Compatible Numbers – Definition with Examples

What is Compatible Numbers?

In mathematics, compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.  Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier. We can round the numbers to the nearest ten, hundred, thousand or ten thousand to make them compatible numbers. For instance, if we have to add 493 and 549, we can make the numbers compatible by rounding them up to the nearest tens or hundreds. 490 and 550 (rounded to the nearest tens) or 500 and 500 (rounded to the nearest hundreds) are much easier to solve. 

So, we know the answer is about 1040 or 1000.

compatible numbers

 Let us see some examples to understand how we can perform subtraction, multiplication and division using compatible numbers. 

Subtraction:

Find the difference between 376.5 and 612.2

Here, we cannot find the difference between 376.5 and 612.2 easily as they are not compatible. So, we make the numbers compatible by rounding both the numbers to the nearest tens.

Actual DifferenceDifference using Compatible Numbers
subtraction without using compatible numbers376.5 changes to 380
612.2 changes to 610
610 – 380 = 230

Multiplication:

Find the product of 24.3 and 18.7.

It is difficult to find the product of 24.3 and 18.7 mentally and quickly. So, we use compatible numbers and find the product which is closer to the actual answer.

Actual ProductProduct using Compatible Numbers
multiplication without using compatible numbers24.3 changes to 24
18.7 changes to 20 
24 × 20 = 480

Division:

Divide 856 by 33.

To find the answer to 856 ÷ 33, will take us time as we need to divide to get the answer.

However, if we make the numbers compatible, we can mentally find an answer close to the actual answer as shown,

Actual DivisionQuotient using Compatible Numbers
division without using compatible numbers856 changes to  900 
33 changes to 30   
900 ÷ 30 = 30
Fun Facts
– Compatible numbers help in simplifying the calculation of an estimate only.