ratios & proportions a ratio is a comparison of two numbers by division. to write ratios, use...
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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
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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)?
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RATIOS & PROPORTIONS
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
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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.
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RATIOS & PROPORTIONS
EXAMPLE#3: Is a proportion?
5
3
7
4
Find the cross products.
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RATIOS & PROPORTIONS
EXAMPLE#3: Is a proportion?
5
3
7
4
Find the cross products.
3754 20 = 21 FALSEIf FALSE, the
statement is NOT a proportion.
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RATIOS & PROPORTIONS
7
3
9
4
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RATIOS & PROPORTIONS
7
3
9
4
3974
2728 FALSE – Not a proportion
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RATIOS & PROPORTIONS
20
9
9
4
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RATIOS & PROPORTIONS
20
9
9
4
99204 8180
FALSE – Not a proportion
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RATIOS & PROPORTIONS
Are the following proportions?
27
12
9
4
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RATIOS & PROPORTIONS
27
12
9
4
129274 108108
TRUE – this is a proportion
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RATIOS & PROPORTIONS
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.
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RATIOS & PROPORTIONS
Find the missing numbers to make the following proportions.
21
93
9213 x
x963
x79 9
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RATIOS & PROPORTIONS
Find the missing numbers to make the following proportions.
10
5
4
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RATIOS & PROPORTIONS
Find the missing numbers to make the following proportions.
10
5
4
5410 x2010 x
10 10 2x
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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?
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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
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Jane drives her delivery van 800 miles in 3 days. At this rate, how far will she drive in 15 days?
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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
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Definition Percent can be defined as “of one hundred.”
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Slide 4- 22
Copyright © 2008 Pearson Education, Inc. Publishing as
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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
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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
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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:
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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?
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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
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Slide 4- 27
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Write an equivalent decimal for 67.34%.
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Slide 4- 28
Copyright © 2008 Pearson Education, Inc. Publishing as
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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
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To change decimal into a percentage
Decimal
PercentageTo change a decimal into a percentage, you X by 100
0.23 23%
X 100
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To change decimal into a percentage
Decimal
PercentageTo change a decimal into a percentage, you X by 100
0.45 ?
X 100
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Slide 4- 31
Copyright © 2008 Pearson Education, Inc. Publishing as
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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
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Slide 4- 32
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5.
8
Find the percent notation
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Slide 4- 33
Copyright © 2008 Pearson Education, Inc. Publishing as
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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
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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
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Slide 4- 35
Copyright © 2008 Pearson Education, Inc. Publishing as
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Example B Translate: 7 is 10% of what? 7 is 10% of
what? | | | | | 7 = 10% x b
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Slide 4- 36
Copyright © 2008 Pearson Education, Inc. Publishing as
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Example B Translate: 7 is 10% of what? 7 is 10% of
what? | | | | | 7 = 10% x b
7 /.10 = 70
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Try these
25% of 32
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.25 x 32 = 8
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75% of 36
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75% of 36 = 27
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Slide 4- 41
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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?
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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
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Slide 4- 43
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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
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Slide 4- 44
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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.
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Monica Yuskaitis
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Pearson Education, Inc. Publishing as Pearson Addison-Wesley