The LessonAlgebraic fractions can be simplified (or reduced). Imagine you wanted to simplify ab⁄bc.
How to Simplify Algebraic FractionsTo simplify algebraic fractions, find any numbers, letters or brackets that appear on both the top and bottom of the fraction. In our example, b appears on the top and bottom: Cancel out the letter (b) that appears on the top and bottom of the algebraic fraction: ab⁄bc is simplified to a⁄c.
A Real Example of How to Simplify Algebraic FractionsIn the example above, b was the greatest common factor of the top and bottom of the fraction, so it could be cancelled. To simplify algebraic fractions, cancel out the greatest common factor of the numerator and denominator.
QuestionSimplify the algebraic fraction below.
Find the top of the fraction (called the numerator). In our example, the numerator is 4x2y.
Find the bottom of the fraction (called the denominator). In our example, the numerator is 2xz.
Find the greatest common factor of the numerator (4x2y) and denominator (2xz). List the factors of the numerator and denominator and look at the letters and numbers that are common to both lists. The greatest common factor of the numerator and denominator is 2x. Read more about how to find the greatest common factor in algebra
Divide the numerator (4x2y) by the greatest common factor (2x).
4x2y ÷ 2x = 2xyThe numerator of the answer is 2xy.
Divide the denominator (2xz) by the greatest common factor (2x).
4x2y ÷ 2x = 2xyThe denominator of the answer is z.