Maths

Common mistakes in fractions of an amount

3 mistakes learners make with fractions of an amount, each one named and explained.

All common mistakes

Divide by the bottom number to find one part, then multiply by the top number to find how many parts you want.

A different fraction of the amount found

What it looks like

A fraction of an amount is worked out for the wrong number of parts.

Why it happens

The two numbers in the fraction are both used and it is easy to use them the wrong way round.

A worked example

Question. 2/5 of 45

A common answer. 15, which is one third

The answer. 18

Why. 45 divided by 5 is 9, and two of those is 18.

Put the two side by side

One fifth of 45 is 9.
Two fifths is 18.

Divide by the bottom number first and write that down. Then multiply by the top.

Finding one part and stopping

What it looks like

2/5 of 45 is answered as 9, which is one fifth rather than two fifths.

Why it happens

Dividing by 5 is the hard half of the work and it was done correctly, so it feels finished.

A worked example

Question. 2/5 of 45

A common answer. 9, which is one fifth

The answer. 18

Why. One fifth is 9, and the question asks for two of them.

Put the two side by side

1/5 of 45 = 9.
2/5 of 45 = 18, which is 9 twice.

Divide by the bottom, then multiply by the top. Two steps, every time.

Multiplying by the top and forgetting the bottom

What it looks like

2/5 of 45 is answered as 90, which is 45 multiplied by 2.

Why it happens

The word of does mean multiply, and only half of the fraction made it into the calculation.

A worked example

Question. 2/5 of 45

A common answer. 90, which is more than you started with

The answer. 18

Why. Two fifths of something has to be smaller than the something, so 90 cannot be right before you check anything else.

Put the two side by side

45 x 2 = 90, larger.
45 x 2/5 = 18, smaller.

Sense check first. A fraction below 1 always makes the amount smaller.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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