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

Related Concept

Addition

Word Problems on Addition

Subtraction

Check for Subtraction and Addition

Word Problems Involving Addition and Subtraction

Estimating Sums and Differences

Find the Missing Digits

Multiplication

Multiply a Number by a 2-Digit Number

Multiplication of a Number by a 3-Digit Number

Multiply a Number

Estimating Products

Word Problems on Multiplication

Multiplication and Division

Terms Used in Division

Division of Two-Digit by a One-Digit Numbers

Division of Four-Digit by a One-Digit Numbers

Division by 10 and 100 and 1000

Dividing Numbers

Estimating the Quotient

Division by Two-Digit Numbers

Word Problems on Division


4th Grade Math Activities

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