Ratio and Proportion

A ratio is a relationship between two or more numbers or things. It tells us how a number or thing is related to another number(s) or thing(s). The ratio of two numbers is denoted as A∶ B or $A/B$. For example,

If the ratio of two numbers is 1:1 this means that both the numbers are equal.

The ratio of the Number of legs to the Number of the nose in human beings is 2:1.

If the ratio of two objects is same then the two objects are proportional or said to be in proportion. For example, $A/B$ and $C/D$ are said to be in proportion if and only if, $(A×D) = (C×B)$.

The Calculator:

This online calculator is very helpful in two different ways:

• It calculates the value of the unknown in the proportion.
• It also checks whether the values are in proportion or not.

If you have to find the missing value in the proportion then enter three values. After entering the values click on the “Calculate” button. The value of the fourth gets displayed on the screen.

If you have to check whether the values are in proportion or not, then enter all four values. Then click on the “Calculate” button. If they are in proportion then the result is TRUE otherwise FALSE.

If you want to work on any other values then click on the “Clear” button. The Calculator will clear all the data entered earlier. Then enter the values again for the calculations.

Calculation of the unknown value:

The calculations are as follow:

• For example, if the value of C is unknown then by using the condition of proportion: $(A×D) = (B×C)$.
• Therefore, we get $C =(A×D)÷B$
• Then, do algebraic calculations to obtain the value of the unknown.

For example, let the value of $A=5, B=10, and D= 50$.

• Then the value of $C = (5× 50)÷50$
• $C = 250÷50$

Hence, the value of $C = 50$.

Checking whether the values entered are in proportion or not:

It gets checked in very simple steps:

• Put the values of A, B, C, and D in the formula: $(A×D)=(B×C)$
• Then do algebraic calculations on the right-hand side and the left-hand side separately.
• Check whether the right-hand side is equal to the left-hand side.
• If yes, they are in proportion otherwise not.

For example, let the value of $A=10, B= 20, C=30, and D=60$.

• A×D=600
• B×C=600
• 600=600
• Since left-hand side is equal to the right-hand side, therefore the values entered are in proportion.

In this way, we get the result that the entered values are in proportion. However, if we entered A= 5, B= 6, C=10, and D=15. Then,

• $(A×D)=50$
• $(B×C)=60$
• $50≠60$
• The left-hand side is not equal to the right-hand side.
• Therefore, the entered values are not in proportion.

In this way, we come to know that the above-entered values are not in proportion.