A ratio is a numerical method of comparing two quantities
of the same type, such as sum of money, length, weight, ages, marks, etc…
As ratio is a comparison of relative magnitude of two quantities, it may not necessarily contain units. It may be in fraction or separated by column in between them. For example; P/Q or P:Q which is pronounced as P ratio Q. A ratio is always numbers.
The following rules should be implemented when dealing
with ratios.
Rule
1;
If a/b and c/d are two different
ratios. Let a/b = c/d
Therefore, ad = bc (when cross multiplied)
Rule
2;
If a/b = c/d
Therefore, b/a = d/c
(alternating the ratios)
Rule
3;
If a/b = c/d
Therefore, a/c = b/d
(inverting the ratios)
Examples;
1. In
a certain class, the ratio of boys to girls is 2:5. If there are 40 boys, find
how many girls are there.
Solution
Let the no of girls be x
Then 2:5 = 40:x
2/5 = 40/x
(cross multiply)
2x = 40 X 5
2x = 200 (divide both sides by 2)
x = 200/2
Therefore, x = 100.
This means that there are 100 girls in the class.
2. Which
ratio is greater, 6:8 or 12:22?
Solution
6:8 is the same as 6/8.
Divide 6 by 8 and the answer is 0.75.
While 12:22 is the same as 12/22.
Divide 12 by 22 and the answer is 0.545.
Which is bigger between 0.75 and 0.545?
Obviously it is 0.75.
Therefore this means that 6:8 is greater than 12:22.
3.
Decrease #110.81 in the ratio 4:7.
Solution
#110.81 X 4/7
This can be written as;
This can be written as;
= #63.92 (final answer)
Practice
these questions below;
1. The ratio of the circumference of a circle to its
diameter is 22:7. What is the circumference of a circle of diameter 15.6m?
2. In each class, find which of the two ratios is greater;
(a) 16 : 7 or 17 : 6
(b) 2.5g : 2kg or 0.4kg : 300kg
(c) #1.60 : #4 or #6 : #11.
3. Divide 490 in the ratio 2:5:7.
4. In preparing a recipe for cake, the ratio of the flour
to sugar is 40:3. Find the required amount of flour to 18kg of sugar.
5. A worker’s income is increased in the ratio 36:30.
Find the increase percent.
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