### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

When dealing with fractions that have the same denominators, addition and subtraction are straightforward. For addition, simply add the numerators, while the denominator remains the same. For subtraction, subtract the second numerator from the first, and again, the denominator remains the same.

## Example: Same Denominators

Addition: Subtraction: If the fractions have different denominators, find a common denominator before adding or subtracting. To do this, multiply the numerators and denominators by appropriate numbers to make the denominators equal.

## Example: Different Denominators

1. Convert to , making the denominator equal to 12. Now, .

So, , which simplifies to or .

2. Convert and to and , respectively. This yields and .

Now, perform the subtraction: .

## More Challenging Examples

### Example 1

Find .

First, find the least common multiple (LCM) of the denominators and :

LCM .

Now, rewrite the fractions with the denominator :   Therefore, .

### Example 2

Find , giving your answer in its simplest form.

First, find the least common multiple (LCM) of the denominators and :

LCM .

Now, rewrite the fractions with the denominator :   So, .

Since is a common factor of both the numerator and the denominator , you can simplify the fraction by dividing both the numerator and the denominator by : Since is a prime number, is the simplest form.