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

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

There are approximately 500 students.

The estimate differs from the actual by 13.

Estimating Difference:

To estimate the difference, we round-off each number to the nearest tens and then subtract the rounded-off numbers.

Let us estimate 48 - 22.

48 is nearer to 50 than 40. So, 48 is rounded up to 50.

The number 22 is nearer to 20 than 30.

So, 22 is rounded down to 20.

When we subtract a 2-digit number from another 2-digit number, we begin subtracting from the ones place.

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

Example on Estimating Difference:

1. Estimate the difference between 59 and 27.

When we estimate the difference between 59 and 27, we subtract the tens (50-20) and say that the difference is about 30.

Actual difference = 59 - 27 = 32

2. There were 82 mangoes in a bag. 38 rotten mangoes had to be thrown away. Estimate the number of good mangoes that remained in the bag?

8 tens less 3 tens = 5 tens. So about 50 good mangoes remained in the bag.

Actual difference = 82 - 38 = 44

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

Estimate the difference in the number of books.

Rounded to TENS

The difference is approximately 20 books.

The estimate differs from the actual number by 4.

Rounded to HUNDREDS

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.

Solution:

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]

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

Solution:

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.

Solution:

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.

4. Round off the numbers 324 and 777 to the nearest 10s. Find the estimated and actual difference.

Solution:

Rounding off the numbers to nearest 10s

324 320                           777 780

Hence, 780 – 320 = 460 is the estimated difference.

Actual Difference

777 – 324 = 453 is the actual difference.

5. Round off the numbers 423 and 885 to the nearest 100s. Find the estimated and actual difference.

Solution:

Rounding off the numbers to nearest 100s

885 900                           423 400

Hence, 900 – 400 = 500 is the estimated difference.

Actual Difference

885 – 423 = 462 is the actual difference.

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.

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 ToyDollsCarsSoft ToysSuper Heroes Quantity Manufactured6731597465856842

(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

III. Round off the given numbers to the nearest 10s. Find the estimated difference and actual difference.

 Estimated Difference Actual Difference (i) 254 from 875 __________ __________ (ii) 214 from 784 __________ __________ (iii) 657 from 954 __________ __________ (iv) 21 from 287 __________ __________

III. (i) 630, 621

(ii)  570, 570

(iii) 290, 297

(iv)  270, 266

IV. Round off the given numbers to the nearest 100s. Find the estimated difference and actual difference.

 Estimated Difference Actual Difference (i) 121 from 145 __________ __________ (ii) 124 from 448 __________ __________ (iii) 215 from 659 __________ __________ (iv) 347 from 728 __________ __________

IV. (i) 0, 24

(ii) 300, 324

(iii) 500, 444

(iv) 400, 381

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