What is Proportion ?
When Two Ratios are equal then we say that they are in Proportion and use the symbol “: :” or “=” to equate two ratios.
Four Numbers in Proportion
Let a, b, c, d are four numbers said to be in proportion.
then, a : b = c : d or a : b :: c : d
here a and d are called the extreme terms or extremes.
b and c are called the middle terms or means.
When Four numbers are in proportion
then, Product of extremes = Product of means.
i.e, In proportion a : b :: c : d,
(a x d) = (b x c)
Proportion Examples
Example 1
Are the ratios 90 cm : 270 cm and 70 m : 210 m in proportion?
Explanation:
We have 90 cm : 270 cm
= 90 : 270
= 90/270
= (90÷90)/(270÷90) (HCF of 90 and 270 is 90 )
= 1/3
70 m : 210 m
= 70 : 210
= 70/210
= (70÷70)/(210÷70) ( HCF of 70 and 210 is 70 )
= 1/3
Since, the ratios 90 cm : 270 cm and 70 m : 210 m are equal to 1/3 . So, they are in proportion.
Example 2
Are 6, 12, 4, 8 in proportion?
Explanation:
We have, 6 : 12 = 6/12 = (6÷6)/(12÷6) = 1/2
and 4 : 8 = 4/8 = (4÷4)/(8÷4) = 1/2
Since, 6 : 12 = 4 : 8
Hence, 6 , 12 , 4 , 8 are in Proportion
Alternative method: Product of extremes = Product of means
Here, Means are 12 and 4
Extremes are 6 and 8
Product of extremes = 6 x 8 = 48
Product of means = 12 x 4 = 48
Since, Product of extremes = Product of means
Hence, 6 , 12 , 4 , 8 are in Proportion
Example 3
If 12 : 20 : : y : 10, find the value of y?
Explanation:
We know that, Product of means = Product of extremes
In the given numbers, we can say that 20 , y are means and 12 , 10 are extremes
20 x y = 12 x 10
y = (12 x 10)/20
y = 6
Hence, y = 6
Example 4
If 12 : y : : y : 48, find the value of y?
Explanation:
Clearly, Product of means = Product of extremes
y x y = 12 x 48
y² = 12 x 48
y² = 576
Hence, y = 24
Example 5
If 3 , 9 , y are in proportion, find the value of y?
Explanation:
3 , 9 , y are in proportion
Which means 3 , 9 , 9 , y are in proportion
i.e, 3 : 9 : : 9 : y
Product of Means = Product of Extremes
here,
Means = 9 and 9
Extremes = 3 and y
9 x 9 = 3 x y
81 = 3 x y
y = 81/3
Hence, y = 27
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