 231 4/16/13 2:22:43 PM4/16/13 2:22:43 PM