Table of Contents
Proportion
If we say that two ratios are equal then it is called Proportion.
We write it as a: b : : c: d or a: b = c: d
And reads as “a is to b as c is to d”.
Example
If a man runs at a speed of 20 km in 2 hours then with the same speed would he be able to cross 40 km in 4 hours?
Solution
Here the ratio of the distances given is 20/40 = 1/2 = 1: 2
And the ratio of the time taken by them is also 2/4 = 1/2 = 1: 2
Hence the four numbers are in proportion.
We can write them in proportion as 20: 40 : : 2: 4
And reads as “20 is to 40 as 2 is to 4”.
Extreme Terms and Middle Terms of Proportion
The first and the fourth term in the proportion are called extreme terms and the second and third terms are called the Middle or the Mean Terms.
In this statement of proportion, the four terms which we have written in order are called the Respective Terms.
If the two ratios are not equal then these are not in proportion.
Example 1
Check whether the terms 30,99,20,66 are in proportion or not.
Solution 1.1
To check the numbers are in proportion or not we have to equate the ratios.
As both the ratios are equal so the four terms are in proportion.
30: 99 :: 20: 66
Solution 1.2
We can check with the product of extremes and the product of means.
In the respective terms 30, 99, 20, 66
30 and 66 are the extremes.
99 and 20 are the means.
To be in proportion the product of extremes must be equal to the product of means.
30 × 66 = 1980
99 × 20 = 1980
The product of extremes = product of means
Hence, these terms are in proportion.
Example 2
Find the ratio 30 cm to 4 m is proportion to 25 cm to 5 m or not.
Solution 2
As the unit is different so we have to convert them into the same unit.
4 m = 4 × 100 cm = 400 cm
The ratio of 30 cm to 400 cm is
5 m = 5 × 100 cm = 500 cm
Ratio of 25 cm to 500 cm is
Here the two ratios are not equal so these ratios are not in proportion.
3: 40 ≠ 1: 20
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