Operations on fractions Revision Notes for Edexcel GCSE Maths

Operations on fractions

Fractions are numbers that represent parts of a whole. You need to be able to add, subtract, multiply and divide fractions without using a calculator.

Adding or subtracting fractions

When adding or subtracting fractions, you need to work with fractions that have the same denominator (bottom number).

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The denominator is the bottom number of a fraction that tells you how many equal parts the whole has been divided into. For fractions to be added or subtracted, they must have the same denominator.

Method for adding or subtracting fractions:

Convert to equivalent fractions - Make both fractions have the same denominator by finding a common denominator
Add or subtract the numerators - Only work with the top numbers
Keep the denominator the same - The bottom number stays unchanged

Finding a common denominator

The easiest common denominator to use is the Lowest Common Multiple (LCM) of both denominators. This gives you the smallest possible common denominator.

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Worked Example: Adding Fractions

To add $\frac{1}{2} + \frac{3}{10}$ :

Step 1: Find the LCM of 2 and 10

The LCM of 2 and 10 is 10

Step 2: Convert to equivalent fractions

$\frac{1}{2} = \frac{5}{10}$

Step 3: Add the fractions

$\frac{5}{10} + \frac{3}{10} = \frac{8}{10} = \frac{4}{5}$

Multiplying fractions

Multiplying fractions is more straightforward than adding or subtracting them. Unlike addition and subtraction, you don't need to find a common denominator.

Method for multiplying fractions:

Convert whole numbers to fractions - Write any whole numbers as fractions with denominator 1
Multiply straight across - Multiply the numerators together and multiply the denominators together

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Worked Example: Multiplying Fractions

To multiply $\frac{2}{3} \times \frac{7}{10}$ :

Step 1: Multiply numerators

$2 \times 7 = 14$

Step 2: Multiply denominators

$3 \times 10 = 30$

Step 3: Write the result

$\frac{14}{30} = \frac{7}{15}$ (simplified)

Dividing fractions

Division of fractions uses a special technique often remembered as "Keep, Change, Flip".

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The "Keep, Change, Flip" method is essential for dividing fractions. This technique transforms division into multiplication, which is much easier to calculate.

Method for dividing fractions:

Convert whole numbers to fractions - Write any whole numbers as fractions with denominator 1
Keep the first fraction - Leave the first fraction unchanged
Change division to multiplication - Replace the ÷ sign with ×
Flip the second fraction - Turn the second fraction "upside down" (find its reciprocal)
Multiply - Now multiply the fractions using the multiplication method

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Worked Example: Dividing Fractions

To divide $\frac{2}{5} \div \frac{4}{3}$ :

Step 1: Keep the first fraction

Keep $\frac{2}{5}$

Step 2: Change ÷ to ×

$\frac{2}{5} \times$

Step 3: Flip the second fraction

$\frac{4}{3}$ becomes $\frac{3}{4}$

Step 4: Multiply

$\frac{2}{5} \times \frac{3}{4} = \frac{6}{20} = \frac{3}{10}$

Important tips

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Simplifying answers

You don't always need to simplify your final answer. Only simplify if the question specifically asks for the answer in simplest form. To simplify, divide both numerator and denominator by their highest common factor.

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Comparing fractions

You can compare fractions by converting them to equivalent fractions with the same denominator. The fraction with the larger numerator is the larger fraction when denominators are equal.

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Key Points to Remember:

Adding/subtracting fractions: Find a common denominator first, then add or subtract only the numerators
Multiplying fractions: Multiply straight across - numerators together, denominators together
Dividing fractions: Use "Keep, Change, Flip" - keep first fraction, change ÷ to ×, flip second fraction
Whole numbers: Always write whole numbers as fractions with denominator 1 when doing calculations
Simplifying: Only simplify if asked for the simplest form in the question

Operations on fractions (Edexcel GCSE Maths): Revision Notes