Estimating Sum and Difference

The procedure of estimating sum and difference are in the following examples.


Working Rules for Estimating Sum or Difference:

Step I: First we need to find the smaller number.

Step II: Then round off the all given numbers to the highest place value of that of the smaller number.

Step III: Finally add or subtract the rounded numbers as per the question.


Solved Examples on Estimating Sum or Difference:

1. Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.

Solution:

(i) Estimating the numbers 5290 and 17986 to their nearest hundreds, we get 5300 and 18000 respectively.

We have,

Estimating Sum and Difference





Therefore, estimated sum is 23300.

(ii) Estimating the numbers 5290 and 17986 to their nearest 

hundreds, we get 5000 and 18000 respectively.

We have, 

Estimated Sum is 23000





Therefore, estimated sum is 23000.


2. Estimate: 5673 – 436 by rounding off the numbers to their greatest places. Also,, find the reasonable estimate.

Solution:

We have, 5673 – 436 = 5237.

The greatest place in 5673 is thousands place and in 436 the greatest place is hundred place.

Estimating 5673 to nearest thousands, we get 6000

Estimating 436 to nearest hundreds, we get 400

Therefore estimated difference = 6000 – 400 = 5600

Clearly, it is not closer to the actual difference. So, it is not a reasonable estimate.

Let us round off 5673 and 436 to nearest hundreds.

5673 rounds off as 5700.

436 rounds off as 400

Therefore estimated difference = 5700 – 400 = 5300


3. Give a rough estimate and also a closer estimate of 489342 – 48365.

Solution:

We have,

489342 – 48365 = 440877

To find rough estimate, let us round off each number to nearest ten thousands.

489342 rounds off as 490000

48365 rounds off as 50000

Estimates difference = 490000 – 50000 = 440000

So, rough estimate = 440000

In order to obtain a closer estimate, let us round off each number to nearest thousands.

489342 rounds off as 489000

48365 rounds off as 48000

Estimated difference = 489000 – 48000 = 441000

Clearly, it is closer to the actual difference 440977

Hence, closer estimate is 441000


Estimating Sum or Difference

4. Estimate the following Sum or Difference:

(i) 578 + 1842

(ii) 8435 - 597

Solution:

(i) Estimate the sum of 578 + 1842

Out of 578 and 1842, the smaller number is 578.

Hence, we have to round off both the numbers (578 and 1842) to the nearest hundred.

578 to the nearest hundred = 600

1842 to the nearest hundred = 1800

1842

     1800

578

      

+    600  

     2400 

Estimated value of 1842 + 578 = 2400


(ii) Estimate the difference of 7645 - 867

Out of 867 and 7645, the smaller number is 867.

Hence, we have to round off both the numbers (867 and 7645) to the nearest hundred.

867 to the nearest hundred = 900

7645 to the nearest hundred = 7600

7645

    7600

867

      

-    900  

     6700 

Therefore, the estimated value of 7645 - 867 = 6700.


Worksheet on Estimating Sum and Difference:

1. Estimate the following:

(i) 243 + 4272

(ii)145 + 2478

(iii) 1248 - 167

(iv) 8465 - 1234

(v) 243 + 1252

(vi) 2431 + 142

(vii) 243 + 178

(viii) 4217 - 398


Answer:

1. (i) 4500

(ii) 2600

(iii) 1000

(iv) 7300

(v) 1500

(vi) 2500

(vii) 400

(viii) 3800


2. Two different size of petrol tanks contain 6325 ℓ and 4890 ℓ water respectively. What is the estimated difference of petrol in the two tanks to the nearest hundred?

Solution:

7325 ℓ    →   7300 ℓ (Round off to the nearest hundreds)

4890 ℓ    →   4900 ℓ (Round off to the nearest hundreds)

The estimated difference of petrol in the two tanks = (7300 - 4900) ℓ

                                                                          = 2400 ℓ

Therefore the required estimated difference = 2400 ℓ

Estimate

Estimate to Nearest Tens

Estimate to Nearest Hundreds

Estimate to Nearest Thousands

Estimating Sum and Difference

Estimating Product and Quotient

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