Skip to main content
Search IntMath

5. Equivalent Fractions

Recall the following fraction properties:


This is true because we have multiplied both the top (numerator) and the bottom (denominator) by `5`. We say `3/4` and `15/20` are equivalent fractions.


This is true because we have divided both the numerator and the denominator by `7`. We say `7/21` and `1/3` are equivalent fractions.

We now apply these ideas to fractions involving algebraic expressions.

Example 1

Divide the numerator and the denominator of `(6a^3b^2)/(9a^5b^4)` by 3ab2.



NOTE: This answer is not in simplest form. We could divide top and bottom again by a2, to give `2/(3a^2b^2)`

Know when to stop!

The following expression cannot be simplified further because there is an addition sign in the numerator and a subtraction in the denominator:


We cannot cancel the x and the x2.

However, if the terms in the numerator and denominator are multiplied, then we can do further simplifying like this:


Example 2

Reduce to simplest form:



We start by factoring the numerator and then observe we can divide top and bottom by one of the factors:


Example 3

Reduce to simplest form:




(1) `(2a^2xy)/(6axyz^2)`

(2) `(t-a)/(t^2-a^2)`

(3) `(x^2-y^2)/(x^2+y^2)`

(4) `(x^2-y^2)/(y-x)`

Problem Solver

AI Math Calculator Reviews

This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of GPT large language models to parse and generate natural language. This creates math problem solver thats more accurate than ChatGPT, more flexible than a calculator, and faster answers than a human tutor. Learn More.

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.