Estimating the Quotient

We will learn estimating the quotient.

To estimate the quotient, we first round off the divisor and the dividend to the nearest tens, hundreds, or thousands and then divide the rounded numbers.

In a division sum, when the divisor is made up of 2 digits or more than 2 digits, it helps if we first estimate the quotient and then try to find the actual number. 

(i) Divide 84 by 21 

Round the number to the nearest ten

84 ÷ 21 → 80 ÷ 20 

Calculate mentally. 

8 ÷ 2 = 4 

Estimated quotient = 4 


(ii) 242 ÷ 22 

Round to the nearest ten

240 ÷ 20

Calculate mentally

24 ÷ 2 = 12

Estimated quotient = 12

In the process of division, the estimation of quotient plays a great role in its solution. Let us see this in the following questions on division.

1. 74 ÷ 35

2. 627 ÷ 23

3. 694 ÷ 56

4. 975 ÷ 48

1. 74 ÷ 35 is approximately the same as 70 ÷ 40, i.e., 7 ÷ 4 (74 → 70 & 35 → 40)

7 ÷ 4 is approximately 2.

So, estimated quotient is 2.


2. 627 ÷ 23 is approximately the same as 600 ÷ 20 = 60 ÷ 2 = 30

(627 → 600 & 23 → 20)

So, the estimated quotient is 30.


3. 694 ÷ 56 is approximately the same as 700 ÷ 60 or 70 ÷ 6

70 ÷ 6 is approximately = 12.

So, the estimated quotient =12


4. 975 ÷ 48 is approximately 1000 ÷ 50 = 100 ÷ 5 = 20

So, estimated quotient = 20


Question and Answers on Estimation in Division:

1. Estimate by rounding each number and then divide. One is done for you. 

Estimation in Division

Answers:

(ii) 90 ÷ 30; Q = 3, R = 0

(iii) 300 ÷ 100; Q = 3, R = 0

(iv) 2400 ÷ 1000; Q = 2, R = 400

(v) 700 ÷ 200; Q = 3, R = 100

(vi) 5400 ÷ 4000; Q = 1, R = 1400

(vii) 9000 ÷ 6000; Q = 1, R = 3000

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