Solving Percents Using Proportions - Amazon S3

12

Solving Percents Using Proportions

Many percent problems can be solved by using this percent proportion.

the number before the word "is"

the number after the word "of"

a certain number

is

a certain percent

of

=

100

a certain number

the number with the percent sign

As long as we have numbers in three of the four positions in this proportion, we can solve to find the fourth. Fill in the three parts of the proportion that are given. Write a variable for the "what number" or "what percent" part of the question.

Now solve like any other proportion. Multiply the diagonal which has two numbers, then divide by the number that is left. Let's look at some examples.

Example 1 What is 20% of 10?

Question

n 10

=

20 100

Set up the problem

10 ? 20 = 200 and

200 ? 100 = 2 so

20% of 10 is 2.

Solution

Example 2 40 is 50%

of what number?

Question

50

40 n

=

50 100

Set up the problem

40 ? 100 = 4,000 and

4,000 ? 50 = 80 so

40 is 50% of 80.

Solution

Lesson 12

Example 3

30 is what percent

of 150?

30 150

=

n 100

30 ? 100 = 3,000 and

3,000 ? 150 = 20 so

30 is 20% of 150.

Question

Set up the problem

Solution

When finding the percent be sure to use the percent symbol in the answer.

Be sure to add the percent symbol.

Remember, always put the number before the word "is" over the number that comes after the word "of."

Memorize this short version of the percent proportion.

is

%

of = 100

Set up proportions and solve. Fill in the blanks. The first one shows you how.

1. 64 is 40% of what number? 160

64 n

=

40 100

64 ? 100 ? 40 = 160

Remember the % symbol.

2. 72 is what percent of 80?

3. What is 60% of 40?

Remember the % symbol.

4. 66 is what percent of 120?

5. 15 is 125% of what number?

51

Lesson 12

We Remember

Fill in the chart for each figure.

A

B

C

6. Number of faces

7. Number of edges

8. Number of vertices

A

cube C tetrahedron

B triangular prism

Write the percent as a decimal. Write the decimal as a percent.

9. a. 25% =

b. 1.6 =

Write each percent as a fraction or mixed number showing hundredths. Reduce to simplest form.

10. a. 132% =

=

b. 14% =

=

Write an expression for each, using an exponent.

11. a. 9 ? 9 ? 9 ? 9 ? 9 ? 9 ? 9

b. Eleven cubed

+?-x S k i l l B u i l d e r s

12.

a.

4 5

?

5 16

?

3

3 4

=

1

7 10

b. ?

2 3

4 1.8 9 c. ? 3 . 6 7

Multiply to find the number. 13. a. 106 =

52

b. 35 =

Lesson 12

Mastery Drill

14. a. 1 century =

years

b. 1 gallon =

quarts

15. a. 1 millennium =

years

b. 1 cubic centimeter =

milliliter

16. a. 1 decade =

years

b. 1 kilogram =

grams

17. An obtuse angle measures between

? and

?.

18. The formula for the volume of a rectangular prism is

.

19. The formula for the perimeter of a rectangle or parallelogram is

.

20. The formula for the area of a circle is

.

Use the formula to find the volume of the rectangular prism. 21.

6 ft 11 ft

9 ft

Simplify the expressions. 22. a. 14x ? 5x + 10 + x

b. 5x + 18 ? 3 ? x + 6x

Substitute 2 for y.

c. 5(13 ? 8) + y ? 3

?. . . Mental Math

82

23.

+ 17

?9

? 40

? 200

? 10 =

53

Lesson 12

24. At sea level, 100 cubic feet of air weighs 3.5 kg. a. How much does 1.5 cubic feet of air weigh?

Set up a proportion to solve.

b. How many grams is this?

25. A water cooler holds 20 L of water. How many 250-mL glasses of water can be drawn from the cooler before it is empty?

Find the perimeter of the polygon.

26.

2 ft

2 ft

2 ft

4 ft 4 ft

4 ft

Write the proportion.

27. The short version of the percent proportion is

.

Set up proportions and solve. 28. 12 is what percent of 48?

29. What is 35% of 80?

30. 70 is 56% of what number? 54

We need air to hear. The

sounds we hear must travel through air.

The world would be silent if there

were no air.

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