Compatible Numbers

Compatible numbers are numbers that help make doing mental math more manageable. They are typically used to estimate quotients. Consider finding the estimation of the following quotient. 612 ÷ 9 It might seem difficult to divide these numbers using mental math. However, both numbers can be rounded to compatible numbers — 612 to 600 and 9 to 10. An estimate for 612 ÷ 9 is then found by mentally dividing 600 by 10, which is equal to 60. That means the given quotient is estimated to be about 60.

The compatible numbers previously chosen are not the only options. Any numbers easily divisible and close to the original numbers are worth exploring. For example, rather than rounding 612 to 600, try 630. Notice that 63 is a multiple of 9. This makes 630 evenly divisible by 9. The estimate for the quotient is then 630÷ 9 = 70.

Compatible numbers are not used to get precise answers. They are used to get quick and rough approximations. The pairs of numbers in the multiplication table are also compatible numbers. This is why it is a good habit to choose a pair from the multiplication table when calculating a quotient. The following table shows some compatible numbers for different quotients.

Keep in mind that the estimates hold value as they are close to the exact values of the quotients.