Cross Multiply

Simplifying equations is often the first step to solving algebra equations with fractions. There are more techniques to simplify equations, for eg. Combine Like Terms, Multiplication and Division of Terms, Removal of Brackets - Distributive Property

In this lesson, we will learn cross multiplication.

The following diagram shows some examples of cross-multiplication with variables.

 

Cross Multiplication

Cross multiplication allows you to remove denominators from fractions in an equation. Note that this technique applies only towards simplifying equations, not to simplifying expressions.

For example, if you have the equation:

then you can multiply the numerator of one fraction with the denominator of the other fraction (across the = sign) as shown:

to obtain the equation

(2 × 6) = a × 3

Example::

Simplify:

Solution:

Step 1: Cross Multiply

4 × a = 8 × 5
4a = 40

Step 2: Isolate variable a

Answer: a = 10

How to Cross Multiply Proportions?

Cross multiplying proportions is a straightforward process that is the same as cross multiplying fractions. Cross multiply by multiplying a numerator by the other side’s denominator. The following video shows some examples of cross multiplication.

Solving Proportions with Mixed Numbers
In order to make solving proportions with mixed numbers easier, we simply turn the mixed number into an improper fraction. We then solve the proportions with mixed numbers by using cross multiplication.

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