   SEARCH HOME Math Central Quandaries & Queries  Question from Khurram: what is ratio and proportion? please give a detailed note on this topic, i am really panic of these calculations Hi Khurram,

Ratios and proportions are alternate ways of expressing fractions.

For example, suppose you are in a class of 25 students, 10 of which are boys and 15 are girls. Thus the fraction of the class that is boys is

$\frac{10}{25} = \frac{2}{5}$

and the fraction that is girls is

$\frac{15}{25} = \frac{3}{5}.$

Proportions are usually expressed as percentages and since $\large \frac{10}{25}$ is 40% you can say that the proportion of the class that is boys is 40% and the proportion that is girls is 60%.

To express the same fractions as a ratio you would say that the ratio of boys to girls is 10 to 15, which is often written 10:15. You can simplify ratios in a similar way to the way you simplify fractions so dividing 10 and 15 by 5 you can say that the ratio of boys to girls is 2:3.

To go the other way suppose the teacher across the hall says that the ratio of boys to girls in her class is 5:8. Since 5 + 8 = 13 that means she could put the students in her class into groups of 13 with each group containing 5 boys and 8 girls. Hence the fraction of her students which is boys is $\large \frac{5}{13}$ and the fraction which is girls is $\large \frac{8}{13}.$ To express this as a proportion divide 5 by 13 to get 0.3846 and hence the proportion of her students which is boys is 38% and hence the proportion which is girls is 62%.

I hope this helps. Write back if you need more assistance,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.