Estimating Sums and Differences

For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand.

Estimating Sums: 

In many practical calculations, only an approximation is required rather than an exact answer. To do this, numbers are rounded off to a given place value of ten, hundred, thousand ... 

Example on Estimating Sums:

1. There are 74 coconut cookies and 48 chocolate cookies in a jar. Estimate the total number of cookies.

Round the numbers to the nearest ten and add.

Rounded to TENS

Estimating Sums

There are approximately 120 cookies.

The actual number of cookies is 122.

The estimate differs from the actual by 2.

2. There are 275 students in class IVth and 238 students in class Vth. Estimate the total number of students in the two classes.

We can round the numbers either to the nearest ten or the nearest hundred and add to get an estimate.

Rounded to TENS


There are approximately 520 students.

The estimate differs from the actual by 7.

Rounded to HUNDREDS

Rounded to HUNDREDS

There are approximately 500 students. 

The estimate differs from the actual by 13. 

Estimating Difference: 

Example on Estimating Difference:

The school library has 284 science books and 268 social sciences books.

Estimate the difference in the number of books.

Rounded to TENS

Estimating Difference

The difference is approximately 20 books.

The estimate differs from the actual number by 4.

Rounded to HUNDREDS

Rounded nNumbers

In this case, rounding number to hundreds will not be meaningful as the difference will be 0.

Examples on estimating sums and differences of the numbers:

1. The number of students in Classes III, IV and V are 154,129 and 118. Estimate the total number of students in the three classes taken together.


The rounded numbers are used to estimate.

So         154     ⇒     200     being more than 150

            129     ⇒     100     being less than 150

            118     ⇒     100     being less than 150

                             400     So total number as estimated is 400

[Note: Actual number is 401, which is one more than 400]

Answer: 400

2. There are 479 girls and 729 boys in a school. Estimate the total number of students in the school.


For estimation the numbers may be taken to the nearest ten or hundred.

(i)         479     ⇒     480

            729     ⇒     730

          1208     ⇒     1210 

[Note: The estimated number is 1210 which is 2 more than the actual number]

(ii)         479     ⇒      500

            729      ⇒      700

          1208      ⇒     1200 

[Note: The estimated number is 1200 which is 8 less than the actual number]

3. There are 216 pages in the mathematics book of Class IV and 196 pages in the English book of the same class. Estimate the difference in the number of pages of the two books.


We use the rounded numbers for estimation.

            216     ⇒      220

           - 196     ⇒     200

               20     ⇒       20 

The estimated difference in number of pages is 20.
The actual difference is also 20.

Questions and Answers on Estimating Sums and Differences:

I. Find the estimated and exact difference for each of the given. First one is done for you.

Estimating Sums and Differences

II. In a toy factory different types of toys are manufactured. Given below is the number of different types of toys made in a month. Observe the data and answer the questions that follow.

Type of Toy



Soft Toys

Super Heroes

Quantity Manufactured





(i) What is the difference between the number of dolls and cars made in a month? Give your answer to nearest 10 and 100.

                                            Dolls                            Cars

          (a) Nearest 10s:    ____________            ____________

          (b) Nearest 100s:  ____________            ____________

(ii) If 1600 Super Heroes are sold in the market, then how many are left for sale?

(iii) How many more soft toys should be made in the factory to make the number 7000?


(i) (a) 6730; 5970

    (b) 6700; 6000

(ii) 5242

(iii) 415

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