# 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

## You might like these

• ### Finding a Fraction of a Whole Number | Finding a Fraction of an Amount

How to find a fraction of a whole number? For finding a fraction of a whole number, we multiply the numerator of the fraction by the given number and then divide the product by the denominator

• ### Division by 10 and 100 and 1000 |Division Process|Facts about Division

Division by 10 and 100 and 1000 are explained here step by step. when we divide a number by 10, the digit at ones place of the given number becomes the remainder and the digits at the remaining places of the number given the quotient.

• ### 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.

• ### 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

• ### Successor and Predecessor | Successor of a Whole Number | Predecessor

The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number. For example, 9,99,99,999 is predecessor of 10,00,00,000 or we can also

• ### Types of Fractions |Like Fractions|Unit fractions|Proper & Improper Fr

The various types of fractions are: 1. Like fractions: The fractions having the same denominators are known as like fractions.

• ### 4th Grade Numbers Worksheets | Place Value Chart | Expended Form

In 5th Grade Numbers Worksheets we will solve how to read and write large numbers, use of place value chart to write a number in expanded form, represent the large number on the abacus, write the number in standard form, compare with another number and arrange numbers

• ### Word Problems on Division | Examples on Word Problems on Division

Word problems on division for fourth grade students are solved here step by step. Consider the following examples on word problems involving division: 1. \$5,876 are distributed equally among 26 men. How much money will each person get?

• ### Word Problems on Multiplication |Multiplication Word Problem Worksheet

Word problems on multiplication for fourth grade students are solved here step by step. Problem Sums Involving Multiplication: 1. 24 folders each has 56 sheets of paper inside them. How many sheets of paper are there altogether? Solution: We can add 56 sheets 24 times

• ### Division by Two-Digit Numbers | Knowledge of Estimation | Division

In division by two-digit numbers we will practice dividing two, three, four and five digits by two-digit numbers. Consider the following examples on division by two-digit numbers: Let us use our knowledge of estimation to find the actual quotient. 1. Divide 94 by 12

• ### Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

• ### Terms Used in Division | Dividend | Divisor | Quotient | Remainder

The terms used in division are dividend, divisor, quotient and remainder. Division is repeated subtraction. For example: 24 ÷ 6 How many times would you subtract 6 from 24 to reach 0?

• ### Multiplication | How to Multiply a One, Two or Three-digit Number?

In multiplication we know how to multiply a one, two or three-digit number by another 1 or 2-digit number. We also know how to multiply a four-digit number by a 2-digit number. We also know the different methods of multiplication. Here, we shall make use of the methods and

• ### Subtraction with Regrouping | 4-Digit, 5-Digit and 6-Digit Subtraction

We will learn subtraction 4-digit, 5-digit and 6-digit numbers with regrouping. Subtraction of 4-digit numbers can be done in the same way as we do subtraction of smaller numbers. We first arrange the numbers one below the other in place value columns and then we start

We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and ‘-‘ signs. We find the sum of the numbers with ‘+’ sign and similarly the sum

Related Concept