# How To Multiply Rational Expressions (With Examples)

# What Are Rational Expressions?

In math, a rational number is one that can be expressed as a ratio, with each number being denoted as p and q respectively. Both numbers are integers, and the only condition is that q cannot be 0. Some examples of rational numbers include: ½, 2/3, 3/5, 5/8, and many others.

An algebraic equation or rational expression, on the other hand, involves the use of operational symbols as well as unknown variables. Some examples of rational expressions include 6x + 3, 5 –2x, and many more.

# Multiplying Rational Expressions

Now, let’s say we want to multiply 6y/5 by 5y/2.How do we go about accomplishing that? Before we start, let’s bring to mind how we multiply factors. To multiply 2/3 by 4/7, we multiply the numerators and the denominators with each other respectively. Simply put, this means that 2/3times 4/7 is (2 x 4)/(3 x 7). The same applies to multiplying rational expressions.

Example1: (6y/5) x (5y/2)

To solve the above, follow these simple steps below:

*Multiply the numerators, 6y and 5y.This gives you 30y 2.*

*Multiply the denominators, 5and 2. This gives you 10.*

Divide the resulting numerator by the resulting denominator and simplify it if possible. In this case, it’s possible to simplify the answer by canceling out 3. 30y 2. / 10 = 3y 2.

You have your answer – it’s that simple!

Keep in mind that not the multiplication of every rational expression will result in a straightforward answer that can be expressed without a fraction. With this in mind, let’s move on to our next example.

*Example2: 2y/3 x 3y/5*

Let’s get started with solving the above rational expression:

*2y x 3y = 6y 2.*

*3 x 5 = 15*

*Your answer is 6y 2 / 15. Because there’s no room to simplify the answer further, that’s your final answer.*

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