# how can a ratio be written as a fraction (maths) GCSE

apparently, if there is a ratio of:
1:2 it can also be written as 1/2
and that is the same for any ratio however i'm struggling to why that is.

if A had 1 part and B had 2 parts, then surely A has 1/3 of the parts and therefore B has 2/3 of the parts as in total, there are 3 parts?
so i don't really understand why it can be written as a half.

one question i was doing in a past paper stated:
x^2 : (3x+5) = 1:2

i looked at the mark scheme and the first step was:
x^2/3x+5 = 1/2

after that, i got the answer as it resulted to be x= 5/2 or x= -1

however, the part i am struggling to understand is why did they make this ratio a fraction in the first place? how do i know when i can do it?
obviously, i don't want to get confused with ratios as there are different types of ratio questions.

thanks so much. (i'm doing GCSE btw)
(edited 1 year ago)
For 1:2, it means the first part is half of the second part.
However, the first part is a third of the total, just as the second part is two thirds of the total.

So the example is correct, it just depends on what you're comparing it with (the other part or the total).

A simple example would be pocket money. Andy and Belinda get £10 and £20, so the ratio is 1;2 and Andy gets 1/2 of Belinda. However, Andy gets 1/3 of their parents money and Belinda 2/3.
(edited 1 year ago)
Okay so you're not far off but that first step is tripping you up.
You are correct that that means that A has 1/3 of the parts total, but A/B = 1/2
If you take the total parts to be u
A = 1/3 U
B = 2/3 U
A/B = (1/3u)/(2/3u)= 1/2

Alternatively, As mqb2766 said above, B is twice of A so B/A = 1/2 like how 8/4 = 1/2