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Solving Proportions

A proportion is a name we give to a statement where two ratios are equal.

It can be written in two ways:as two equal fractions,  








or,using a colon 






Cross products are equal


When two ratios are equal, then the cross products of the ratios are equal. Let us explain what that means.

In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.That is, for the proportion  












Here’s an example. 








The cross products are: 








Using cross product to find a missing term


We can also use cross products to find a missing term in a proportion

.Here’s an example, expressed as a word problem:


A car travels 120 miles in 3 hours (with a constant speed). How far will it take to travel 200 miles? 







 Cross-multiplying we get: 

















Did you see what we did there? 

We are trying to get our unknown number, d, on the left side of the equation, all by itself. Since d is multiplied by 120, we can use the "inverse" of multiplying, which is dividing, to get rid of the 120.

To keep the proportion, we also need to divide on the right hand side – by 120. Both sides are divided by 120.

From there on the equation is easy to solve.


We have a number of grade 6 proportions worksheets in our free worksheet centre for you to practice.