Application of Proportions Math 8

Lesson EQ How do you use proportions to convert measurements, find the unknown side length of polygon or real life objects, and interpret and construct scale models?

Vocabulary Proportion – two ratios that are equivalent Customary system – a system of measurement used in the United States Metric system – a decimal system of weights and measures

Proportions With the help of a calculator, we can determine if two ratios are proportional. Proportion means two ratios that are equivalent or can be written with an equal sign between them. Example: 7 2 21 and 6 Nonexample: 9 16 12 and 24

Your turn. Determine if these ratios are proportional or not. 3 2 27 and 18 12 27 15 and 36 1 12 2 and 24

Solving Proportions We know that when two ratios are equal to each other they are called proportional or proportions. We can use the knowledge that two ratios are equal in a proportion to help us find a missing numerator or denominator in one of those ratios.

Solving Proportions In order to find a missing number in a ratio, we use cross products. What does the word product mean when we are talking about math? When you picture a cross, what does it look like?

Cross Products Cross products are used in proportions that are equal. You multiply the numerator of one proportion by the denominator of another. Here is an example without any missing numbers. 3 = 9 4 12 3 = 9 4 12 3x12 = 4x9 ~~ 36=36

Cross Products We can use cross products to determine if two ratios are proportional. Example: 6 ? 4 15 = 10 Nonexample: 5 ? 15 6 = 21

Additional Examples 4 ? 5 12 = 15 3 ? 6 9 = 12 10 ? 20 15 = 30

Your turn: tell if the ratios are proportional 2 ? 6 3 = 10 3 ? 6 4 = 8 5 ? 4 9 = 12

Solving Proportions When you do not know one of the 4 numbers in a proportion, set the cross products equal to each other and solve. Here are some examples: 12 = 4 d 14 4d = 12  14 4d = 168 d = 168 ÷ 4 = 42 r = 9 4 11 11r = 4  9 11 r = 36 r = 3.27

Additional Examples 1 = x 5 12 5x = 1  12 5x = 12 x = 12 ÷ 5 x = 2.4

Additional Examples 2 = 6 3 y 2y = 6  3 2y = 18 y = 18 ÷ 2 y = 9

Additional Examples 1 = 9 h 36 9h = 1  36 9h = 36 h = 36 ÷ 9 h = 4

Your Turn! Solve the Proportion 4 = 9 8 d 3 = 7 j 9 r = 8 5 12

4 = 9 8 d 4d = 9  8 4d = 72 d = 72 ÷ 4 d = 18

3 = 7 j 9 7j = 3  9 7j = 27 j = 27 ÷ 7 j = 3.86

r = 8 5 12 12r = 5  8 12r = 40 r = 40 ÷ 12 r = 3.33

Homework Page 358 #1-9 SKIP #8