EDEXCEL GCSE FOUNDATION MATHS - What is Adding Fractions

Edexcel GCSE Foundation Maths: Adding Fractions

What are fractions?

A fraction represents a part of a whole. It is written as a ratio of two numbers, the numerator and the denominator.

• Numerator: The top number tells you how many parts you have.
• Denominator: The bottom number tells you how many parts the whole is divided into.

For example, the fraction 3/4 represents 3 out of 4 equal parts of a whole.

Adding Fractions with the Same Denominator

Adding fractions with the same denominator is straightforward. Simply add the numerators and keep the same denominator.

Example:

• 1/5 + 3/5 = (1 + 3)/5 = 4/5

Explanation:

We have 1 part out of 5 and then add another 3 parts out of the same 5. This gives us a total of 4 parts out of 5.

Adding Fractions with Different Denominators

To add fractions with different denominators, we need to find a common denominator. This means finding a number that both denominators divide into.

Steps:

1. Find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators divide into.
2. Convert each fraction to an equivalent fraction with the LCM as the denominator. To do this, multiply both the numerator and denominator of each fraction by the factor that makes the denominator equal to the LCM.
3. Add the numerators and keep the common denominator.

Example:

• 1/3 + 2/5

• The LCM of 3 and 5 is 15.

• • 1/3 = (1 x 5)/(3 x 5) = 5/15
  • 2/5 = (2 x 3)/(5 x 3) = 6/15
• 5/15 + 6/15 = (5 + 6)/15 = 11/15

Explanation:

We converted both fractions to have a denominator of 15. Then, we added the numerators to get the final answer.

Simplifying Fractions

After adding fractions, it's important to simplify the answer if possible. This means reducing the fraction to its lowest terms.

Steps:

1. Find the greatest common factor (GCF) of the numerator and denominator. The GCF is the largest number that divides into both numbers.
2. Divide both the numerator and denominator by the GCF.

Example:

• 11/15

The GCF of 11 and 15 is 1. Since both numbers are already in their lowest terms, the fraction cannot be simplified further.

Summary

Adding fractions is an important skill in mathematics. By understanding the concepts of numerators, denominators, common denominators, and simplifying, you can confidently add fractions with different denominators.