How to Simplify Fractions - Easy Steps for Even the Most Mathematically Challenged

For some people math comes easily, almost as a native language. For the rest of us, we have to study it regularly just to remember the basics. Fractions can be confusing and extremely complicated for those not mathematically inclined. However, the reason many of us struggle with fractions can also be that we've never fully comprehended the basics of fractions. We've never fully figured out the significance of the fraction, and how to manipulate it.

What is a Fraction?

Starting from the beginning, we'll break down the parts of a fraction. In the fraction ¾ the 3 is called the numerator, and the 4 is called the denominator. The meaning of a fraction is to explain how many parts of the whole are present. For the fraction ¾, we can imagine a pie that has been cut into four pieces. Three of those pieces are still present, one is missing. This means that we have ¾ (three fourths or three quarters) of the pie left.

Simplifying Fractions

In many algebraic problems you'll be asked to simplify a fraction in order to solve the problem. Simplifying a fraction is also known as "writing the faction in lowest terms." Simplifying a fraction involves creating a fraction in which the numerator and denominator have no factors in common, save for 1.

For example:

Let's take the fraction 42/49 and simplify it.

In order to simplify a fraction we first find the numerator and denominator as products of prime numbers. Remember that prime numbers are numbers that factor only to 1 and itself, such as 2 and 3.

42 can be created by any of these following sets: 2 x 21, 7 x 6, and 3 x 14

Let's further break these down...

2 x 21

= 2 x 3 x 7

Now, let's break down 49: 7 x 7

In terms of a fraction these primes are 2 x 3 x 7 / 7 x 7

Now, cross out like terms. This crosses out the one seven on the top, and one seven from the bottom leaving 2 x 3 / 7 = 6/7.

So the simplified 42/49 is 6/7.

Application

So, now that you know how to simplify fractions, you need to know how to apply the knowledge. In a multiplication problem such as: ½ x ¾ you'll have to multiply the fractions, and then write them in lowest terms. Remember that this means you have to simplify the answer.

The rule for multiplication of fractions states that Z/Y x A/B = Z x A / Y x B so our problem looks like this: 1 x 3 / 2 x 4 = 3/8

Factor this = 1 x 3 / 2 x 2 x 2

Since there are no common factors here, we can't simplify past 3/8, so the answer is 3/8.

Another:

2/3 x 3/4

2x 3 / 3 x 4

6/12

Factor: 6 = 2 x 3

12 = 2 x 2 x 3

Now cross out the common factors (the two on the top and the two on the bottom, and the three on the top and the three on the bottom). This leaves a one on the top (since there is always one on the top even if both factors have been crossed out), and 2 on the bottom. Thus, the answer to 2/3 x 3/4 = 1/2.