Chapter 5: Proportions

Question Solve the proportions: 3 : 12 :: 4 : x multiply the means and extremes x = 16 10 : 100 :: x : 20 multiply the means and extremes x = 2

Solving a Simple Proportion Problem Multiply the extremes. Multiply the means. a : b :: c: d If three terms in the proportion are known and one is unknown, what should be used to represent the unknown term? An x is inserted in the place of an unknown term in a proportion.

Objectives Solving simple proportion problems Solving proportion problems involving fractions, decimals, and percents

Proportions (con’t) A proportion sets two ratios equal to each other. In one ratio, one of the quantities is not known. You then use multiplication and solve the equation for the missing value. Example: 6 : 10 :: 3 : 5 Proportions

The first and fourth terms are the extremes. The second and third terms are the means. Example: 6 : 10 :: 3 : 5 10 3 = 30, product of the means 6 5 = 30, product of the extremes Which products are equal in a proportion? The product of the means equals the product of the extremes because the ratios are of equal value.

Proportions 20x = 1440 x = 72 chicken fingers Suppose it takes 48 chicken fingers to feed Mr. Young’s 4th grade class of 20 students. How many chicken fingers would be needed for 30 students? 48 CF : 20 kids :: x CF : 30 kids (48CF) (30 kids) = (xCF)(20 kids) 20x = 1440 x = 72 chicken fingers How is the example read? Six is to ten as three is to five.

Solve the following Proportion Problem Involving Fractions Example: : :: x : 25 x = 62.5 What is the missing term? Multiply the means, (1/125) × x, and extremes, (1/50) × 25. Place each product on the proper side, (1/125)x = 1/2. Divide the product of the known terms by the number next to x to get (1/2) ÷ (1/125). The quotient will be the value of x. In this example, x = 62.5.

Solving a Proportion Problem Involving Decimals Example: 0.6 : 0.12 :: 0.2 : x x = 0.04 What is the missing term? Multiply the means, 0.12 × 0.2. Multiply the extremes, 0.6 × x. Placing the products on the correct side, you get 0.6x = 0.024. Divide the product of the known terms by the number next to x to get 0.024/0.6. The quotient will be the value of x. In this example, x = 0.04.

Solving a Proportion Problem Involving Fractions and Percents Example: 2/3% : 1/5 :: 50 : x x = 1500 What is the missing term? Convert mixed number fractions to improper fractions. Convert percents containing fractions to proper fractions, [1/5% = (1/5) × (1/100) = 1/500]. Multiply the means, (1/500) × 20, and extremes, (26/25) × x. Place products on the proper side: (26/25)x = 1/25. Divide: (1/25) ÷ (26/25). In this example, x = 1/26.

Assignment Complete Ch 5 worksheet 1-30

Assignment Ch 5 Proportions word problems