GCSE maths. I don't understand how division works

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Advanced-08234
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#1
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#1
If 8 chocolate bars cost £6, calculate the cost of 10 chocolate bars.

£6/8 = £0.75

then 10 bars cost £0.75 x 10 = £7.50

I don't understand how that works. How does dividing £6 by 8 find the cost of one unit? I guess I'm looking for a proof.

Thank you
Last edited by Advanced-08234; 4 months ago
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l.r.
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#2
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It is £6 per 8 chocolate bars, which can also be written as £6/8 chocolate bars (the word per is interchangeable with a /, for example metres per second can be written as m/s). So if you then divide the £6 by the 8 bars you will see that it is £0.75 per single chocolate bar… Does that make sense?
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Kogomogo
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#3
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I worked it out by dividing by four because it's an easier division to work with:

If you have 8 bars and divided them between four people, everyone would get two bars each. 8÷4=2.

£6 divided by four would be £1.50. You can make dividing by four easier by halving and halving again, so 6 divided by two would be 3, and 3 divided by two would be 1.5.

Therefore, two chocolate bars are worth £1.50.
£6 plus £1.50 would £7.50 which is the answer.

Sorry if that seemed long winded but just my way of thinking about it. There are sometimes shortcuts you can take like keeping on halving to find out quarters, eighths, sixteenths etc.
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Marr.sar
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#4
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(Original post by Advanced-08234)
If 8 chocolate bars cost £6, calculate the cost of 10 chocolate bars.

£6/8 = £0.75

then 10 bars cost £0.75 x 10 = £7.50

I don't understand how that works. How does dividing £6 by 8 find the cost of one unit? I guess I'm looking for a proof.

Thank you
hi, you can just think of it as in a ratio form so 8 bars:£6 so to figure out what 1 bar costs, you divide 8 by 8 to get to 1 bar and because it is a ratio you do the same to the other side therefore do 6 divided by 8 so 1 bar: 0.75 p and that's the cost of one bar. Hope that helped.
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Advanced-08234
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#5
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(Original post by l.r.)
It is £6 per 8 chocolate bars, which can also be written as £6/8 chocolate bars (the word per is interchangeable with a /, for example metres per second can be written as m/s). So if you then divide the £6 by the 8 bars you will see that it is £0.75 per single chocolate bar… Does that make sense?
So a division means per unit?

So if a car travels 100 metres and it does so in 2 seconds then the car has travelled 100 metres in 2 seconds. If we write this as a division then we get 100 metres / 2 seconds = 50 metres per second.

So a division means per unit. The per unit part we are using is seconds. I understand this now.

Back to the chocolate bars, we pay £8 for 6 chocolate bars. If we wanted to find the cost of one chocolate bar i.e. per unit then we divide the cost, £6, by the total amount to find the cost per unit.

What I don't understand is, why not have 8/£6. Why does it have to be £6/8?

Thank you
Last edited by Advanced-08234; 4 months ago
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Muttley79
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#6
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(Original post by Advanced-08234)
If 8 chocolate bars cost £6, calculate the cost of 10 chocolate bars.

£6/8 = £0.75

then 10 bars cost £0.75 x 10 = £7.50

I don't understand how that works. How does dividing £6 by 8 find the cost of one unit? I guess I'm looking for a proof.

Thank you
I'm not sure what you mean by a proof.

If we know what 6 cost then we need to divide by 6 to get the cost of ONE [textbooks sometimes call this the unitary method] Once we know what one cost then we can find the cost of any number.
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erinls2
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Here is the best way I can think to explain it
So we know the total cost for 8 chocolate bars is £6. So the overall total of our "equation" if you like = 6

We know we have 8 chocolate bars, so 8 times *something* (the cost of 1 bar which is what we're trying to work out) = 6

We will call that something "x"

So you could think of it as 8 x X = 6 or simply 8x = 6

Now we need to work out what x, the price of 1 bar is. To separate the 8 and the X we have to divide by 8, and you have to do this on both sides.

So x = 6/8 which is £0.75

Does that make sense?
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0ptics
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#8
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(Original post by Advanced-08234)
What I don't understand is, why not have 8/£6. Why does it have to be £6/8?
Think of it as a ratio. For every 8 chocolate bars, the price is £6. This can be expressed as:

C:M
8:6
You want to find the cost of 1 chocolate bar. To do that, we must divide 8/8 to get 1. However, what we do to one side of the ratio, we also have to apply to the other. That’s why you have to do 6/8, not 8/6. Just to show how the ratio would work here:
C:M
8:6

C: M
8/8 6

C:M
1:6/8

C:M
1:0.75
Last edited by 0ptics; 4 months ago
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CJ05
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#9
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(Original post by Advanced-08234)
If 8 chocolate bars cost £6, calculate the cost of 10 chocolate bars.

£6/8 = £0.75

then 10 bars cost £0.75 x 10 = £7.50

I don't understand how that works. How does dividing £6 by 8 find the cost of one unit? I guess I'm looking for a proof.

Thank you
This seems more like direct proportionality than division, if you use the methods that I would use to approach it
So here's how I would write it out:
1) If 8 bars of chocolate cost £6, then this can be written as 8 CB = £6 (CB meaning chocolate bars)
2) You can then work out the cost of 1 chocolate bar so 1 CB = £0.75 (as the amount of CB is lower the price of each would have to decrease as well)
3) To work out the cost of 10 chocolate bars it would be 10 CB = £7.50 (as the amount of CB is higher the price of each would have to increase)

So let me explain in more detail:
At step 2 the reason 1 CB became £0.75 because you had to divide by 8 on both sides, so I did 8/8 to get to 1 CB and because I divided by 8 on one side I would have to do it again on the other side, meaning I would have to do £6/8 to get £0.75.
At step 3 it is the same concept, except that you have to multiply it to find 10 CB.

There is a much quicker way of doing this you could just do 8 CB = £6
10 CB = £7.50 (here you need to get from 8 to 10 to do this you need to do 10/8 which gives you 1.25, o to get from 8 to 10 you times by 1.25 so this means you would have to do the same thing on the other side, meaning you'll do £6 x 1.25 which equals £7.50)

I think my explanation was quite confusing if so sorry about that.
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black tea
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#10
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#10
(Original post by Advanced-08234)
So a division means per unit?

So if a car travels 100 metres and it does so in 2 seconds then the car has travelled 100 metres in 2 seconds. If we write this as a division then we get 100 metres / 2 seconds = 50 metres per second.

So a division means per unit. The per unit part we are using is seconds. I understand this now.

Back to the chocolate bars, we pay £8 for 6 chocolate bars. If we wanted to find the cost of one chocolate bar i.e. per unit then we divide the cost, £6, by the total amount to find the cost per unit.

What I don't understand is, why not have 8/£6. Why does it have to be £6/8?

Thank you
Because £6 is how much 8 chocolate bars cost. So in order to find out the cost of one, you have to divide the £6 by 8. Dividing 8 by £6 pounds will just tell you how many times £6 will go into 8.
Last edited by black tea; 4 months ago
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