ratios & proportions a ratio is a comparison of two numbers by division. to write ratios, use...

$: RATIOS & PROPORTIONS A ratio is a comparison of two numbers by division. To write ratios, use the word to, a colon, or a fraction bar. EXAMPLE #1: John$
RATIOS & PROPORTIONS A ratio is a comparison of two

numbers by division. To write ratios, use the word to, a

colon, or a fraction bar.EXAMPLE #1: John read 3 books in 4

days. Write the ratio of books to days.

Words: 3 to 4

Colon: 3:4

Fraction: 3/4

RATIOS & PROPORTIONS

There are 5 men and 6 women in my class.

1. What is the ratio of women to men using a fraction?

2. What is the ratio of women to students in my class (use a colon)?

3. What is the ratio of men to students in my class (use words)?


There are 5 men and 6 women in my class.

1. What is the ratio of women to men using a fraction? 5

6

2. What is the ratio of women to students in my class (use a colon)? 6:11

3. What is the ratio of men to students in my class (use words)?

5 to 11

RATIOS & PROPORTIONS A proportion is a statement that

two ratios are equal.

EXAMPLE#2: Is a proportion?15

6

5

2

Find the cross products.

65152 30 = 30 TRUEIf TRUE, the

statement is a proportion.


EXAMPLE#3: Is a proportion?

5

3

7

4



EXAMPLE#3: Is a proportion?

5

3

7

4


3754 20 = 21 FALSEIf FALSE, the

statement is NOT a proportion.


7

3

9

4


7

3

9

4

3974

2728 FALSE – Not a proportion


20

9

9

4


20

9

9

4

99204 8180

FALSE – Not a proportion


Are the following proportions?

27

12

9

4


27

12

9

4

129274 108108

TRUE – this is a proportion


EXAMPLE#4: Solve the proportion:10

4

5

Find the cross products. Multiply both sides of the proportion.

4510 x2010 x

10 10

2x

Divide both sides by 10.


Find the missing numbers to make the following proportions.

21

93

9213 x

x963

x79 9



10

5

4



10

5

4

5410 x2010 x

10 10 2x

If 5 ounces of a medicine must be mixed with 8 ounces of water, how many ounces of medicine would be mixed with 36 ounces of water?

If 5 ounces of a medicine must be mixed with 8 ounces of water, how many ounces of medicine would be mixed with 36 ounces of water?

Solution Let m represent how much medicine would be needed.

5

8 3

Medicine needed How much medicine

Ounces of water Ounces of 6 water

m

5 36 8 m 8

8

36

8

5 m

22.5 m

22.5 ounces of medicine would be needed.

m8180 8 8

Find the cross products. Multiply both sides of the proportion by the denominator of the fraction containing the unknown

Jane drives her delivery van 800 miles in 3 days. At this rate, how far will she drive in 15 days?

Jane drives her delivery van 800 miles in 3 days. At this rate, how far will she drive in 15 days?

Jane would drive 4000

Miles in 15 days

d800

3 15

Find the cross products. Multiply both sides of the proportion by the denominator of the fraction containing the unknown

Distance in 3 days

Distance in 15 days

time time

800 x 15 = 3d

3 3 800 x 15 = 12000

12000 3

d=4000

Definition Percent can be defined as “of one hundred.”

Slide 4- 22

Copyright © 2008 Pearson Education, Inc. Publishing as

Pearson Addison-Wesley

Notation for n %

Percent notation, n%, can be expressed using:

ratio n% = the ratio of n to 100 =

fraction notation

decimal notation

,100

n

1% , or

100n n

% 0.01.n n

Slide 4- 23

To solve a problem involving percents, it is helpful to translate first to an equation. For example, “23% of 5 is what?”

“Of” translates to “” or “”.multiplication

“Is” translates to “=”.equal

“What” translates to any letter.

“%” translates to 1

" " or " 0.01".100

How to Find the Percent of a Whole Number

What number is 75% of 4?

3 is what percent of 4?

Using the PROPORTION METHOD, the set-up is always the same:

PERCENT --

the number with the percent sign (%).

PART -- the number with the word is.

WHOLE -- the number with the word of.

What number is 75% of 4?

4

n

100

75

4

3

100

n

3 is what percent of 4?

NOW, to change a percentage into a decimal, you can divide by 100 or replace the percent symbol with 0.01, and

35%/ 100 35x0.01 0.35 .35

Slide 4- 27



Write an equivalent decimal for 67.34%.

Slide 4- 28



Write an equivalent decimal for 67.34%.

a) Replace the % symbol with * 0.01. 67.34 * 0.01

b) Multiply to move the decimal point two places to the left. 0.67.34

67.34% = 0.6734. or Divide67.34%/100=0.6734

To change decimal into a percentage

Decimal

PercentageTo change a decimal into a percentage, you X by 100

0.23 23%

X 100

To change decimal into a percentage

Decimal

PercentageTo change a decimal into a percentage, you X by 100

0.45 ?

X 100

Slide 4- 31



To convert from fraction notation to percent notation,

a) find decimal notation by division, and

b) convert the decimalnotation to percent notation.

Fraction not3

5

ation

0.65 3.0

30

0

0.6 = 0.60 = 60%3

60%5

Percent notation

Slide 4- 32



5.

8

Find the percent notation

Slide 4- 33



a) Find decimal notation by division.b) Convert the decimal notation to percent notation. To do so, multiply by 100 to move the decimal point two places to the right, and write a % symbol.

5.

80.625

8 5.000

48

20

16

40

40

0

162.5% o

50.625 r 62 %

28

Slide 4- 34

Translate: What is 19% of 82?

What is 19% of 82? | | | | a = 19% x 82 19/100 = .19 .19 x 82 = 15.58

Slide 4- 35



Example B Translate: 7 is 10% of what? 7 is 10% of

what? | | | | | 7 = 10% x b

Slide 4- 36



Example B Translate: 7 is 10% of what? 7 is 10% of

what? | | | | | 7 = 10% x b

7 /.10 = 70

Try these

25% of 32

.25 x 32 = 8

75% of 36

75% of 36 = 27

Slide 4- 41



The sales tax rate in Ohio is 6%. How much tax is charged on the purchase of 4 books at $15.95 each? What is the total price?

Slide 4- 42

The sales tax rate in Ohio is 6%. How much tax is charged on the purchase of 4 books at $15.95 each? What is the total price?Solution a) We first find the cost of the books. 4 × $15.95 = $63.80b) The sales tax on items costing $63.80 is Sales tax rate × Purchase price 0.06 × $63.80 or $3.83

Slide 4- 43



A person’s sales commission is 8%. What is the commission from the sale of $73,230 worth of new car sales?Commission = Commission rate × Sales

Slide 4- 44



A person’s sales commission is 8%. What is the commission from the sale of $73,230 worth of new car sales?

Commission = Commission rate × Sales C = 8% × 73,230 C = 0.08 × 73,230 C = 5858.40The commission is $5858.40.

Monica Yuskaitis

CreditsClipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/clipgallerylive/default.asp

Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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