# Estimating the Quotient

We will learn estimating the quotient.

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

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