Understanding Proportion

Ratio

A ratio is the comparison of two numbers by division.

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 boys15 girls

Ratios can be part-to-whole16 boys

31 students

Ratio, continued

If a ratio is part-to-whole, you can divide and find a decimal or a percent.

16 boys31 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:

2 = 6 2 x n = 6 x 8 2n = 488 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