GCSE Maths Practice: fractions

Question 8 of 12

This question checks your ability to subtract fractions with the same denominator. When denominators are equal, you only subtract the numerators and keep the denominator unchanged. Simplify if possible.

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\( \text{Calculate }\frac{4}{7}-\frac{2}{7}. \)

Choose one option:

If denominators are the same, subtract the numerators only and keep the denominator. Simplify if possible to ensure your answer is in lowest terms.

Understanding Subtraction of Fractions

Subtracting fractions is a basic but essential skill in GCSE Maths. When two fractions have the same denominator, subtraction becomes very straightforward. The denominator tells you the size of each part, and because the parts are already equal, you only need to subtract the numerators (the number of parts). The denominator stays exactly the same.

Step-by-Step Method

  1. Check denominators: Ensure both fractions have the same denominator. If they do not, find the least common denominator (LCD) first.
  2. Subtract numerators: Subtract the top numbers only, since both fractions describe parts of the same size.
  3. Keep the denominator: Do not change it. The denominator represents the equal divisions of the whole.
  4. Simplify if needed: Reduce the fraction to its lowest terms by dividing numerator and denominator by their greatest common divisor (GCD).

For this question, the denominators are already equal (both 7). Subtracting gives \(4-2=2\), so the result is \(\frac{2}{7}\). Because 2 and 7 share no common factors other than 1, this is already simplified.

Worked Examples

  • Example 1: \(\frac{9}{10}-\frac{3}{10}=\frac{6}{10}=\frac{3}{5}\).
  • Example 2: \(\frac{7}{12}-\frac{5}{12}=\frac{2}{12}=\frac{1}{6}\).
  • Example 3: \(\frac{5}{7}-\frac{2}{7}=\frac{3}{7}\) (already simplified).
  • Example 4 (different denominators): \(\frac{5}{8}-\frac{1}{4}\). LCD = 8 → \(\frac{1}{4}=\frac{2}{8}\). Then \(\frac{5}{8}-\frac{2}{8}=\frac{3}{8}\).

Common Mistakes to Avoid

  • Subtracting denominators: \(\frac{4}{7}-\frac{2}{7}\neq\frac{2}{0}\)! Denominators never change when they’re already equal.
  • Forgetting to simplify: Always check if the result can be reduced to lowest terms.
  • Mixing up the order: Remember that subtraction is not commutative. \(\frac{2}{7}-\frac{4}{7}\) would give \(-\frac{2}{7}\), not the same as \(\frac{2}{7}\).
  • Trying to find LCD unnecessarily: If denominators already match, you can subtract immediately.

Real-Life Applications

Subtraction of fractions appears in many everyday tasks. Imagine a 4/7-metre ribbon, and you cut away 2/7 metres. The remaining length is \(\frac{2}{7}\) metres. In recipes, you might remove 2/7 of an ingredient or measure remaining fuel as a fraction of a tank. Understanding how to subtract equal-denominator fractions quickly saves time and helps prevent errors in real calculations.

FAQs

Q1: What if denominators are not the same?
A1: Find the least common denominator first, then rewrite each fraction before subtracting.

Q2: What if the result is negative?
A2: A negative fraction means the first value was smaller than the second. For example, \(\frac{2}{5}-\frac{3}{5}=-\frac{1}{5}\).

Q3: Can we convert improper results to mixed numbers?
A3: Yes, for example \(\frac{11}{8}=1\tfrac{3}{8}\). However, for this question the answer is a proper fraction.

Study Tip

When denominators match, subtraction is simply a matter of working with numerators. Say aloud the pattern: “same bottom, subtract the top.” Practising with visual models like fraction bars or circles helps reinforce this rule. Building fluency here supports future topics such as algebraic fractions, percentages, and ratio calculations in GCSE Maths.

Understanding and mastering same-denominator fraction subtraction is a stepping-stone toward confident arithmetic and advanced problem-solving.