Proportions

Proportions show the equality of two ratios:

For example: 1/3 = 3/9
10/14 = 20/28

How can you find out if a proportion is equal?
There are many ways! Here are two.

1. Find the Cross Products (Cross Multiply)

Example: 1/3 = 3/9

1 x 9 = 3 x 3
9 = 9

2. Simplify either fraction and see if they are equal

Example: 10/16 = 30/48

10/16 = 5/8
30/48 = 15/24 = 5/8

So, 10/16 = 30/48


How do I set up a proportion with a WORD PROBLEM?

Example:
12 math problems in 45 min. How long does it take to do 20 math problems?

12 problems/45 min = 20 problems/x min

1. Cross multiply: 12 x x = 45 x 20

2. 12x = 900

3. Divide both sides by 12.

4. x = 75 min

CHECK YOUR WORK:

Plug in 75 into x. Are the ratios equal?


Try one on your own:

12 copies cost $0.66. Melissa needs 56 copies. How much should they cost?

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1. Set up the proportion:

12 copies/$0.66 = 56 copies/x

2. Cross multiply: 12 x x = 0.66 x 56

12x = 36.96

3. Divide both sides by 12.

4. x = $3.08

Did you get it right? Check your work!