3 mistakes learners make with fractions of an amount, each one named and explained.
Divide by the bottom number to find one part, then multiply by the top number to find how many parts you want.
A fraction of an amount is worked out for the wrong number of parts.
The two numbers in the fraction are both used and it is easy to use them the wrong way round.
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.
Divide by the bottom number first and write that down. Then multiply by the top.
2/5 of 45 is answered as 9, which is one fifth rather than two fifths.
Dividing by 5 is the hard half of the work and it was done correctly, so it feels finished.
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.
Divide by the bottom, then multiply by the top. Two steps, every time.
2/5 of 45 is answered as 90, which is 45 multiplied by 2.
The word of does mean multiply, and only half of the fraction made it into the calculation.
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.
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.