GCSE Maths Practice: fractions

Question 5 of 12

This question tests your ability to add fractions with the same denominator — one of the most fundamental arithmetic skills used in GCSE Maths and everyday life.

‹ ›

\( \text{Calculate }\frac{2}{5}+\frac{3}{5}. \)

Choose one option:

When denominators match, add the numerators and keep the denominator. Simplify your answer if possible or express it as a whole number if it equals one.

Understanding Addition of Fractions

When adding fractions, the most important rule is that the denominators must be the same. The denominator tells you the size of each part, so fractions can only be added or subtracted when the parts are of equal size. Once denominators match, you simply add the numerators — the number of parts — and keep the denominator the same. This makes adding same-denominator fractions one of the easiest and most useful fraction operations in GCSE Maths.

Step-by-Step Method

  1. Check denominators: Ensure both fractions have the same denominator. If they don’t, find the least common denominator (LCD).
  2. Add the numerators: Add only the top numbers; the denominator stays the same.
  3. Simplify if needed: Divide numerator and denominator by any common factors, or convert to a whole or mixed number if appropriate.

For this question, \(\frac{2}{5}+\frac{3}{5}=\frac{5}{5}=1\). This result represents one whole — five parts out of five.

Worked Examples

  • Example 1: \(\frac{1}{8}+\frac{3}{8}=\frac{4}{8}=\frac{1}{2}\).
  • Example 2: \(\frac{5}{12}+\frac{4}{12}=\frac{9}{12}=\frac{3}{4}\).
  • Example 3: \(\frac{7}{10}+\frac{2}{10}=\frac{9}{10}\) (already simplified).
  • Example 4: \(\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\).

Visual Explanation

Imagine a chocolate bar divided into 5 equal pieces. Having 2 pieces means you have \(\frac{2}{5}\). If you get 3 more pieces, you now have \(\frac{3}{5}\) added on. Altogether, you have all 5 out of 5 pieces, which is one complete chocolate bar — \(1\).

Common Mistakes to Avoid

  • Adding denominators: \(\frac{2}{5}+\frac{3}{5}\neq\frac{5}{10}\). The denominator does not change.
  • Mixing different denominators: You cannot directly add fractions like \(\frac{1}{2}+\frac{1}{3}\) without first finding a common denominator.
  • Forgetting to simplify: Always check if the result can be reduced or converted to a whole number or mixed number.
  • Swapping numerator and denominator: This changes the value entirely; always keep denominators fixed when adding.

Real-Life Applications

Adding fractions appears in daily life — cooking, budgeting, and measurement. If a recipe uses \(\frac{2}{5}\) of a litre of milk and you add another \(\frac{3}{5}\), you now have one whole litre. The same principle applies when combining lengths, times, or probabilities. Recognising when parts add to form a whole helps in estimating, measuring, and problem-solving.

FAQs

Q1: What if denominators are different?
A1: Find the least common denominator first. For example, \(\frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}\).

Q2: What if the answer is improper, like \(\frac{9}{5}\)?
A2: Convert it to a mixed number: \(1\tfrac{4}{5}\).

Q3: Why can we keep the denominator the same?
A3: Because both fractions represent parts of the same-sized whole, so the size of the parts (denominator) doesn’t change.

Study Tip

Always visualise fractions as pieces of a whole. If denominators are equal, just count the pieces on top. Say aloud: “same bottom, add the top.” Practising this pattern helps reinforce mental fluency with fraction arithmetic — an essential foundation for algebraic fractions, ratios, and percentages in GCSE Maths.

Understanding how equal-denominator fractions combine into a whole or larger fraction helps build confidence and accuracy for all higher-level number operations.