Primary 4 · Mathematics

P4 fractions

One error costs most of the marks here: adding the bottoms of two fractions as well as the tops. Here is why 1/2 + 1/3 is not 2/5, and how to spot it at the kitchen table.

Level
P4
Usually taught
Term 2
Covers
3 concepts

What changes at P4

In Primary 4, your child adds and subtracts fractions, meets mixed numbers and improper fractions, and finds a fraction of a quantity. Adding two fractions with different bottoms is the part that trips most children up.

The rule that carries the marks: you can only add fractions once the pieces are the same size. The bottom number names the size of the piece, so you cannot add the bottoms, you make them match first, then add the tops.

The sentence that costs the mark

Work out 12+13\frac{1}{2} + \frac{1}{3}.

What the working usually does

add across12+13\frac{1}{2}+\frac{1}{3}=25\frac{2}{5}

Adds the tops and the bottoms: 1 + 1 over 2 + 3. It lands on a tidy fraction, so the working looks finished.

What the question asked

same size12+13\frac{1}{2}+\frac{1}{3}=56\frac{5}{6}

Makes the pieces the same size first, sixths, then adds only the tops: 3/6 + 2/6 = 5/6.

2/5 looks like a real fraction, and adding straight across is exactly how whole numbers work, so nothing flags as careless. But 2/5 is smaller than 1/2, and you cannot add something to a half and end up below it. The pieces have to match in size before they add.

Cut both into sixths so the pieces match. 1/2 is 3/6 (indigo), 1/3 is 2/6 (violet), and they add to 5/6.

The same question, worked properly

  1. The pieces are different sizes

    halves and thirds do not match

    You cannot add halves and thirds as they are, because the pieces are different sizes. The first job is to make them the same size.

  2. Make them the same size

    12=36\frac{1}{2}=\frac{3}{6}, 13=26\frac{1}{3}=\frac{2}{6}

    This is the step that fails. Sixths fit both: 1/2 becomes 3/6, and 1/3 becomes 2/6. Skipping this and adding straight across is exactly what gives the wrong 2/5.

  3. Add the tops only

    36+26=56\frac{3}{6}+\frac{2}{6}=\frac{5}{6}

    Now the pieces match, so add only the top numbers and keep the sixths: 3 + 2 = 5, giving 5/6. A quick check: 5/6 is more than a half, and 2/5 would be less, which is impossible.

How can you tell it has clicked?

Write 1/2 + 1/3 and ask for the answer. If they stop to make the bottoms match before adding, they have understood it. If they write 2/5 straight away, that is the exact slip.

The sense-check catches it every time: is the answer bigger than the half you started with? 5/6 is, 2/5 is not. A child who checks that rarely leaves 2/5 standing.

One thing to try tonight

Cut one slice of bread into halves and another into thirds. A half and a third do not stack into a neat piece until you cut both into the same smaller size, sixths. Then they add.

Ask why "two out of five" cannot be right when you started with a whole half. Seeing that the answer must be bigger than 1/2 is the check that makes the mistake obvious.

What your child will meet in this topic

  • Mixed Numbers
  • Improper Fractions
  • Fraction of a Number

Most Singapore schools introduce this in Term 2, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Adding unlike fractions is the groundwork for P5, where fractions are multiplied, divided and tracked through several steps, and for the common denominators that ratio and percentage lean on. The "same size first" habit runs through all of it.

A child who always matches the pieces before adding tends to stay accurate when the fractions get heavier in P5 and P6, where a straight-across slip costs a whole answer.

The methods your child will use here

Each one is the same method wherever it turns up, so it is worth learning once.

The same topic in other years

It comes back each year and gets harder, so it helps to see what came before and what is coming.

More in Primary 4

Other topics in the same year, so you can see what sits either side of this one.

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

Try it free