11 Plus Exams Forum

Hello everyone.
Please what is the quickest and easiest way of working this question out?

The local bookshop has a sale. Every item in the shop is reduced by 25%.
Melanie bought a picture for £1.50
What was the price of the picture book BEFORE the sale started?

if the picture cost £1.50 and has been reduced by 25% then that means that £1.50 is 75% of the original price.

75% is 3/4 so divide £1.50 into 3 = 50p. 50p then is 25%.

Add on 25% (50p) making original cost £2.00.

I taught dd one way to do nearly all these kind of percentage and fraction questions as she was getting confused-

part percentage
------ x -------------
whole 100

put in the numbers you have, then multiply by the diagonal number and divide by the other number.

1.50( part of the whole number) 75( you know 1.50 is 75% of the whole)
----- x ----
? 100

1.50x100 / 75 = 2.00
I hope I've put that in right, gotta dash up to school now.

If you are asked to find an original price, put 100 over the percentage you have (75, in the above example), cancel this improper fraction down to its lowest terms, and multiply the resulting 'constant fraction' by any discounted price, cross-cancelling if possible, to find the original cost.

Taking the above example:

100/75 x 150/1 = 4/3 x 150/1 = 4/1 x 50/1 = 200 = £2 (This obviously would benefit from standard fraction formatting!)

If you have the original price and need to find out what the discounted price would be, you just need to invert the 'constant fraction'.

E.g. 3/4 x 200/1 = 3/1 x 50/1 = 150 = £1.50

Cross -cancelling is a very dodgy idea to teach someone as it only works if you have one fraction equal to another - again it's something a maths teacher would tend to avoid because of problems later on with harder fractional equations.