Maths and calculator question

[Redraptor]

I'm a little embarrassed to be asking this, I'm not sure what I'm doing wrong but...

When doing percentages I've always used the following on my calculator (totally made up maths used, just an example)

6000x1.20 =7200. This has added the 20%. Or 7200÷1.20 =6000. This shows me 20% of the 7200

Anyway, the point is I would usually multiply or divide by 1.xx. which ever percentage I'm using

Last night I was doing some sums and for ease at the time (I can work it out in my head) I tried doing 6000÷1.10 to try and get 10% off. I know this is 5400 but my calculator says 5454.54.

Only happens when I'm trying to minus 10%. Any ideas why? My calculator broken?

If you are trying to remove 10% from 6000, then you subtract the 0.1 from 1 and multiply that by 6000 to get 90% of it.

0.9 * 6000 = 5400

If I was doing it by calculator I'd just type in 6000-10% to get the answer. I get the same answer as you for 6000÷1.10

I'd just divide it by 10 and then times 9

Your first example is wrong. Taking off 20% of 7200 from 7200 isn't 6000! (Hope you don't work in a shop!) That's 20% of 6000. So your initial assumption is wrong hence why the technique doesn't work for 10%.

1/1.1 = .909090...

or 90.9%, or about 91%.

If you want 10% off, you need to multiply by 0.90 not multiply by 0.909090...

7200÷1.20 =6000. This shows me 20% of the 7200

6,000 is very much not 20% of 7,200.

The easiest way to work out a reduction of 10% is to multiply by 0.9 (i.e. 90%) as @yeOldeTrout said above.

@Redraptor

I'm a little embarrassed to be asking this, I'm not sure what I'm doing wrong but...

When doing percentages I've always used the following on my calculator (totally made up maths used, just an example)

6000x1.20 =7200. This has added the 20%. Or 7200÷1.20 =6000. This shows me 20% of the 7200

Anyway, the point is I would usually multiply or divide by 1.xx. which ever percentage I'm using

Last night I was doing some sums and for ease at the time (I can work it out in my head) I tried doing 6000÷1.10 to try and get 10% off. I know this is 5400 but my calculator says 5454.54.

Only happens when I'm trying to minus 10%. Any ideas why? My calculator broken?

In your first example it doesn't work the way you think it does. All you are doing is adding 20% to the 6000 and then taking it back off again, and it only works because 7200 is 120% of what you started with.

You're not doing the right calculation OP. You need to take the percentage off of 1 and then multiply by that OP. So 10 percent off, multiply by (1-0.1)=0.9.

Hey OP
Your rule works for adding on percentages so carry on with the 1.xx for that.
For taking away percentages use 100-x (e.g 100 - 20 = 80). And then your answer goes after a 0. E.g. 0.80 for taking away 20%.
Before anyone turns up to tell me you don't need the second 0, I am giving a general rule that works for all situations. 0.xx where xx is the difference between 100 and the percentage you want to subtract.

@titchy

Your first example is wrong. Taking off 20% of 7200 from 7200 isn't 6000! (Hope you don't work in a shop!) That's 20% of 6000. So your initial assumption is wrong hence why the technique doesn't work for 10%.

Sorry I haven't explained very well. My maths is usually used for working out the VAT of something hence my earlier showing, I get the price before VAT for standard 20% VAT.

I'm more confused now 🙈 and embarrassed. Thank god I just work with 20% haha will read the replies again and practice

To address your confusion, you need to think through what represents 100% in your calculation.

For VAT, you start with the pre-VAT price, and with VAT the price is 120% of the pre-VAT price. So the pre-VAT price is the "100%": you multiply by 1.2 to get the price with VAT; you divide the price incl VAT by 1.2 to get the pre-VAT price.

When you want to take 20% off a price (eg to apply a discount), the pre-discount price is the "100%" and the discounted price is 80% of that: you multiply by 0.8 [which is not the same as dividing by 1.2] to get the discounted price.

There are several different calculations that you could be doing:

Increasing/Decreasing original prices to find new ones:

finding 20% off a price - i.e., a sale discount, for example.

In this case, multiply the original price by 0.8, to find the 80% of the price you have to pay. (or equivalently, multiply the original by 0.2, to find 20% of the price, and subtract it from the original).

increasing a price by 20% - e.g., prices needing to rise because costs going up

Here you multiply the original by 1.2, to find 120% of the original amount. (or again, you could multiply the original by 0.2, to find 20%, and then add it on).

OR - reverse percentages, when you are trying to find original prices from ones that have been increase/decreased:

finding the original price when what you have is the price that has already been increased by 20%. This is not the same as "taking off 20%".

In this case, dividing by 1.2 is fine. The original price had been multiplied by 1.2 to get the final price, so you can undo that to get back to the original.

Or if something was in an 80% sale and you wanted to know the original price, you could divide by 0.8 to get back to the original.

Basically - if you know the original amount (100%) and are finding an adjusted amount, you will be multiplying by something. If you know the adjusted amount, and want the original (100%) amount, you'll be dividing. You need to know what your original (100%) amount is defined as.

for adding 20% you are fine
6000 x 1.2 = 7200 which is 6000 plus 20%

But to remove the 20%, what you are doing is wrong.

Because 20% of 7200 is 1,440.
You can see that if you do what you did to the 6000
7200 x 1.2 = 8640
So the 7200 has increased by 1,440.

So your 1.2 only works because you are interested in the 6000, adding and removing the VAT from it. You are not taking 20% off the 7200, you are working out what the original number was that had 20% added. So dividing by 1.2 removes the VAT to return you to the original price.

But to work out a 20% discount from 7200, you are starting with 7200, not with 6000 plus 20%

I (possibly unhelpfully) have to think about these in a semi algebraic way to understand it.

For VAT the VAT free price is X, with VAT is Y.

So X * 1.2 = Y. So here we are multiplying by 1 + 20% hence 1.2

But then if you want to get from Y to X you can rearrange the equation to Y / 1.2 = X

But if you want to have a 20% off sale of something that's £10, you have to multiply by 1 - 20% so 1 - 0.2 so 0.8

So A * 0.8 = B where A is the original price and B is the new price

So if something is reduced to £8 in a 20% off sale we rearrange the equation to

B ÷ 0.8 = A

So a 20% off sale makes the post sale price for an item that was originally £10 to be £8.

Not sure if that helps or not...

To add VAT to a price. Do price x 1.2

To work out what a price was before VAT. Do price ÷ 12 x 10.

I (possibly unhelpfully) have to think about these in a semi algebraic way to understand it

Algebra is always helpful.

I love reverse percentages.
People have explained it clearly.

chomalungma

Well algebra is always helpful to me too, but it's something that I understand reasonably instinctively so it just doesn't always help if I'm trying to explain things and the person doesn't like algebra!