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Adding Fractions

In one line: To add fractions, make the bottom numbers the same, then add the top numbers and keep the bottom number.

Why it works

Fractions show up whenever we share or measure things: half a cup of flour plus a quarter of a cup, or one third of a race run before lunch and one quarter after. Adding fractions correctly helps children with cooking, money, time and measuring. It is also the base for later topics like decimals, percentages and algebra. A fraction has two parts. The numerator is the top number and tells you how many pieces you have. The denominator is the bottom number and tells you how many equal pieces make one whole.

Think of it like: Think of fractions as slices of cake. If you have 2 slices of a cake cut into 8 equal slices, and a friend gives you 3 more slices of the same size, you now have 5 slices out of 8, which is 5/8. You add the slices, but the slice size (the 8) stays the same. If one cake is cut into halves and another into quarters, the slices are different sizes, so you cannot just count them together. First you cut the halves into smaller pieces so every slice is a quarter. Then counting works. (Where this breaks: The cake picture breaks down when your answer is bigger than one whole, because you then need more than one cake. It also hides the fact that fractions can be parts of anything, such as a group of objects, a length or an amount of time, not just round shapes.)

Worked example

Work out 2/3 + 1/4.

  1. Check the denominators (bottom numbers): 3 and 4 are different, so the pieces are different sizes.
  2. Find a common denominator, which is a number both denominators divide into. The smallest is 12, because 3 × 4 = 12 and 12 is in both the 3 and 4 times tables.
  3. Change each fraction into an equivalent fraction (a fraction worth the same amount) with 12 at the bottom. 2/3: multiply top and bottom by 4 to get 8/12. 1/4: multiply top and bottom by 3 to get 3/12.
  4. Add the numerators (top numbers) and keep the denominator: 8/12 + 3/12 = 11/12.
  5. Check if the answer can be simplified. 11 and 12 share no factor except 1, so 11/12 is in its simplest form.

Answer: 2/3 + 1/4 = 11/12

Common mistakes

  • Adding the tops and the bottoms (for example 1/2 + 1/4 = 2/6); instead, only add the numerators once the denominators are the same.
  • Changing the denominator but forgetting to change the numerator (for example turning 2/3 into 2/12); always multiply the top and bottom by the same number.
  • Adding fractions with different denominators without changing them first; always check that the bottom numbers match before you add.
  • Leaving an answer like 6/8 or 9/7 without tidying it; simplify where you can (6/8 = 3/4) and, if asked, turn top-heavy fractions into mixed numbers (9/7 = 1 2/7).

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What is 2/7 + 3/7?

Questions parents ask

What year do kids learn adding fractions?

In the UK, children start adding fractions with the same denominator in Year 3 and move on to different denominators in Years 5 and 6. In Australia, adding fractions with the same or related denominators is taught around Years 5 and 6, with any denominators in Year 7. In the US, like denominators are taught in Grade 4 and unlike denominators in Grade 5.

How can I help my child with adding fractions at home?

Use real objects such as pizza, chocolate bars or measuring cups so your child can see that fractions are equal parts of a whole. Ask questions while cooking, like 'If we add 1/2 a cup and 1/4 of a cup, how much is that?' Short, regular practice with times tables also helps, because finding common denominators relies on them.

Why can't you just add the top and bottom numbers?

The denominator tells you the size of each piece, and adding pieces does not change their size. For example, 1/2 + 1/2 makes one whole, but adding tops and bottoms gives 2/4, which is only a half. That shows the shortcut gives the wrong answer.

Do you always need the lowest common denominator?

No, any common denominator will give a correct answer. Multiplying the two denominators together always works, but the lowest one keeps the numbers smaller and the answer easier to simplify. If you use a bigger one, just remember to simplify at the end.