GCSE Maths Practice: fractions

Understanding How to Add Fractions

Adding fractions is one of the key number skills in GCSE Maths. The rule is simple: fractions must have the same denominator before you can add or subtract them. The denominator tells you the size of each part, and you can only combine fractions that refer to parts of equal size. Once denominators match, you simply add the numerators (top numbers) and keep the denominator unchanged.

Step-by-Step Method

1. Find the least common denominator (LCD) – The smallest number that both denominators divide into.
2. Rewrite each fraction using the LCD by multiplying top and bottom by the same number.
3. Add the numerators and keep the denominator unchanged.
4. Simplify or convert to a mixed number if the result is improper (numerator larger than denominator).

In this question, \(\frac{5}{8}+\frac{3}{4}\): the LCD of 8 and 4 is 8, so \(\frac{3}{4}=\frac{6}{8}\). Then \(5+6=11\), giving \(\frac{11}{8}\). As a mixed number, that’s \(1\tfrac{3}{8}\).

Worked Examples

• Example 1: \(\frac{2}{3}+\frac{1}{6}\). LCD = 6 → \(\frac{2}{3}=\frac{4}{6}\). Then \(\frac{4}{6}+\frac{1}{6}=\frac{5}{6}\).
• Example 2: \(\frac{7}{10}+\frac{3}{5}\). LCD = 10 → \(\frac{3}{5}=\frac{6}{10}\). Then \(\frac{7}{10}+\frac{6}{10}=\frac{13}{10}=1\tfrac{3}{10}\).
• Example 3: \(\frac{1}{8}+\frac{3}{4}\). LCD = 8 → \(\frac{3}{4}=\frac{6}{8}\). Then \(\frac{1}{8}+\frac{6}{8}=\frac{7}{8}\).
• Example 4: \(\frac{5}{8}+\frac{3}{4}=\frac{5}{8}+\frac{6}{8}=\frac{11}{8}=1\tfrac{3}{8}\).

Common Mistakes to Avoid

• Adding denominators: \(\frac{1}{2}+\frac{1}{3}\neq\frac{2}{5}\). The denominator must represent equal parts, not the sum of denominators.
• Forgetting to find a common denominator: You can’t add fractions until the parts are the same size.
• Leaving answers unsimplified: Always check if the result can be reduced or written as a mixed number.
• Incorrect conversion: Be careful when converting one fraction — both top and bottom must be multiplied by the same factor.

Real-Life Applications

Adding fractions appears in everyday contexts such as cooking, construction, and budgeting. For example, if you pour 5/8 litres of milk into a jug and add another 3/4 litres, you’re combining unequal parts. Converting both to eighths (\(\frac{5}{8}+\frac{6}{8}\)) shows that the total is \(1\tfrac{3}{8}\) litres. This process helps in recipes, measurements, and any situation involving mixed quantities.

FAQs

Q1: What if denominators are already the same?
A1: Just add the numerators directly. For example, \(\frac{3}{8}+\frac{4}{8}=\frac{7}{8}\).

Q2: What if the result is an improper fraction?
A2: Convert it into a mixed number by dividing the numerator by the denominator. For example, \(\frac{11}{8}=1\tfrac{3}{8}\).

Q3: How do I handle three or more fractions?
A3: Find the LCD for all denominators, convert each fraction, and then add all numerators together.

Study Tip

Remember the golden rule: the denominator shows the type of slice, and the numerator shows how many you have. Only add fractions that describe the same type of slice. Practise visualising pizzas or bars divided into equal parts — this strengthens understanding and helps you avoid common mistakes in GCSE Maths fraction questions.

Fluency with adding fractions lays the foundation for algebraic fractions, ratio problems, and percentages — all essential for higher-level success.