1. Proportion

2. Proportion
When two ratios (a:b) and (c:d) are equal, we say that the ratios are in proportion.
It is denoted as a:b :: c:d
Read as ‘a is to b’ as ‘c is to d’

3. Proportion law a : b :: c : d
If two ratios are in proportion i.e., a : b :: c : d then the product of extremes is equal to product of means.
Here a and d are called as extremes and b and c are the means
a : b :: c : d
Product of extremes = a x d
Product of means = b x c
Product of extremes = Product of means
a x d = b x c
Extremes
Means

4. Example 1 : Check whether 3:5 and 6:10 are in proportionality
Solution: To find if the two ratios are in proportion, Lets check if
Product of extremes = Product of means
3 x x 6
Hence they are in proportion
3 : :: : 10
Extremes
Means =

5. Example 2: Check whether 4:7 and 8:21 are in proportionality
Solution: To find if the two ratios are in proportion, Lets check if
Product of extremes = Product of means
4 x x 8
Hence they are not in proportion
4 : 7 :: : 21
Extremes
Means ≠

6. Given : The ratios 3:4 and 12:a are in proportionality
Example 3: If 3:4 and 12:a are in proportionality, find the missing term
Given : The ratios 3:4 and 12:a are in proportionality
We know that If two ratios are in proportion then
Product of extremes = Product of means
3 x a = x 12
3 x a =
a = ÷3
a =
Hence, a = 16
3 : 4 :: : a
Extremes
Means

7. Try these Check whether the following ratios are in proportions.
b. 4 : 2  10 : 15
2. If 3 : 6 and x : 12 are in proportion, Find the missing term