# 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.

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

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

## You might like these

• ### Place Value | Place, Place Value and Face Value | Grouping the Digits

The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know that the position of a digit in a number determines its corresponding value

• ### Worksheet on Word Problems on Division | Solve Division Problems

In worksheet on word problems on division, all grade students can practice the questions on word problems involving division. This exercise sheet on word problems on division can be practiced by the students to get more ideas to solve division problems.

• ### Worksheet on Estimating Sums and Differences | Find the Estimated Sum

In 4th grade worksheet on estimating sums and differences, all grade students can practice the questions on estimations.This exercise sheet on estimating sums and differences can be practiced

• ### Worksheet on Mixed Addition and Subtraction | Questions on Addition

In worksheet on mixed addition and subtraction the questions involve both addition and subtraction together; all grade students can practice the questions on addition and subtraction together.

• ### Worksheet on Word Problems on Addition and Subtraction Together | Ans

In 4th grade worksheet on word problems on addition and subtraction, all grade students can practice the questions on word problems based on addition and subtraction. This exercise sheet on

• ### Check for Subtraction and Addition | Checking Subtraction | Problems

We will learn to check for subtraction and addition answers after solving. Difference of two numbers is correct when the sum of the subtrahend number and the difference is equal to the minuend.

• ### Rounding off Numbers | Nearest Multiple of 10 | Nearest Whole Number

Rounding off numbers are discussed here, where we need to round a number. (i) If we purchase anything and its cost is $12 and 23¢, the cost is rounded up to it’s nearest$ 12 and 23¢ is left. (ii) If we purchase another thing and its cost is \$15.78. The cost is rounded up

• ### Standard Form of a Number | Expanded Form | Numeral in Standard Form

We will learn how to write the numeral in standard form. Here the standard form means the process of writing very large expanded form of a number into small form or small number. How to write the number in standard form? Here we will convert expanded form into standard

• ### Expanded Form of a Number | Writing Numbers in Expanded Form | Values

We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its digits. This is shown here: In 2385, the place values of the digits are

• ### Money Bills | Prepare a Bill for the Purchases | Copy of an Invoice

We often buy things and then we get money bills of the items. The shopkeeper gives us a bill containing information about what we purchase. Different items purchased by us, their rates and the total

• ### Worksheet on Bills | Bills & Billing of Different Items |Cost of items

We will practice the questions given in the worksheet on bills and billing of different items. We know bill is a slip of paper on which a shopkeeper notes down the requirements of a buyer

• ### Estimating Products | Estimation in Multiplication | Rounding Numbers

To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers. Estimating products by rounding numbers to the nearest ten, hundred, thousand etc., we know how to estimate

• ### Worksheet on Forming Numbers with Digits | Smallest & Greatest Numbers

In the worksheet on forming numbers with digits, the questions will help us to practice how to form different types of smallest and greatest numbers using different digits. We know that all the numbers are formed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

• ### Worksheets on Comparison of Numbers | Find the Greatest Number

In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging the numbers etc…. Find the greatest number:

• ### Formation of Greatest and Smallest Numbers | Arranging the Numbers

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the

Related Concept