Year 6

Fractions

By Year 6, children draw together everything they have learned about fractions and start handling any fractions at all, not just ones with friendly, related denominators. They simplify a fraction to its lowest terms, and they compare and order a mixed bunch by first rewriting them over a common denominator, so the pieces are the same size and easy to judge.

Practise Fractions

Have a guess, even if you're not sure. Get one wrong and we'll show you why, so every miss is a chance to learn.

Timed practice

The same practice, just with a gentle clock. Pick a length and see how many you can answer.

Good to know

The fraction wall

Every bar is the same whole, split into more and more equal pieces, so equal fractions line up one above another and you can see when one simplifies to another.

Spot the matching pieces
One whole
Halves
Thirds
Quarters
Fifths
Sixths
Eighths
Tenths

For grown-ups

Year 6 fraction work grows into full calculation: adding and subtracting fractions and mixed numbers with different denominators, multiplying a pair of proper fractions, dividing a proper fraction by a whole number, and finding a fraction of a quantity, often with two or three of these steps woven into one problem. Underneath it all sits the idea that a fraction is really a division, with the denominator naming the size of each piece while the numerator counts how many. That understanding is exactly what secondary maths leans on when fractions turn into algebra, ratio and proportion, so the time spent making it solid now pays off for years.

What is in this topic

How to help at home

By Year 6, fractions pull lots of skills together, so keeping the fraction wall in view helps your child see why each step works. Short, frequent sessions where they talk through what they are doing beat one long sit-down.

  • Simplify by dividing the top and bottom by the same number, and keep going until you cannot. For 6/8, both divide by 2 to give 3/4, and on the wall 6/8 and 3/4 sit at exactly the same length.
  • To add or subtract fractions with different denominators, rename them so the bottoms match first. For 1/2 + 1/3, turn both into sixths: 3/6 + 2/6 = 5/6.
  • To find a fraction of an amount, divide by the bottom, then times by the top. For 3/4 of 20, divide 20 by 4 to get 5, then times by 3 to get 15.
  • When multiplying two fractions, times the tops and times the bottoms, no common denominator needed. For 2/3 x 4/5, that is 2 x 4 over 3 x 5, giving 8/15.

Where children get stuck

The most common slip is adding the bottoms as well as the tops, writing 1/2 + 1/3 as 2/5. The fix is to say out loud that the bottom only names the size of the piece, so it cannot change while you add. Rename both into the same sized pieces first (sixths here), then only the tops are added: 3/6 + 2/6 = 5/6.

The other frequent wobble is muddling multiplying and dividing a fraction. Dividing a fraction by a whole number makes the pieces smaller, so 3/4 divided by 2 is 3/8, not 3/2. A quick check is to ask 'should the answer be bigger or smaller?': sharing 3/4 between 2 must give less than 3/4, which rules out the wrong answer straight away.

More Year 6 maths

Decimals and PercentagesRatio and ProportionAlgebra