# Estimating a Sum

We will learn the basic knowledge for estimating a sum. Here we will learn an easy way to estimate a sum of two numbers by rounding.

In case of two digit numbers we can only round the number to the nearest tens place i.e. only one place estimate.

For example, let us estimate the following sums:

(i) 47 + 32

We need to round the number to the nearest 10.

47 → 50

32 → 30

50 + 30 = 80

(ii) 25 + 34

We need to round the number to the nearest 10.

25 → 30

34 → 30

30 + 30 = 60

(iii) 75 + 13

We need to round the number to the nearest 10.

75 → 80

13 → 10

80 + 10 = 90

To estimate the sum we round-off each number to the nearest tens and then add the rounded-off numbers.

Let us estimate 38 + 23.

38 is nearer to 40 than 30.

So, 38 is rounded up to 40.

The number 23 is nearer to 20 than 30.

So, 23 is rounded down to 20.

Solved Examples on Estimating the Sum:

1. Estimate the sums of 72 and 48

Solution:

We round the number to the nearest 10.

72 → 70

48 → 50

So, 72 is nearest to 70 and 48 is nearest to 50

70 + 50 = 120

Thus the estimated sum = 120

2. Estimate the sums to the nearest ten and also find the actual sum of 87 and 79.

Solution:

We round the number to the nearest 10.

87 → 90

79 → 80

So, 87 is nearest to 90 and 79 is nearest to 80

90 + 80 = 170

Thus the estimated sum = 170

The actual sum of 87 and 79

87 + 79 = 166

Thus the actual sum = 166

Note: To estimate to the nearest 10, we see the digit/number at one’s place. It is converted to 0 or 10 as proper. If the digit/number is < 10/2, it is converted to zero and if it is > 10/2, it is converted to 10.

In case of three digit numbers we can only round the number to the nearest tens place i.e. only one place estimate.

For example, let us estimate the following sums:

1. Estimate the sums of 586 and 120

Solution:

We round the number to the nearest hundred.

586 → 600

120 → 100

So, 586 is nearest to hundred is 600 and 120 is nearest to hundred 100

600 + 100 = 700

Thus the estimated sum to nearest hundred = 700

We round the number to the nearest tens.

586 → 590

120 → 120

So, 586 is nearest to ten is 590 and 120 is nearest to hundred 120

590 + 120 = 710

Thus the estimated sum to nearest ten = 710

2. Round off the numbers 389 and 535 to the nearest 100s. Find the estimated and the actual sum.

Solution:

Rounding off the numbers to nearest 100s

Hence, 400 + 500 = 900 is the estimated sum.

In general

When we add two 2-digit numbers we begin adding from the ones place.

For estimating the sum of two 2-digit numbers, just add the tens place and add ten more. The actual answer may be a little more or a little less, but the difference will never be more than 10. That is a fair estimate.

3. Estimate the sum of 34 and 22.

Sotution:

 Step I: Add the tens.           30 + 20 = 50Step II: Add 10 to the sum obtained in step I.            50 + 10 = 60 Actual Sum           3     4     +    2     2           5     6

Thus, we say that the sum of 34 and 22 is about 60.

4. There are 45 mangoes and 28 oranges in a bag. About how many fruits are there in the bag?

 Solution:Step I: Add the tens.4 tens + 2 tens = 6 tens.40 + 20 = 60Step II: Add 10 to the sum obtained in step I.60 + 10 = 70So, there are about 70 fruits in the bag. Actual Sum           4     5     +    2     8           7     3

Questions and Answers on Estimating a Sum:

I. Estimate the sum. One has been done for you.

(i) 19 + 23

(ii) 27 + 44

(iii) 54 + 36

(iv) 41 + 38

(v) 52 + 17

(vi) 26 + 28

I. (ii) 30 + 40 = 70

(iii) 50 + 40 = 90

(iv) 40 + 40 = 80

(v) 50 + 20 = 70

(vi) 30 + 30 = 60

II. Round off the given numbers to the nearest 100s. Find the estimated and the actual sum.

 Estimated Sum Actual Sum (i) 582 and 157 __________ __________ (ii) 245 and 163 __________ __________ (iii) 812 and 111 __________ __________ (iv) 345 and 198 __________ __________

II. (i) 800, 739

(ii) 400, 408

(iii) 900, 923

(iv) 500, 543

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