GCSE Maths Practice: fractions

Understanding Fraction Subtraction

Subtracting fractions is a core skill in the GCSE Maths Number topic. To subtract correctly, both fractions must refer to the same-sized parts of a whole. This means they need a common denominator. Once denominators match, you simply subtract the numerators while keeping the denominator unchanged. The key is to ensure both fractions represent quantities measured in equal parts before combining or comparing them.

Step-by-Step Process

1. Find the least common denominator (LCD) – This is the smallest number that both denominators divide into exactly.
2. Convert each fraction so that they share the same denominator by multiplying numerator and denominator by the same number.
3. Subtract the numerators – only the top numbers change.
4. Keep the denominator the same because the size of the parts hasn’t changed.
5. Simplify the result if possible.

Worked Examples

• Example 1: \(\frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4}\).
• Example 2: \(\frac{7}{12} - \frac{1}{3}\). LCD = 12 → \(\frac{1}{3}=\frac{4}{12}\). So \(\frac{7}{12}-\frac{4}{12}=\frac{3}{12}=\frac{1}{4}\).
• Example 3: \(\frac{9}{10} - \frac{1}{2}\). LCD = 10 → \(\frac{1}{2}=\frac{5}{10}\). Then \(\frac{9}{10}-\frac{5}{10}=\frac{4}{10}=\frac{2}{5}\).
• Example 4: \(\frac{7}{10} - \frac{2}{5}\). LCD = 10 → \(\frac{2}{5}=\frac{4}{10}\). Therefore, \(\frac{7}{10}-\frac{4}{10}=\frac{3}{10}\).

Common Mistakes to Avoid

• Subtracting denominators: The denominator never changes during addition or subtraction.
• Forgetting to find a common denominator: You can’t subtract parts of different sizes (like tenths and fifths) directly.
• Leaving the answer unsimplified: Always reduce to the simplest form if possible, such as \(\frac{4}{10}=\frac{2}{5}\).
• Mixing up the order: \(\frac{a}{b}-\frac{c}{b}\) is not the same as \(\frac{c}{b}-\frac{a}{b}\). The order matters.

Real-Life Applications

Fraction subtraction is common in practical situations. For instance, if a recipe requires 7/10 litres of milk but you already poured 2/5 litres, how much more do you need? The answer, 3/10 litres, tells you exactly how much milk remains to be added. Similar reasoning applies in measuring fuel, budgeting, or comparing probabilities where quantities must be expressed with equal denominators before subtraction.

FAQs

Q1: What if denominators are already the same?
A1: Subtract numerators directly. For example, \(\frac{6}{7}-\frac{2}{7}=\frac{4}{7}\).

Q2: What if one denominator is a multiple of the other?
A2: Use the larger as the common denominator. For example, with 10 and 5, use 10.

Q3: Can I use cross multiplication to check my answer?
A3: Yes. Multiply each numerator by the opposite denominator to compare values or verify results, but always express the final answer with a single denominator.

Study Tip

Think of denominators as the size of slices in a pizza. You can only subtract slices of the same size. Always equalise denominators first. Practising with visual models (like shaded circles or bars) helps you remember that only numerators change when fractions are subtracted. This concept also prepares you for subtracting algebraic fractions later in GCSE Maths.

By mastering fraction subtraction, you build a strong base for tackling equations, ratios, and probability questions — all essential for exam success and real-world numerical fluency.