PROPORTIONS Vocabulary A proportion is an equation stating

PROPORTIONS

Vocabulary • A proportion is an equation stating that two ratios are equal. – Examples: or – The cross products of a proportion are equal. or

If two ratios are proportional, then their cross products will be equal. ? Since 60 = 60, then this is a proportion.

If two ratios are proportional, then their cross products will be equal. ? Since 6 ≠ 8, then this is NOT a proportion.

If two ratios are proportional, then their cross products will be equal. ? Since 6 = 6, then this is a proportion.

Example #4 Solve for x in the proportion below. Since this is a proportion, the cross products are equal. Divide both sides by 7 to get x alone.

Example #5 Solve for y in the proportion below. Since this is a proportion, the cross products are equal. Divide both sides by 10 to get y alone.

Writing a verbal model will help us set up a proportion when we are solving story problems. Example #6 A recipe that serves 10 people calls for 3 cups of flour. If you want to make the recipe for 25 people, how many cups of flour would you need? Write a verbal model of what you are comparing. Substitute in the values you are given. Use x to represent the quantity that you are looking for. Solve the proportion using cross products. You will need 7. 5 cups of flour to serve 25 people.

We can use proportions to convert units of measurement. Example #7 The Circleville Pumpkin Show in Circleville, Ohio, boasts the world’s largest pumpkin pie. The pie weighs 350 pounds and is 5 feet in diameter. Find the diameter of the pie in centimeters if 1 foot = 30. 48 centimeters. Write a verbal model of what you are comparing. When you substitute, the conversion information is kept together on one side of the proportion. Solve the proportion using cross products. The diameter of the pie is 152. 4 centimeters.