Chapter 6 Ratio, Proportion, and Line/Angle/Triangle Relationships 6.3 Proportions Chapter 6 Ratio, Proportion, and Line/Angle/Triangle Relationships

6.3 Proportions Objectives Write proportions. Determine whether proportions are true or false. Find the unknown number in a proportion. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Objective 1: Write proportions. A proportion states that two ratios (or rates) are equivalent. is a proportion that is read as Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 4

Objective 1: Write proportions. Example Write each proportion. 6 feet is to 11 feet as 18 feet is to 33 feet. $9 is to 6 liters as $3 is to 2 liters. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 5

Objective 2: Determine whether proportions are true or false. Example Determine whether the proportion is true or false by reducing each ratio to lowest terms. Because is not equivalent to the proportion is false. The ratios are not proportional. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 6

Objective 2: Determine whether proportions are true or false. Example Determine whether the proportion is true or false by reducing each ratio to lowest terms. Both ratios are equivalent to so the proportion is true. The ratios are proportional. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 7

Objective 2: Determine whether proportions are true or false. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 8

Objective 2: Determine whether proportions are true or false. Example Use cross products to determine whether the proportion is true or false. The cross products are equal, so the proportion is true. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 9

Objective 2: Determine whether proportions are true or false. Example Use cross products to determine whether the proportion that follows is true or false. The cross products are unequal, so the proportion is false. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 10

Objective 3: Find the unknown number in a proportion. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 11

Objective 3: Find the unknown number in a proportion. Find the unknown number in the proportion. Example Recall that ratios can be rewritten in lowest terms to obtain the following proportion. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 12

Objective 3: Find the unknown number in a proportion. Example (continued) Step 1 Step 2 Show that the cross products are equivalent. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 13

Objective 3: Find the unknown number in a proportion. Example (continued) Step 3 Step 4 Check solution using the original proportion. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 14

Objective 3: Find the unknown number in a proportion. Example Find the unknown number in the proportion. Round answers to the nearest hundredth. Find the cross products. Step 1 Show the cross products are equivalent. Step 2 Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 15

Objective 3: Find the unknown number in a proportion. Example (continued) Step 3 Step 4 Check. Very close, but, not equal due to rounding. The cross products are not equal but are close enough. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 16

Objective 3: Find the unknown number in a proportion. Find the unknown number in the proportion. Example Step 1 Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 17

Objective 3: Find the unknown number in a proportion. Example (continued) Show the cross products are equivalent. Step 2 Step 3 Divide both sides by 6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 18

Objective 3: Find the unknown number in a proportion. Example (continued) Step 4 Check The cross products are equal, so is the correct solution. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 19

Objective 3: Find the unknown number in a proportion. Find the unknown number in the proportion. Example Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 20

Objective 3: Find the unknown number in a proportion. (continued) Example The cross products are equal, so 0.8 is the correct solution. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.3 - 21