Percentages.

[adhdad]

First of all I would like to say a big hi to ever1 on here. Ive read many topics on this site and have found them to be of great interest. Anyway to my question as the title says its percentages. My ds will be hopefully sitting the birmingham based 11 plus exam as he is currently in year 5. I would just hope that some1 could give me some information about what sorts of percentage questions he needs to know and offor some examples if any. I do believe the ke test is non calculator which means dc will have to work all sums out on paper. If you had to for eg work out the percentage in a test eg 22/150 what would be the best method for dc to use. Thanks in advance.

[UmSusu]

Hello adhdad

If you go over to the Birmingham section and look at the sticky past exam content you find some examples. Have a look on there first and if you still have questions, just ask.

There have been questions before on how much profit was made on an item, adding VAT, or prices before / after discount. Sometimes, there have been simpler find x% of y

[adhdad]

thankyou for that umsusu, just the question list you gave me has given me food for thought. I will goover to the birmingham sticky and try to gather some info and take it from there.

[parent2013]

For % tages, the key word is "out of 100".

Bexley, Kent usually go for simple calculations like

1. simple q like 25% of 75 --> use 25/100 X 75.

2. other q type is 30% of 80 --> calc 10% of 80 which is 8 then times 3 = 24

Super-selectives test the application of % in real world problems

3. word problems for selling price, discount & cost price where discount is subtracted

4. word problems for vat, excise duty where vat is added

Another type is comparison of 5 numbers which are mix of decimal, fraction and %tage.

5. approx % where one has to compare 5 numbers. This is the one you mentioned like 22/150.
First option - You can assume 22 is 21, get the answer and increase slightly.

21
--- X 100
150

21
--- X 2 --> 14% approx.
3
Second option - do long division & get the accurate answer.

The child should know not only to calculate % tages but also how it is inter-convertible with Fractions and Decimals.

[AEC]

First of all I would like to say a big hi to ever1 on here. Ive read many topics on this site and have found them to be of great interest. Anyway to my question as the title says its percentages. My ds will be hopefully sitting the birmingham based 11 plus exam as he is currently in year 5. I would just hope that some1 could give me some information about what sorts of percentage questions he needs to know and offor some examples if any. I do believe the ke test is non calculator which means dc will have to work all sums out on paper. If you had to for eg work out the percentage in a test eg 22/150 what would be the best method for dc to use. Thanks in advance.

Hi

First of all it is important to understand what percentage means. For example,
22% of 55.

One could work, 10%, double it, 1% double it and obtain an answer and it works will with some children. However, in my opinion, the traditional methods is the best way forward for percentages.

write 22% as 22/100 and 55 as 55/1, so we have

22% of 55 as

22/100 * 55/1. Now it will reinforce the knowledge on fractions,
multiplying the numerator 22*55= 1210
multiplying the denominator 100*1=100

we have now 1210/100=12.10

It seems long, but requires little practice.

Regards
AEC

[adhdad]

Thankyou to all parents for replies and I can say they have been of great use to me.

@ AEC I think the example you gave mayb the one that we go with, this is because my dc likes to work answers out in formats. The way you set it out could prove to be very fruitful for us with lots of practice. If im not being to cheeky could I ask how you would change test scores into percentages.

eg Tim scored 58/200 what percent did he score ?

I can work the answer out as 29, but what im looking for is a method to teach my dc. Thanks

[hasmum]

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.

[parent2013]

Two things:

1. Tip of the day - "if the denominator is not multiple of 10, multiplying the numbers to make a bigger number and then dividing by denominator" may not be the best approach. One should know how to simplify the numbers into smaller ones to get the answer.

Try this: What is 21/75 of 1/7 of 100?
You should get the answer 4 in one step

2. Another variation is What % of 55 is 22?

[Proud_Dad]

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.

i.e.
10% = 1/10
20% = 1/5
25% = 1/4
50% = 1/2
75% = 3/4

[southbucks3]

Two things:

1. Tip of the day - "if the denominator is not multiple of 10, multiplying the numbers to make a bigger number and then dividing by denominator" may not be the best approach. One should know how to simplify the numbers into smaller ones to get the answer.

Try this: What is 21/75 of 1/7 of 100?
You should get the answer 4 in one step

2. Another variation is What % of 55 is 22?

My brain hurts? Come again?