Solving proportions

This lesson presents solving proportions by using cross product to find unknown terms.

Terms to know:

x : A letter used to stand for an unknown number

Unknown term: The missing or unknown number in a proportion.

We have seen in the lesson about proportions that we can use cross product to determine if the fractions are in proportions.

Therefore, you can use cross products to find an unknown term in a proportion. Here is how!

We will illustrate this with a couple of examples.

5/x = 10/16

Here, the unknown term (x) is the denominator for 5/x. In general, when a number is unknown, we use x or any other letter to represent the unknown number.

Since these two fractions are in proportions, we know that the cross product must be equal.

The cross products are 5 times 16 = 80 and

10 times x

Setting the cross product equal, we get:

10 times x = 80

If you know your multiplication table you can quickly get the answer.

If 10 times x = 80, then x should be 8 because 10 times 8 is 80.

There is a faster way to get the answer when solving proportions. Look at the fractions again:

5/x = 10/16

Notice that to get 10, 5 was multiplied by 2. By the same token, to get 16, something or a number must be multiplied by 2. What number multiplied by 2 will give you 16? No doubt it is 8!

let look at one more example: 8/10 = n/25

Doing cross products we get:

8 times 25 = 200 and