GCSE Maths Practice: fractions

Question 11 of 12

This question tests your ability to simplify fractions using the greatest common divisor (GCD). Reducing \(\frac{12}{60}\) gives a cleaner, easier-to-work-with result.

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\( \text{Simplify }\frac{12}{60}. \)

Choose one option:

Find the GCD of the numerator and denominator, divide both by it once, and confirm no further simplification is possible. Re-multiply to check accuracy.

Understanding Simplifying Fractions

Simplifying fractions is a key skill in GCSE Maths that appears throughout the Number topic. To simplify a fraction means to reduce it to its lowest terms so that the numerator (top number) and the denominator (bottom number) share no common factors except 1. This keeps your answers neat and makes future calculations, such as adding or comparing fractions, far easier.

Why Simplify?

Every fraction can represent the same value in more than one way. For example, \(\frac{12}{60}\), \(\frac{2}{10}\), and \(\frac{1}{5}\) all represent the same proportion of a whole. Writing it as \(\frac{1}{5}\) is simplest and clearest. Simplifying avoids large numbers, reduces errors, and helps you instantly see relationships between quantities such as ratios, probabilities, or percentages.

Step-by-Step Method

  1. Find the GCD (Greatest Common Divisor) — the largest number that divides both numerator and denominator exactly.
  2. Divide both numbers by the GCD to remove all shared factors.
  3. Check the result — ensure no further simplification is possible.

For example, with \(\frac{12}{60}\): 12 = 22×3 and 60 = 22×3×5. Cancelling the common part 22×3 leaves 1/5. The prime-factor approach is especially useful for harder fractions or algebraic forms.

Worked Examples

  • Example 1: Simplify \(\frac{8}{12}\). GCD = 4 → \(\frac{2}{3}\).
  • Example 2: Simplify \(\frac{9}{15}\). GCD = 3 → \(\frac{3}{5}\).
  • Example 3: Simplify \(\frac{18}{24}\). GCD = 6 → \(\frac{3}{4}\).
  • Example 4: Simplify \(\frac{25}{100}\). GCD = 25 → \(\frac{1}{4}\).

Common Mistakes to Avoid

  • Dividing only one part: Reducing the numerator or denominator alone changes the value of the fraction.
  • Stopping too soon: Always check if more factors can be cancelled; \(\frac{20}{60}\) → \(\frac{10}{30}\) → \(\frac{1}{3}\).
  • Mixing up GCD and LCM: The least common multiple is used when adding fractions, not when simplifying.

Real-Life Applications

Fractions occur everywhere. In a recipe, if you use 12 g of sugar out of 60 g of total mixture, sugar makes up one fifth of the recipe. Builders use simplified ratios for materials; scientists simplify data ratios; and finance problems often require fractions reduced to simplest form before converting to percentages (\(\frac{1}{5}=20\%\)). Simplification makes these calculations intuitive and quick.

FAQs

Q1: What if both numbers are prime?
A1: Then they share no common factor other than 1, so the fraction is already simplified, e.g. \(\frac{3}{7}\).

Q2: Is there a trick to find the GCD quickly?
A2: Use divisibility rules: if both are even, divide by 2; if they end in 0 or 5, divide by 5; if the digit sum is a multiple of 3, divide by 3.

Q3: Will the exam mark me down if I forget to simplify?
A3: Yes — GCSE Maths mark schemes often require the final answer in simplest form. You could lose a method mark otherwise.

Study Tip

Think of simplification as cancelling out “matching factors.” Practice recognising number patterns — powers of 2, multiples of 5 and 10, and simple ratios like 3 : 6 = 1 : 2. Consistent practice will make it automatic and improve your fluency for later topics such as algebraic fractions and ratios.

By mastering simplification, you strengthen your foundation for percentages, proportion, and algebra — all core parts of GCSE Maths and everyday problem-solving.