### GCSE Maths

Numbers
Vectors
Probability
Statistics
Algebra
Sequences

If two fractions have the same denominators, we can easily perform the addition or subtraction. For addition, simply add the numbers on top. The denominator remains the same.

#### Example

To subtract, we subtract the second number from the first. The denominator remains the same
.

#### Example

If the fractions differ in their denominators, we multiply the top and bottom by appropriate numbers to make them equal, before we add or subtract.

#### Example:

Then we convert as , multiplying the top and bottom by .
Now
Therefore
Which simplifies to or

#### Example:

Find
We convert and as and
Or and . Then we do the subtraction:

#### A much harder example is the following:

Find

We should first express the given fractions with the same denominator. To do this, we need what we call the least common multiple of the numbers and .
The lease common multiple (LCM)

First express the numbers and in their prime factorisation.

8=2\times 2\times 2
To find the LCM, choose the smallest multiple common to the numbers. Here this is
So, we can rewrite the fractions ,and with the denominator .

• and
• Therefore

#### We consider another example

So is the LCM

• Now
• and
• Hence
• Since is common from the top and the bottom , we can remove it by dividing the top and bottom by .

is the prime, so that 29/80 is the simplified form.

#### Evaluate

LCM

• and .
• Therefore
• is a prime number, so we cannot divide it anymore. is the simplest form.