Understanding Proportion

Ratio A ratio is the comparison of two numbers. A classroom has 16 boys and 12 girls. Also written as 16 boys, 16:12 or 16 to 12 12 girls Generally, ratios are in lowest terms: 16 = 16/4 = 4 12 12/4 3

Ratio, continued Ratios can compare two unlike things: Joe earned $40 in five hours The ratio is 40 dollars or 8 dollars 5 hours 1 hour When the denominator is one, this is called a unit rate.

Ratio, continued Let’s look at a classroom: Ratios can be part-to-part 16 boys 15 girls Ratios can be part-to-whole 16 boys 31 students

Ratio, continued If a ratio is part-to-whole, you can divide and find a decimal or a percent. 16 boys 31 students 31/16.00 = .516, or 51.6% are boys

Proportion Proportion is a statement that says two ratios are equal. In an election, Damon got three votes for each two votes that Shannon got. Damon got 72 votes. How many votes did Shannon get? Damon 3 = 72 so 3 x 24 = 72 Shannon 2 n 2 x 24 48 n = 48, so Shannon got 48 votes.

Proportion, continued Tires cost two for $75. How much will four tires cost? # of tires 2 = 4 so 2 x 2 = 4 tires cost 75 n 75 x 2 $150 n = 150, so four tires cost $150

Proportion, continued One more way to solve proportions is called the cross products property. 2 = 6 2 x n = 6 x 8 2n = 48 8 n 2 2 n = 24

Proportion, continued Now you try! Three cans of soup costs $5. How much will 12 cans cost? # of cans 3 = 12 3 x 4 = 12 cans cost 5 n 5 x 4 20 dollars n = 20, so 12 cans cost $20