For Estimating Sums and Differences we use the concept of Rounding Off Numbers. Estimation is nothing but taking the values that is closer to the exact answer. Estimating Sums and Differences means writing answers that are approximately equal to the exact answer. Estimating the Values helps your child to improve mental math. Refer to the Solved Examples on Estimating the Sums and Differences explained step by step in the later modules.

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## How to Estimate the Sums and Differences of Whole Numbers?

Estimation means finding the answer closer to the accurate solution. The concept which is used for estimating addition and subtraction is round-off numbers. We can round the number nearest to ten, hundred, thousand, etc to estimate the answer. Bullet points to keep in mind is

- If the number is less than 5, round down (means 0)
- If the number is greater than 5, round up (means 1)

### Advantages of Estimating Sum and Difference

There are many benefits of estimating sums and differences. Some of the advantages are shown below.

- Estimating Addition and subtraction helps to improve mental math.
- Your fluency in calculation will be improved.
- You can understand the concept of rounding off numbers in the number system by learning the concept of estimation.

### Estimating Sums and Differences Examples

**Example 1.**

Estimate the sum of 79, 89, 58.

**Solution: **

9 is greater than 5, so you can add 1 to the tens place value and 0 to the unit place value.

The number 79 nearest to ten is 80

The number 89 nearest to ten is 90

The number 58 nearest to ten is 60

Now add three numbers 80 + 90 + 60 = 230

Now check whether the estimated answer is closer to the actual answer.

79 + 89 + 58 = 226

6 is greater than 5, so you can add 1 to the tens place value and 0 to the unit place value.

226 nearest to 10 is 230.

**Example 2.**

Estimate the difference between 219 and 17.

**Solution:**

9 is greater than 5, so you can add 1 to the tens place value and 0 to the unit place value.

7 is greater than 5, so you can add 1 to the tens place value and 0 to the unit place value.

219 nearest to ten is 220.

17 nearest to ten is 20.

Estimated difference is 220 – 20 = 200

Now check whether the estimated answer is closer to the actual answer.

219 – 17 = 202

202 nearest to ten is 200.

**Example 3.**

Estimate the sum and difference of 311 and 92.

**Solution:**

1 is less than 5, so you can round down to 0 to the unit place value.

2 is less than 5, so you can round down to 0 to the unit place value.

311 nearest to ten is 310

92 nearest to ten is 90

Estimated Sum: 310 + 90 = 400

Estimated Difference: 310 – 90 = 220

Now check if the estimated answer is closer to the actual answer.

311 + 92 = 403

403 is closer to 400.

311 – 92 = 219

219 is closer to 220.

So, the solution is correct.

**Example 4.**

Estimate the following additions and subtractions to the nearest ten, hundred and thousand.

i. 27 – 19

ii. 126 + 112

iii. 1002 + 996

iv. 2009 – 122

v. 39 – 12

**Solution:**

i. 27 – 19

9 is greater than 5, so you can add 1 to the tens place value and 0 to the unit place value.

7 is greater than 5, so you can add 1 to the tens place value and 0 to the unit place value.

27 to the nearest ten is 30.

19 to the nearest ten is 20.

Estimated Difference:

30 – 20 = 10

27 – 19 = 8

8 is closer to 10.

ii. 126 + 112

If the tens place is greater than 50, round up to the next hundred.

If the tens place is less than 50, round up to the previous hundred.

126 rounded to the nearest hundred is 100

112 rounded to the nearest hundred is 100

100 + 100 = 200

126 + 112 = 236

236 is closer to 200.

iii. 1002 + 996

If that digit is less than 5, you will round down to the previous thousand.

If that digit is greater than 5, you will round up to the next digit.

1002 to the nearest thousand is 1000.

996 to the nearest thousand is 1000.

1000 + 1000 = 2000

1002 + 996 = 1998

1998 is closer to 2000.

iv. 2009 – 122

If that digit is less than 5, you will round down to the previous thousand.

If that digit is less than 5, you will round down to the previous hundred.

2009 to the nearest thousand is 2000.

122 to the nearest hundred is 100.

2000 – 100 = 1900

2009 – 122 = 1880

1880 is closer to 1900.

v. 39 – 12

9 is greater than 5, so you can add 1 to the tens place value and 0 to the unit place value.

2 is less than 5, so you round down to 0 to the unit place value.

39 rounded to nearest ten is 40.

12 rounded to the nearest ten is 10.

40 – 10 = 30

39 – 12 = 27

27 is closer to 30.

**Example 5.**

Estimate the sum 711 and 625 to the nearest hundred.

**Solution:**

If that digit is less than 5, you will round down to the previous hundred.

If that digit is greater than 5, you will round up to the next hundred.

The unit place value is less than 5 so you have to round down to 0

711 number nearest to the hundred is 700.

The unit place value is equal to 5 so you have to round down to 0

625 number nearest to the hundred is 600.

700 + 600 = 1300

Now check if the estimated answer is closer to the actual answer.

711 + 625 = 1336

1336 is closer to 1300.

### FAQs on Estimation of Addition and Subtraction

**1. What is the actual difference and estimated difference?**

If the exact difference is obtained, then it is called the actual difference. The estimated difference means the difference is obtained from the rounding off the given numbers.

**2. How do you estimate the sum?**

We estimate the addition by rounding off to the nearest numbers.

**3. How do you estimate the difference?**

We estimate the subtraction by rounding off to the nearest place values.