I just worked this out and this is what I would teach my dd:-
58/200 in its simplest form is 29/100
numerator x100 divided by denominator.
29 x100 =2900
divide by 100=29
I dont know if this is the simplest way but works for us.
In my experience the biggest mistake people make with percentages is that they make them seem more complicated than they need to.
Parents, teachers and even a few posters on here (
) all seem to be guilty of this.
A percentage is just a hundredth. That's all anyone needs to know or understand. After that its just basic multiplication or division.
Take the above example. I would have started off in exactly the same way.
58/200 = 29/100
And then...nothing. That's all you need to do. 29/100 is 29 hundredths is 29%. Simple!
All this stuff about multiplying the numerator by 100 and dividing by the demoninator will probably just confuse the child unnecessarily. (Well it confuses me because I always forget which is which!
Hopefully anyone taking the 11plus should be able to divide a number by 100 and be comfortable with the idea of a hundredth both as a fraction and as a decimal (i.e. 1/100 and 0.01). If not then they need to first understand this. After that its easy.
So for example, what's 37% of 494?
Well hopefully every child should be able to work out that 1% of 494 is 494/100 = 4.94. So 37% of 494 is just 37 lots of 4.94.
i.e. 37 x 4.94 = 182.78
Obviously its a bit easier with a calculator but its still a straight froward multiplication on paper so long as they can handle decimals.
Similarly if you need to find what percentage "a" is of "b" then you just divide a by b.
e.g. what percentage is 68 of 235?
68/235 = 0.28936.
If the child is familiar with decimal placements (tenths, hundreths, thousandths etc) they should be able to see that 0.28936 is 28.936 hundredths, i.e. 28.936%. There isn't really any need to multiply anything by 100 although they can if they want to I suppose.
I've deliberately used difficult random numbers in the examples above just to show that its straightforward even with those (so long as you have a calculator). But in the 11plus they don't get a calculator so the numbers in the questions should be more easy to calculate mentally.
Its probably also worth them remembering a few standard percentages as fractions which might help them be a bit quicker with some of the questions.
10% = 1/10
20% = 1/5
25% = 1/4
50% = 1/2
75% = 3/4