ratio, proportion, and percent
DESCRIPTION
Chapter 6. Ratio, Proportion, and Percent. Ratio and Proportion. 6.1. 53% =. Writing Ratios as Fractions. A ratio is the quotient of two quantities. For example, a percent can be thought of as a ratio, since it is the quotient of a number and 100. or the ratio of 53 to 100. a. b. - PowerPoint PPT PresentationTRANSCRIPT
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter 6
Ratio, Proportion, and
Percent
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
6.1
Ratio and Proportion
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
A ratio is the quotient of two quantities.
Writing Ratios as Fractions
For example, a percent can be thought of as a ratio, since it is the quotient of a number and 100.
53% = 53100
or the ratio of 53 to 100
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
The ratio of a number a to a number b is their quotient. Ways of writing ratios are
andab
a to b, a : b,
Ratio
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
A proportion is a statement that two ratios are equal.
Solving Proportions
If and are two ratios, then
is a proportion.
ab
cd
ab
cd
=
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Solving Proportions
A proportion contains four numbers. If any A proportion contains four numbers. If any three numbers are known, the fourth number three numbers are known, the fourth number can be found by solving the proportion. To can be found by solving the proportion. To solve use cross products. solve use cross products.
bd
bd
a
b
c
d
a
b
c
d=
Multiply both sides by the LCD, bd
Simplify ad = bc
cross product cross product
ad
bc
These are calledcross products.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Determining Whether Proportions are True
Is 3
8= 12
32 a true proportion?
3 12=8 32
3 32 = 8 12?
96 = 96 True proportion
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Finding Unknown Numbers in Proportions
Solve 26
x= 28
49.
26 49 = 28x Cross multiply.
1274 = 28x Simplify the left side.
45.5 = x Divide both sides by 28.
Check: 26
45.5= 28
49?
26
45.5= 52
91= 4
7= 28
49
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
A 16-oz Cinnamon Mocha Iced Tea at a local coffee shop has 80 calories. How many calories are there in a 28-oz Cinnamon Mocha Iced Tea?
Solving Problems by Writing Proportions
16 ounces 28 ounces80 calories caloriesx Solve the proportion.
16 80 28x Cross multiply.
16 2240x Simplify the right side.
140x Divide both side by 140.
A 28-oz Cinnamon Mocha Iced Tea has 140 calories.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
When writing proportions to solve problems, write the proportions so that the numerators have the same unit measures and the denominators have the same unit measures.
For example, 2 7inches5 miles
inchesmiles
n
Helpful Hint