Find two ratios that are equivalent to each given ratio , , , , Possible answers: Warm Up

Pre-Algebra 7.4 Solving Proportions

Learn to solve proportions. … A Proportion is an equation that shows 2 ratios are equivalent …

cross product Vocabulary

Cross Products

The cross product represents the product of the extremes is equal to the product of the means. Helpful Hint means 2:6 = 3:9 extremes

Tell whether the ratios are proportional A. Since the cross products are equal, the ratios are proportional. 60 = ? 60 = 60 Find cross products Example: Using Cross Products to Identify Proportions

A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct? 4 parts gasoline 1 part oil = ? 15 quarts gasoline 5 quarts oil 4 5 = = ≠ 15 The ratios are not equal. The mixture will not be correct. Set up ratios. Find the cross products. Example: Using Cross Products to Identify Proportions

Tell whether the ratios are proportional. Since the cross products are equal, the ratios are proportional = 20 Find cross products A. = ? Try This

A mixture for a certain brand of tea should be 3 parts tea to 1 part sugar. If you combine 4 tablespoons of sugar with 12 tablespoons of tea, will the mixture be correct? 3 parts tea 1 part sugar = ? 12 tablespoons tea 4 tablespoons sugar 3 4 = = = 12 The ratios are equal. The mixture will be correct. Set up ratios. Find the cross products. Try This

When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve. Solving with Cross-Products

Solve the proportion. 6p = 12 5 p = 10 6p = 60 Find the cross products. Solve by dividing both sides by p 12 = ; the proportion checks = Example: Solving Proportions

Solve the proportion = 2g 21 = g 42 = 2g Find the cross products. Solve by dividing both sides by g = ; the proportion checks = Try This

Voyager I travels through space at about 38,600 mph. At that rate, about how far would Voyager I travel in a half hour? Set up the proportion. Let x represent the unknown distance. Find the cross products. Multiply. Voyager I travels 19,300 miles in a half hour. 19,300 = x = 1x x = miles 1 hours 1 = miles 2 hours 2 Example: distance = rate x time

If apples sell at 3 for $.75, how many apples can be bought with $4.25?.75x = 17 = x Set up the proportion. Let x represent the unknown amount of apples Find the cross products. Multiply. Solve by dividing both sides by.75 $4.25 will buy 17 apples =.75x =.75x x = apples cost = Try This apples cost

Tell whether each pair of ratios is proportional = ? = ? Solve each proportion A cake recipe calls for 1.5 cups of milk and 3 cups of flour. Mrs. Perona made a mistake and used 5 cups of flour. How many cups of milk should she use to keep the proportions correct? yes no n = 30 n = cups of milk n 12 = n = Lesson Quiz

Writing Proportions When you write a proportion, be sure that 2 equivalent ratios compare similar things…

Write 2 equal rates of miles to gallons. Try This Mrs. Perona gets 30 miles to a gallon of gas. At that given rate, how many gallons would Mrs. Perona use on a 3600 mile trip? Use cross product to solve…

Solve the proportion. 30x = x = x = 3600 Find the cross products. Solve by dividing both sides by mi x gal 30 mi 1 gal Writing & Solving Proportions = Check Cross Product to make sure equal.

Writing Proportions Bob delivers 4 newspapers in 5 minutes. At this rate, how many newspapers can he deliver in 1 hour. x = Newpapers minutes x = 48 Newspapers

More Practice… Go to Workbook and Practice some more! 11-4 Proportions 11-5 Solve Proportions 11-6 Write Proportions