UNIT 3 Ratio and Proportion Copyright 2011 Delmar

Key Terms • • • Extremes Means Proof Proportion Ratio Copyright © 2011 Delmar,

Ratios • Ratio: Way of expressing relationship between two similar components – Example: The

Ratio Expressions • As a quotient – One number divided by the other •

Proportions • Proportion: Way of expressing comparative relationships • In mathematics, proportions show relationship

Proportions • Must determine unknown by solving for x • When part of problem

Solving for X • Steps to solve for x 1. 2. 3. 4. 5.

Prove Your Answer • Once you find the unknown, prove your answer using the

Solving for X Using Fractions • Steps to solve for x 1. 2. 3.

Solving for X Using Decimals • Steps to solve for x 1. Set up

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Ratios • Ratio: Way of expressing relationship between two similar components – Example: The relationship of 3 to 1 is written as 3 : 1 • May be expressed as quotient, fraction, or decimal Copyright © 2011 Delmar, Cengage Learning. ALL RIGHTS RESERVED.

Ratio Expressions • As a quotient – One number divided by the other • As a fraction – Breaking whole number into parts • As a decimal – Based on multiples of 10 Copyright © 2011 Delmar, Cengage Learning. ALL RIGHTS RESERVED.

Proportions • Proportion: Way of expressing comparative relationships • In mathematics, proportions show relationship between two ratios – Example: 3 : 5 = 12 : 20 (continues) Copyright © 2011 Delmar, Cengage Learning. ALL RIGHTS RESERVED.

Solving for X • Steps to solve for x 1. 2. 3. 4. 5. Set up proportion: 3 : 5 = 12 : x Multiply outer terms (extremes): 3 x Multiply inner terms (means): 5 x 12 = 60 Divide product of x into other terms: 60 / 3 x = 20 Copyright © 2011 Delmar, Cengage Learning. ALL RIGHTS RESERVED.

Prove Your Answer • Once you find the unknown, prove your answer using the following steps: 1. 2. 3. 4. Replace x with the answer you obtained Multiply the means by the means Multiply the extremes by the extremes Results will equal each other Copyright © 2011 Delmar, Cengage Learning. ALL RIGHTS RESERVED.

Solving for X Using Fractions • Steps to solve for x 1. 2. 3. 4. 5. Set up proportion: 1/4 x : 250 = 1 : 500 Multiply outer terms (extremes): 1/4 x x 500 = 125 x Multiply inner terms (means): 250 x 1 = 250 Divide product of x into other terms: 250 / 125 = 2 x=2 Copyright © 2011 Delmar, Cengage Learning. ALL RIGHTS RESERVED.

Solving for X Using Decimals • Steps to solve for x 1. Set up proportion: 0. 25 : 0. 5 = 0. 5 : x 2. Multiply outer terms (extremes): 0. 25 x 3. Multiply inner terms (means): 0. 5 x 0. 5 = 0. 25 4. Divide product of x into other terms: 0. 25 / 0. 25 = 1 5. x = 1 Copyright © 2011 Delmar, Cengage Learning. ALL RIGHTS RESERVED.