Question

Find the fourth proportional 3, 12 and 4.

Answer 1

Hint: Here we have to find the fourth proportional of these three numbers. For that, we will assume the fourth to be x, then we will take the ratio of 3 and 12 and then we will take the ratio of 4 and the assumed variable x. We will equate the ratio of 3 and 12 with the ratio of 4 and x. After calculation, we will get the fourth proportional.

Complete step-by-step answer:
Let’s first assume the fourth number to be x.
To solve this question, we will first find the ratio of 3 and 12.
Ratio of 3 and 12
  $=\dfrac{3}{12}$
This ratio can be further simplified as
$=\dfrac{1}{4}$
Now, we will find the ratio of 4 and the assumed variable x.
So the ratio of 4 and x
$=\dfrac{4}{x}$
Now, we will equate the ratio of 3 and 12 with the ratio of 4 and x.
$\Rightarrow$ $\dfrac{1}{4}=\dfrac{4}{x}$
Now, we will apply the cross multiplication method here i.e. we will multiply the numerator of first fraction with the denominator of the second fraction and the numerator of second fraction with the denominator of the first fraction.
$\Rightarrow$ $1\times x=4\times 4$
On multiplying the terms on right hand side and left hand side, we get
$\Rightarrow$ $x=16$
So, the required fourth proportion of 3, 12 and 4 is 16.

Note: We have calculated the fourth proportional of three numbers, so we need to know the meaning of it before using it.
If there are four numbers, let say a, b, c and d, and if the ratio of ‘a’ and ‘b’ are equal to the ratio of ‘c’ and ‘d’ i.e. $a:b=c:d$ then we can say that a, b, c and d are in proportional and we can also say that a, b, c and d are proportional. If a, b, c and d are proportional, then ‘d’ , which is the last term is called as the fourth proportional.