Estimating Sums and Differences

Introduction

Rounding each number before subtracting using rounded numbers is the simplest. Finding an answer that is closer to the correct solution is called estimating. Round-off numbers are a notion that is used to estimate addition and subtraction. To estimate the result, we can round the number to the closest ten, hundred, thousand, etc. Technique to estimate the difference between the given numbers. Although the result won't be a precise number, it will be close. We'll talk about the following in this chapter.

General rules of  Rounding

• Round down if the amount is less than five (means 0)

• Round up the number if it is larger than five (means 1) 

Estimating a Sum Definition

The estimation of a sum is close to the answer of an original sum, but it will not be exact. For example\[29 + 12 = 41\]. The estimated sum of \[29,12{\rm{ }}is{\rm{ }}30 + 10 = 40\]. We will understand it by solving various examples.

How to Estimate a Sum?

To estimate the sum of two numbers. Estimating a sum of numbers includes two following steps. They are as follows

• First, take the two given whole numbers.

• Now, consider the first number and round off the number to the nearest 10-place value.

• Again repeat the same step for the second number ie., round off to the nearest 10-place value.

• Next, Add those two rounded values and get the estimated sum for the given numbers.

Example of Estimating Sums

Example 1: Estimate the sum of 38,12 i.e., 38 + 12.

Solution:  We have to round the numbers to the nearest 10.

\[38{\rm{ }} \to {\rm{ }}40\]

\[12{\rm{ }} \to {\rm{ }}10\]

38 number is nearest to 40

And 12 is nearest to 10

Now we have to add the rounded numbers.

\[40{\rm{ }} + {\rm{ }}10{\rm{ }} = {\rm{ }}50\]

Therefore, the estimated sum of rounded 38, 12 is 50.

Example 2:Estimate the sum of 55,13 i.e. 55 + 13?

Solution: We have to round the number to the nearest 10.

\[55{\rm{ }} \to {\rm{ }}60\]

\[13{\rm{ }} \to {\rm{ }}10\]

55 is nearest to 60.

13 is nearest to 10.

Now we will add the rounded numbers.

60+10=70

Therefore, the estimated sum of 55,13 is 70.

Estimate Differences

How to Estimate Differences

In the last topic, we learned how to use rounding to estimate sums.

Do you know that you can also use rounding to estimate differences?

You can also estimate a difference by first rounding the minuend and subtrahend individually.

Then subtract the rounded numbers to get a difference that is close to the exact difference.

For Example, Estimating a Difference, 

Example 1 Estimate 923 - 486.

Ans:  Let’s round the numbers

Tip: Unless otherwise stated, always round each number to its highest place value. 

What's 923 rounded to the nearest hundred?

That's right, 900.

What's 486 rounded to the nearest hundred?

500.

Let's subtract those rounded values.

Estimated Example

So, the difference between 923 and 486 is about 400. 

Solved Questions

1:Estimate the sum of \[62,{\rm{ }}28?\]

Solution:

First, we have to round the numbers to the nearest 10.

\[62{\rm{ }} \to {\rm{ }}60\]

\[28{\rm{ }} \to {\rm{ }}30\]

so 62 is nearest to 60

28 is nearest to 30.

Now we will Add the rounded numbers.

\[60 + 30 = 90\]

Hence, the estimated sum of 62, 28 is 90.

2. Estimate the sum of \[57,{\rm{ }}78?\]

Solution:

Let’s round the numbers to the nearest 10.

\[57{\rm{ }} \to {\rm{ }}60\]

\[78{\rm{ }} \to {\rm{ }}80\]

so 57 is nearest to 60

78 is nearest to 80.

Now we will add the rounded numbers.

\[60 + 80 = 140\]

Hence, the estimated sum of 57, 78 is 140.

Summary

We looked at estimating the sums and calculating the difference in this chapter. Finding an answer that is closer to the correct solution is called estimating. Round-off numbers are a notion that is used to estimate addition and subtraction. To approximate the solution, we can round the number closest to ten, hundred, thousand, etc. We also solved approximate sums and differences questions by using a variety of examples.