Compatiblenumbers are numbers that can be divided easily. So it can be used to estimate the quotient. If two numbers are compatible, one divides the other evenly. The word 'compatible' means *well matched.* So compatible numbers are friendly numbers.

Nowlet us see a number 12 and 3 . They are compatible numbers because 3 divides 12 completely. 3 is a factor of 12 and 12 is a multiple of 3. So they are well matched and so they are compatible numbers.

But when 13 is to be divided by 3, we find a compatible number of 3, say 3x4="12" and 3 x 5 =15

12 is closer to 13 . so we say 3 divides 13 four times because 12 ÷ 3 = 4 . hence the quotient is about 4.

Let us do a few problems of estimating quotient using compatible numbers.

# Estimate 192 ÷ 5

Step 1 : 5 always divides numbers ending in 5 or 0

Step 2 : Let us round off 192 to 200

Step 3 : Let us divide 200 by 5 = 200 ÷ 5 = 40

Step 4 : The quotient is about 40

**Example on Estimating Quotient Using Compatible Numbers:-**

Let us do another problem to estimate quotient using compatible numbers:-

# Divide 31 by 5.5

Step1 : See whether 31 and 5.2 are compatible numbers. No. They are not.

Step2 : Let us find two numbers that are nearer to 31 and 5.2that are compatible.

Step3 : 30 is nearer to 31 and 5 is nearer to 5.2

Step4 : So let us divide 30 by 5. 30 ÷ 5 = 6

Step 5: The solution is 6

**Problems on Estimating Quotient Using Compatible Numbers:-**

Sofar we used compatible numbers of small size to estimate quotient. Now let us take a big number such as a four digit number and divide it by a two digit number.

# Estimate quotient of 1,053 divided by 42

Step 1 : Let us look at the divisor. It is 42. It can be rounded off to 40

Step 2 : Now let us look at the dividend. It is 1,053. Round it to 1,000

Step 3 : 1,000 and 40 are compatible numbers because if you cancel the 0's in the unit place in both numbers you get

100 and 4 and 100 ÷ 4 gives 25. hence 1,000 ÷ 40 also gives 25

Step 4 : Hence 1,053 ÷ 42 is about 25