Adding and Subtracting Fractions
Grade 3The rule you cannot skip
You can only add or subtract fractions when the bottom numbers (denominators) are the same. If the denominators differ, you must find a common denominator first — a number that both denominators divide into.
The easiest common denominator to find is simply the product of the two denominators. It's not always the smallest, but it always works.
Adding fractions — step by step
Once you have a common denominator, scale each fraction up so both share it, then add the numerators. The denominator stays the same.
Mixed numbers — convert first
A mixed number like 2¹⁄₃ combines a whole number and a fraction. Before adding or subtracting, convert every mixed number into an improper fraction (where the numerator is larger than the denominator).
To convert: multiply the whole number by the denominator, add the numerator, keep the denominator. So 2¹⁄₃ = (2 × 3 + 1)/3 = ⁷⁄₃.
Try this one
Work out \ \( \dfrac{3}{4} + \dfrac{1}{6} \).
Give your answer as a fraction in its simplest form.
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This uses the skill of adding fractions with different denominators.
Ask yourself: 'What is the lowest common multiple of the two denominators?' Try converting both fractions so they share the same denominator before adding the numerators. For example, \( \frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} \).
