Estimating Quotients Using Compatible Numbers

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
Solution :-
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
Answer: 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
Solution:
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
Answer:- Hence we can say that 31 ÷ 5.2  gives a quotient that is about 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
Solution:-
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
Answer :-  So we can say that 1,053 divided by 42  gives a quotient that is about 25.