Simplifying fractions

Simplifying fractions

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Tutor: Toby


Simplifying fractions

In a nutshell

To simplify a fraction, you reduce the fraction to its lowest form.  The lowest form of a fraction occurs when the numerator (top number) and denominator (bottom number) have no common factors except 11​. 

Example 1

Below are some examples of fractions in their lowest form.

13,29,1320\frac{1}{3}, \frac{2}{9}, \frac{13}{20}​​

Simplifying fractions

The quickest way to simplify a fraction is to divide by the highest common factor (HCF). The highest common factor is the largest factor that the numerator and denominator have in common.


Determine the HCF of the numerator and the denominator.
Divide both the numerator and the denominator by the HCF.  The resulting fraction is in its simplest form.

Example 2

Give the fraction 1220\frac{12}{20}​ in its simplest form.

List the factors of the numerator and the denominator:

Numerator: 1,2,3,4,6,121, 2, 3, 4, 6, 12​​

Denominator: 1,2,4,5,10,201, 2, 4, 5, 10, 20​​

Identify the largest number that appears on both lists:


Divide the numerator and denominator by the HCF:

12÷420÷4=35\frac{12\div4}{20\div4}= \underline{\frac{3}{5}}​​

Tip: If the numerator and denominator are even, you can always divide by 22.

Expanding fractions

To add, subtract or compare fractions the denominators need to be the same. 


Identify the multiplier needed to give both fractions a common denominator.
Multiply the numerator and denominator by the answer found in Step 1.

Example 3

Which fraction is greater, 34\frac{3}{4}​ or 78\frac{7}{8}​?

Identify the multiplier needed to give each fraction a common denominator:

4×2=84\times2 = 8​​

Multiply the numerator and denominator by the multiplier:

3×24×2=68\frac{3\times2}{4\times2} = \frac{6}{8}​​

Compare the two fractions:

68<78\frac{6}{8}<\frac{7}{8}​ therefore 34<78\underline{\frac{3}{4}<\frac{7}{8}}

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FAQs - Frequently Asked Questions

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