Solving Proportions Examples

Solve the following proportion for x using multiplication:

To get rid of those denominators, we multiply both sides of the equation by (5)(15). The 5's cancel on the left, and the 15's cancel on the right.

(15)(4) = (x)(5)

60 = 5x

Now divide 60 by the coefficient (5).

60 ÷ 5 = x

So x = 12.

Solve the following proportion for x using equivalent fractions:

Since 5 × 3 = 15, to find an equivalent ratio, all we need to do is multiply the numerator by 3.

Solve the following proportion for x using multiplication:

Kick those denominators to the curb. In other words, multiply both sides by (3)(4.5). The 3's cancel on the left, and the 4.5's cancel on the right.

(4.5)(2) = (x)(3)

9 = 3x

Now divide both sides by 3 to free up x.

9 ÷ 3 = x

x = 3

Solve the following proportion for x using equivalent fractions:

Hmm...if we multiply the denominator by 1.5, we get 3 × 1.5 = 4.5.

Nice. Now we can multiply the numerator by 1.5 as well to find the equivalent ratio.

An Alaskan wildlife preserve Ranger wants to figure out how many moose live in the preserve. To do this, she randomly catches and tags 50 moose and releases them. A few months later, she catches 75 moose and sees that 20 of them are tagged. Approximately how many moose live on the preserve?

In the caught sample of 75 moose, 20 were tagged. There are 50 tagged moose in the whole population. The ratio of tagged moose to total moose will be approximately equal, so we can set up a proportion of tagged to total moose:

Now multiply both sides by 75x.

(x)(20) = (50)(75)

20x = 3750

Finally, divide 3750 by the coefficient 20.

x = 3750 ÷ 20

x = 187.5

Since you can't have half a moose, you can round this number to 188. You can tell the Ranger that there are approximately 188 moose living on the preserve.