IGCSE Maths / Fractions, decimals and rounding

Adding and subtracting fractions

Edexcel International GCSE Maths (4MA1), chapter 1: Fractions, decimals and rounding, specification point 1.2f. Free lesson.

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To add or subtract fractions, first rewrite them with a common denominator, then add or subtract only the numerators. Convert mixed numbers to improper fractions before you begin to avoid borrowing.

Why the denominators must match

The denominator tells you the size of each fraction piece. You cannot count different-sized pieces together, so rewrite both fractions using the same denominator. Once the pieces are the same size, add or subtract their numerators and leave the denominator unchanged. For fractions with the same denominator: a/n + b/n = (a + b)/n. Adding the denominators is a common error. The bottom tells you the size of the pieces, so it is matched, not added.

How to find a common denominator

Choose a number that both denominators divide into. The lowest common multiple (LCM) is the smallest such number, which usually keeps the calculations simpler. When you change a denominator, multiply its numerator by the same amount so the fraction keeps its value.

Adding fractions with different denominators

For 2/3 + 1/4, twelfths work because both 3 and 4 divide into 12. Rewrite each fraction in twelfths, then count the numerators. 2/3 = 8/12 and 1/4 = 3/12. So 8/12 + 3/12 = 11/12.

Convert mixed numbers before subtracting

Convert each mixed number to an improper fraction before finding a common denominator. This avoids needing to borrow when the fractional part being subtracted is larger. 3 1/2 = 7/2 and 1 2/3 = 5/3. Sixths are a common denominator because both 2 and 3 divide into 6. 7/2 − 5/3 = 21/6 − 10/6 = 11/6 = 1 5/6.

Check your answer makes sense

Adding both the numerators and denominators gives the wrong result. For example, 1/2 + 1/3 is not 2/5. That answer is smaller than 1/2, even though something has been added. Match the denominators first, then add only the numerators. 1/2 + 1/3 = 3/6 + 2/6 = 5/6. You do not have to multiply the denominators together. For 1/6 + 1/8, 24 is the lowest common denominator, so 1/6 + 1/8 = 4/24 + 3/24.

Practise adding different denominators

For 3/4 + 2/5, twenty is the smallest number that both denominators divide into. Rewrite both fractions as twentieths before adding. 3/4 = 15/20 and 2/5 = 8/20. 15/20 + 8/20 = 23/20 = 1 3/20.

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