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Solving a Proportion

5   15   
- = --
x   12

This time the variable is in a different position, but the same steps are used to solve it. Make an equation with the multiplication of the means on the left and the multiplication of the extremes on the right. Then solve it like we did below.

x * 15 = 5 * 12

15x = 60
---   -- Divide each side by 15.
15    15

x = 4
Solving a proportion without a variable:

If you encounter a proportion that has one of its means or extremes left blank, or uses another symbol such as a question mark you can treat it as if it was a variable. Or you can replace the question mark or blank space with a variable such as x. See the example below.

9   90
- = --
5   ?

Becomes:

9   90
- = --
5   x

5 * 90 = 9 * x

450 = 9x
---   --
9     9

50 = x
50 = ?
Solving a proportion with two variables:

A proportion with two of the same variable, can also be solved. Take the problem below for example.

25   x
-- = -
x    1

x * x = 25 * 1

x2 = 25

When you encounter a situation like the above, a variable squared equals a number, you can do one of two things.

1. Find what number squared is equal to 25. Use our perfect squares chart for reference.

(or)

2. Change the problem to x = the squareroot of 25. The resulting number from either method will be equal to x and will be the answer.

When a whole number is in place of a fraction:

Take a look at the problem below, notice it doesn't have a fraction on one side.

x
-- = 3
12

To solve this proportion, you have to change the whole number to a fraction, just as you did in math class, by putting it over a 1. The problem above would turn into the following:

x    3
-- = -
12   1

It could then be solved like any other proportion.

More resources:

Proceed to the next page to find more proportion resources.


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