How to Cross Multiply

How to Cross Multiply: Method 1

Cross Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and which is smaller. Cross multiply them, the side with the larger product corresponds to the large fraction.
In particular, if the cross multiplication products are the same then the fraction is the same.

How to Cross Multiply: Method 2

In this section, we look at the useful procedure of cross multiplication.

Many procedures with two fractions utilize the operation of cross-multiplication as shown below.

Take the denominators and multiply them diagonally across.
What we get are two numbers.

Make sure that the denominators cross over and up so the numerators stay put. Do not cross downward as shown here.

How to Cross Multiply – Method 3

Here are some operations where we may cross multiply.

Rephrasing Fractional Ratios

If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional fatio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers.

Example A

Rewrite a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour into ratio of whole numbers. 
                           3
Write 3/4 cup of sugar as ---S and 2/3 cup of                            4
          2
flour as ---F.
          3      
                   3      2
We have the ratio ---S : ---F cross multiply 
                   4      3
we've 9S : 8F. 
Hence in integers, the ratio is 9 : 8 for sugar : flour. 
Remark: A ratio such as 8 : 4 should be simplified to 2 : 1.