Maths: Reverse percentages!

I posted on Facebook that I was doing reverse percentages with Chiara a while back and a few of my Facebook friends said: you can explain it to me when you have her.  I said I would so here is my explanation and I've tried to make it as fun as I can. 

1. The first thing you do is write down, or list in your head what we know: the original price = 100%, the price has been increased by 25% therefore the new price = 125%
2. Divide the new price by the increased percentage, in this case 125% (The percentage increase + the original 100%)  Now you have found 1% of the original price
3. Multiply that 1% by 100 and you will have your original price.

So here is a simple example question you might find in your maths books...

A box of chocolate costs £12 we know it was increased by 20% of it's original price.  How much was the box of chocolates originally?

• Original price 100%
• 12/120 = 0.1
• 0.1 x 100 = 10
• Original price was £10

What if the percentage is less that 100% not more? It's pretty much the same really...

 

1. Again list what you know: the current price is 80% of the original price.  The original price was 100%.
2. Divide the current price by 80 (because it is 80%) giving you 1% of the original price
3. Times this 1% of the original price by 100 and you will have 100% which is, of course, the original price.
    

Here is another example question you might find in your maths books...

 

You see a second hand mobile phone in a shop window, it says a phone is £76, 80% of it's original price.  How much was the phone before the reduction?

 

So...

• 76 divided by 80 = 0.95 = 1% of the original price
• 0.95 x 100 (because we want 100%) = 95
• So the Original price was £95 

 

I hope this helps but if you want to see this in a more visual way you can...

Try this, use either fake pizza (it helps to have more than one pizza) or real pizza or cake if you'd rather.  There are other ways too, you could use lego or bricks of another kind too. It just helps to use something physical, I certainly find with my 8 year old, to understand the concept of it all. 

This is what we did.  We used lego in the end as Honi couldn't bare to chop up her fake pizza, it was more a lesson for Naomi and Chiara anyway so I chose to do it with lego.  I picked out 15 pieces of lego and layed them out like this...


I told them that it was 50% more than I first had and asked: How can we find out how much the original 100% was.

We counted that there was 15 blocks and I explained that the new amount of blocks were the 100% + the 50% more

 

So 150%.  I then explained that we divide the 15 (blocks) into by 150 giving us 0.1 and then times it  by 100 (100%)   Giving us the answer that there were 10 blocks originally.

You can show then the orignal amount of blocks left, when halved 50:50, is the same as the 50% left therefore we know we are right.

This helped in grasping the idea for Naomi in particular, probably because she is such a visual learner, but Chiara enjoyed it too.  So much, infact, that she had several different goes with the lego and different reverse percentages exercises before we moved on today.