Ratio of Multiple Expressions: Let us suppose that the number of apples, oranges and mangoes in a basket are 8, 5 and 9 respectively.
Thus, ratio of apples, oranges and mangoes in the basket can be written as,
Apples: Oranges: Mangoes = 8 : 5 : 9.
As we can see, the ratio of 3 or more quantities is called Ratio of Multiple Expressions.
Successive Ratio: When two ratios are put together, we get Successive Ratio. For example, the ratio of weight of Kamal and Jamal is 30 kg: 35 kg. The ratio of weight of Jamal and Sohel is 35 kg: 31 kg.
Hence the Successive Ratio here can be written as,
Ratio of weights of Kamal, Jamal and Sohel is 30 : 35 : 31.
We can see that subsequent of first ratio is equal to the antecedent of second ratio. If they were not equal, a Successive Ratio would not be obtained.
To convert two ratios into successive ratio, both the antecedent and the subsequent of second ratio are to be multiplied by the subsequent of first ratio and both antecedent and subsequent of first ratio are to be multiplied by the antecedent of second ratio
Proportion: In proportion where two ratios are equal. It can be written in two ways:
A proportion is an equation written in the form stating that two ratios are equivalent.
In other words, two sets of numbers are proportional if one set is a constant times the other.
In proportions, a & b are same quantities and c & d are same quantities. a & b might be different quantities than c & d but the two ratios will be equal. We can find the value of a, b, c or d by cross multiplication.
For example, can be written as (a x d) = ( b x c) ; through cross multiplitcation.
Thus, if we want to find the value of a, then a =
Example of Proportion Problems:
- If a: b = 4 : 3, b: c = 2 : 9, determine, a: b: c.
Solution: We multiply (a: b) with 2 to get (4 : 3) x 2 = (8 : 6).
And multiply (b: c) with 3 to get (2 :9) x 3 = (6 : 27).
Thus, we get an equal value of b for both the equations.
So, a: b: c = 8 : 6 : 27
Worksheet : Which one is heavier – a micro oven weighing 50000 gm or a small deep freeze weighing 49.5 kg?