Help with multiplying decimals and percentages

[DilysPrice]

DD (9) is very mathematically competent, as am I. But she's just had a SATs practice paper home which requires some percentage and decimal calculations and it has become apparent that she doesn't have a clue how to do it (apart from knowing that 10% => divide by 10, 20% => divide by 5 etc). Apparently she was off sick that day or something .

I can explain that (say) 17% of 800 = 17 800 / 100 but she doesn't really seem to be getting it, and when it comes to explaining why 0.5 0.5 = 0.25 I'm a bit baffled where to start. Does anyone have any hints on how to start, or links to good online resources or books?

Please?

With the decimals I would return to vulgar fractions. What do we do to find, say 2 fifths of something? (you say to her) We divide it by 5 then x it by 2.

So we want to find 17%. This is the same as 17 hundredths. Divide the number by 100, then x this by 17. For every question ask her to tell you what fraction this is (25% is 1 quarter, 13% is 13 hundreths and so on) to remind her of the technique.

With decimal x decimal I would us column method, alway reminding her to keep the decimal in the same place. Yes, it is bad practice to teach children methods without teaching the mathematical concepts but a half x a half is a very had concept at 9 years old! Try discussing 1x something and 0x something. 0.5 x 1 would be 0.5. Multiplying it by something smaller than 1 will surely give an answer smaller than 0.5? But she may not understand this, its simply too advanced.

Anyway column method:

0.5
0.5 x

Put a point in under the other ones and explain that this never ever moves, only the numbers move. 5x 5 = 25 so the answer is 0.25.

Keep showing examples, she wont get it with just 1. 0.6 x 0.3. What is 6 x 3? 18 etc

Hope this helps.

Thanks wellthen, that's really helpful.

The percentages thing works for me, but although I get your point about the difficulty of teaching decimals properly I don't think I'm psychologically capable of teaching them simply as a mechanical process like that - I'm going to need to look for resources which give me the words to use.

I do have some equivalence cubes somewhere - I'll dig them out.

Sometimes a visual representation is useful. Ie half of a half, cut an apple in half, then cut the half in half, gives a quarter. As said by Wellthen, above, 0.5 is just another way of saying 1/2.

Imagine the apple cut up into 100 pieces, and each piece is 1%. So if you want 17% you have to have 17 of them.

Once this is understood, you can extend the concept to include numbers ie 17% of 264, not just 17% of 1.

Agree that you should probably teach x 0.5 as another way of saying divide by 2. (because 0.5 is less than 1 and 1 x something...blah blah). Th trouble then arises of how to teach 0.6 x 0.2 or 0.3 x 0.1 or whatever.

Having thought again you could explain it like this:

0.6 x 0.3
Multiply 0.6 by 10 and multiply the 0.3 by 10 making it 6 x 3 = 18.
Because we multiplied the 6 AND the 3 we have to now divide the answer by 10 TWICE. (If she is quick as you say then she will probably see it is easier just to divide by 100).
18 divided by 10 and divided by 10 again = 0.18
0.6 x 0.3 = 0.18

Not quite the exact concept but also not just 'learning a written method'.

As a side note I would ask her teacher how she expects it to be done. This is a hard topic at Year 5 (?). I teach year 5s and I wouldnt ask my highest achievers to do this just yet. The teacher may have something specific in mind.

Ah yes wellthen - I asked DH and that new suggestion how he remembered learning it - seems to make more sense to me, and reasonably well linked to the real maths, so I think that's how we'll go.

I was wondering why I couldn't remember learning this, and have finally recalled that I was taught using log tables which obviously have their own very specific solutions to these issues.

This will be long... sorry

With percentages (without a calculator) I would explain it this way:

1. what is 10 % of 800? to find 10 % of any number, you divide that number by 10 (let's assume this is ok with the child), so 800/10= 80 Answer: 80
2. what is 15 % of 800? if 10 % is 80, and 5 % is half of 10 %, so 5 % of 800 must be half of 80 = 40 So I can find 15 % by adding 10 % and 5 % : 80 and 40 = 120 Answer : 120
3. what is 16 % of 800? if 10 % is 80, then 1% is 80/10=8 So to find 16 %, you add 10 % , 5 %, 1 % = 80+40+8=128 Answer 128
4. what is 17 % of 800? Add 10 %, 5%, 1 %, 1% = 80+40=8+8=136 Answer: 136

Or, especially if you are allowed to use a calculator:

1. what is 17 % of 800? First find 1 % of 800: 800/100=8 then multiply that 1 % by 17 = 8*17 = 136

With multiplying decimals, I would show the pattern:

5 x 5 =25
5x 50 =250 (so If I multiply by a number 10 times bigger, the answer is 10 times bigger)
5 x 500 = 2500 (similar comment as above)

Going the other way:
5 x 5 = 25
5 x 0.5 = ? if you multiply by a number 10 times smaller (0.5 instead of 5), the answer will be 10 times smaller. What is the number that is 10 times smaller than 25? 2.5
So 5 x 0.5 = 2.5
What is 0.5 x 0.5 ? The answer to this must be 10 smaller than the answer to 5 x 0.5 because the first number (0.5) is 10 times smaller than 5, so the answer must be 10 times smaller than 2.5, which is 0.25

I like Maths!

Haven't read the other replies so sorry if I repeat but with percent I think of it in words i.e. per Cent (French for 100) and of is "maths-ese for multiply so 17% of 800 is 17 per 100 of 800

17/100 =0.17

0.17 x 800 = 136.

It works the other way to check it...136/800 x 100 = 17% to remember this she could move the 100 to the other side (basic algebra to divide both sides by 100- apologies if they haven't done this concept yet though) to make it "per 100" so 136 per 800 is equal to 17 per cent (per 100).

With 0.5 x 0.5 it is 1/2 of 1/2 (of=multiply again) which is 1/4 but mathematically you are either doing 5*5 after the decimal point (0.25) or 1/2 x 1/2 multiplying the denominators (2x2=4) so 1/4.

Thanks all - lots to work from there.

Another way of explaining it to begin with may be to make the numbers simpler.

eg. 9 out of 10 cats prefer brand x.

If we asked 10 cats, how many would prefer brand x?
If we asked 80 cats?
This then can progress to:
If 17 out of 100 prefered brand x and we asked 800?