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
In a sale, a television is reduced by 18% to £516.
(a) Work out the original price of the television. [2]
After the sale, the price is increased by 18% from the sale price.
(b) Explain why the price after the increase is not the same as the original price, and find the new price. [2]
Part (a) is a reverse percentage; part (b) explores why percentage changes are not symmetrical.
Ask yourself: 'What percentage of the original price is £516, and what do I divide by to reverse a percentage reduction?' Think about whether 18% of £516 is the same value as 18% of the original price.
