Converting a ratio into percentage.

Question

As per many websites and text books, 3:4 converted into % is 75%. But as per my understanding, its not. If 3:4 is the ratio of boys and girls in a class, then it means that 3 out 7 are boys and 4 out of 7 are girls. 2:3 is the ratio of apples and oranges means 40% are apples and 60% are oranges. where am i going wrong?

Answer 1

There is a distinction between the following usages/interpretations, since your base is different:

1. In the first, you are viewing $3:4$ as a fraction of a whole, for example "3 out of 4 pupils are boys", hence 75% of all pupils. In other words: "$3:4$ of the pupils are boys" coud be rephrased as "the ratio between boys and all pupils is $3:4$"
2. In the second example, the ratio of boys to girls is $3:4$ (you could say the number of boys is 75% of the number of girls), but the ratio between boys and all pupils is $3:(3+4) = 3:7$.

In other words, when we say "the ratio between A and B is $3:4$", we need to distinguish which quantitiy we are interested in:

• comparing A to B, i.e. the number of A is 75% of the number of B, or
• comparing A to the whole (A+B), i.e. the A are $3:7$ of the whole (A and B).

Answer 2

You need to specify what you are taking the percentage of. In your calculations you are finding the percentage of one kind out of the total. If there are $3$ boys to $4$ girls there are $75\%$ as many boys as girls. You are correct that the boys are about $43\%$ of the total children.

Also what is converted to $75\%$ is often $3/4$ or $\frac 34$, which are different from $3:4$