5 mistakes learners make with sharing in a ratio, each one named and explained.
Add the parts to find how many shares there are altogether, find what one share is worth, then take as many as you need.
18 : 24 is simplified to 2 : 3, using a divisor that does not work for both parts.
2 : 3 is the most familiar simple ratio and it looks like the kind of answer expected.
Question. 18 : 24
A common answer. 2 : 3
The answer. 3 : 4
Why. Both parts divide by 6, giving 3 : 4, and 18 does not divide by 9 to give 2.
Find the highest common factor of both numbers and divide both by it.
Sharing 15 counters in the ratio 2:3, you divide by 3 rather than by 5.
Both numbers are sitting right there in the ratio, and one of them is the one you want at the end.
Question. 15 shared in the ratio 2:3
A common answer. 15 divided by 3, then doubled, giving 10
The answer. 9
Why. There are 2 + 3 = 5 shares altogether, so one share is 3, and the blue part is three of them.
Add the parts first. That total is what you divide by, every time.
Asked for the blue counters you give the red ones, or asked for the larger share you give the smaller.
The work was done correctly and the two answers sit side by side, so the wrong one is easy to copy out.
Question. 15 in the ratio 2 red to 3 blue, how many blue
A common answer. 6, which is the red share
The answer. 9
Why. The 3 in the ratio belongs to blue, so blue gets three shares of 3.
Label each share as you work it out. Then read the question again before writing.
£60 shared in the ratio 2:3 is given as £30 each.
Sharing usually means fairly, and fairly usually means equally.
Question. £60 in the ratio 2:3
A common answer. £30 and £30
The answer. £24 and £36
Why. The ratio says the shares are not equal, and 2:3 means five parts of £12.
A ratio is an instruction to share unequally. Equal shares would need 1:1.
2 : 3 is used as the fraction two thirds of the whole amount, so £60 gives £40.
A ratio and a fraction are both two numbers with something between them, and both are about parts of a whole.
Question. Divide £60 in the ratio 2 : 3, larger share
A common answer. 60 x 2/3 = £40
The answer. £36
Why. The parts are 2 and 3 out of 5, so the larger share is three fifths.
A ratio compares the parts with each other. A fraction compares a part with the whole.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.