Mathematics is essential to daily life, although some people get intimidated by fundamental concepts and basic operations. One of the concepts that can confuse students is simplifying fractions. Here are some techniques and operations that you should be familiar with when you’re tasked to simplify numbers expressed in fraction form.

Why Simplify Fractions?

A fraction is a number that signifies a part of a whole. Fractions are technically division operations, with two numbers representing the part of the whole that the fraction represents. A fraction has two parts:

• The numerator represents the part taken from the whole.
• The denominator is the integer that represents the whole.

While it is possible to work with fractions that are expressed in large numbers, it’s best to express a fraction in its simplest terms to speed up calculations.

Reduce the Fraction

One way to reduce a fraction is to divide the numerator and the denominator by the least common multiple (LCM). The LCM is the smallest number that acts as a divisor between two numbers. Here’s an example for a given fraction 9/27:

• List the multiples of 9 and 27. The number 9 is 3 x 3 x 3, and 27 is 9 x 3.
• The least common multiple is 3.
• Divide both 9 by 3 until you can no longer divide the numerator by the multiplier, and come out with the product 1 (9 ÷ 3 = 3, 3 ÷ 3 = 1).
• Divide 27 by 3 until you arrive at the lowest possible product not equal to or lower than the numerator (27 ÷ 3 = 9, 9 ÷ 3 = 3).
• The value of the reduced fraction is 1/3.

Find the Greatest Common Factor

Another way to simplify fractions is to find the greatest common factor (GCF). All numbers are made up of factors, and the GCF is the largest factor shared by both the numerator and the denominator. Here’s an example for a given fraction 6/18:

• List the factors of 6 (1, 2, 3, and 6).
• List the factors of 18 (1, 2, 3, 6, 9, and 18).
• Note the common factors of both the numerator and the denominator (1, 2, 3, and 6).
• Remember that the GCF is the largest factor; the GCF of 6 and 18 is 6.
• Divide the numerator by 6 to get the product 1.
• Divide the denominator by 6 to get the product 3.
• The value of the simplified fraction is 1/3.

Many mathematical operations may tempt you to break out a calculator or to find a suitable program on the Internet. With these tips, all you need is an alert mind, a pen, and a piece of paper to simplify complex fractions.