Cross Products of a Proportion

The cross products of a proportion are the products ad and bc of the proportion

a / b  = c / d  

If a / b = c / d , we can show that ad = bc

Start with a / b  = c / d and then multiply both sides by bd

(a / b)bd  = (c / d)bd

(abd / b)  = (cbd / d)

(abd / b)  = (cbd / d)

b and d will be canceled 

ad  =  cb

ad  =  bc

For example, since 2 / 5 = 12 / 30, then 2 × 30 = 5 × 12

How to use the cross products of a proportion

You can use the cross products of a proportion to find 1 missing number in a proportion.

Example

A box of ice cream containing 840 grams of ice cream contains 210 grams of sugar. Find the number of grams of sugar in the recommended serving size of 100 grams.

Let x be the number of grams of sugar in 100 grams

840 / 210 = 100 / x

840x = 210 × 100

840x = 21000

x = 21000 / 840

x = 25 grams