Estimating Sum and Difference
The procedure of estimating sum and difference are in the following examples.
Working Rules for Estimating Sum or Difference:
Step I: First we need to find the smaller number.
Step II: Then round off the all given numbers to the highest place value of that of the smaller number.
Step III: Finally add or subtract the rounded numbers as per the question.
Solved Examples on Estimating Sum or Difference:
1. Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.
Solution:
(i) Estimating the numbers 5290 and 17986 to their nearest hundreds, we get 5300 and 18000 respectively.
We have,
Therefore, estimated sum is 23300.
(ii) Estimating the numbers 5290 and 17986 to their nearest
hundreds, we get 5000 and 18000 respectively.
We have,
Therefore, estimated sum is 23000.
2. Estimate: 5673 – 436 by rounding off the numbers to their greatest places. Also,, find the reasonable estimate.
Solution:
We have, 5673 – 436 = 5237.
The greatest place in 5673 is thousands place and in 436 the greatest place is hundred place.
Estimating 5673 to nearest thousands, we get 6000
Estimating 436 to nearest hundreds, we get 400
Therefore estimated difference = 6000 – 400 = 5600
Clearly, it is not closer to the actual difference. So, it is not a reasonable estimate.
Let us round off 5673 and 436 to nearest hundreds.
5673 rounds off as 5700.
436 rounds off as 400
Therefore estimated difference = 5700 – 400 = 5300
3. Give a rough estimate and also a closer estimate of 489342 – 48365.
Solution:
We have,
489342 – 48365 = 440877
To find rough estimate, let us round off each number to nearest ten thousands.
489342 rounds off as 490000
48365 rounds off as 50000
Estimates difference = 490000 – 50000 = 440000
So, rough estimate = 440000
In order to obtain a closer estimate, let us round off each number to nearest thousands.
489342 rounds off as 489000
48365 rounds off as 48000
Estimated difference = 489000 – 48000 = 441000
Clearly, it is closer to the actual difference 440977
Hence, closer estimate is 441000
4. Estimate the following Sum or Difference:
(i) 578 + 1842
(ii) 8435 - 597
Solution:
(i) Estimate the sum of 578 + 1842
Out of 578 and 1842, the smaller number is 578.
Hence, we have to round off both the numbers (578 and 1842) to the nearest hundred.
578 to the nearest hundred = 600
1842 to the nearest hundred = 1800
|
1842 |
→ |
1800 | |||
|
578 |
→ |
+ 600 | |||
|
2400 |
Estimated value of 1842 + 578 = 2400
(ii) Estimate the difference of 7645 - 867
Out of 867 and 7645, the smaller number is 867.
Hence, we have to round off both the numbers (867 and 7645) to the nearest hundred.
867 to the nearest hundred = 900
7645 to the nearest hundred = 7600
|
7645 |
→ |
7600 | |||
|
867 |
→ |
- 900 | |||
|
6700 |
Therefore, the estimated value of 7645 - 867 = 6700.
Worksheet on Estimating Sum and Difference:
1. Estimate the following:
(i) 243 + 4272
(ii)145 + 2478
(iii) 1248 - 167
(iv) 8465 - 1234
(v) 243 + 1252
(vi) 2431 + 142
(vii) 243 + 178
(viii) 4217 - 398
Answer:
1. (i) 4500
(ii) 2600
(iii) 1000
(iv) 7300
(v) 1500
(vi) 2500
(vii) 400
(viii) 3800
2. Two different size of petrol tanks contain 6325 ℓ and 4890 ℓ water respectively. What is the estimated difference of petrol in the two tanks to the nearest hundred?
Solution:
7325 ℓ → 7300 ℓ (Round off to the nearest hundreds)
4890 ℓ → 4900 ℓ (Round off to the nearest hundreds)
The estimated difference of petrol in the two tanks = (7300 - 4900) ℓ
= 2400 ℓ
Therefore the required estimated difference = 2400 ℓ
● Estimate
Estimating Product and Quotient
You might like these
Counting Natural Numbers | Definition of Natural Numbers | Counting
Natural numbers are all the numbers from 1 onwards, i.e., 1, 2, 3, 4, 5, …... and are used for counting. We know since our childhood we are using numbers 1, 2, 3, 4, 5, 6, ………..
Reading and Writing Large Numbers | Large Numbers in Words in Billion
In reading and writing large numbers we group place values into periods ‘ones or unit’, ‘tens’, ‘hundred’, ‘thousand’, ‘10 thousand’, ‘100 thousand’, ‘million’, ’10 million’, ‘100 million
Numbers | Notation | Numeration | Numeral | Estimation | Examples
Numbers are used for calculating and counting. These counting numbers 1, 2, 3, 4, 5, .......... are called natural numbers. In order to describe the number of elements in a collection with no objects
Properties of Addition | Identity, Commutative, Associative, Additive
The properties of addition whole numbers are as follows: Closure property: If a and b are two whole numbers, then a + b is also a whole number. In other words, the sum of any two whole numbers i
Estimating Product and Quotient |Estimated Product |Estimated Quotient
The procedure of estimating product and quotient are in the following examples. Example 1: Estimate the product 958 × 387 by rounding off each factor to its greatest place.
Properties of Whole Numbers | Closure Property | Commutative Property
The properties of whole numbers are as follows: The number 0 is the first and the smallest whole numbers. • All natural numbers along with zero are called whole numbers.
Representation of Whole Numbers on Number Line | Compare Whole Numbers
Numbers on a line is called the representation of whole numbers on number line. The number line also helps us to compare two whole numbers, i.e., to decide which of the two given whole numbers
Properties of Subtraction |Whole Numbers |Subtraction of Whole Numbers
1. When zero is subtracted from the number, the difference is the number itself. For example, 8931 – 0 = 8931, 5649 – 0 = 5649 2. When a number is subtracted from itself the difference is zero. For example, 5485 – 5485 = 0 3. When 1 is subtracted from a number, we get its
Whole Numbers | Definition of Whole Numbers | Smallest Whole Number
The whole numbers are the counting numbers including 0. We have seen that the numbers 1, 2, 3, 4, 5, 6……. etc. are natural numbers. These natural numbers along with the number zero
Addition of Numbers using Number Line | Addition Rules on Number Line
Addition of numbers using number line will help us to learn how a number line can be used for addition. Addition of numbers can be well understood with the help of the number line.
Subtraction of Numbers using Number Line |Subtracting with Number Line
Subtraction of numbers using number line will help us to learn how a number line can be used for subtracting one number from the another number.
Worksheet on Reading and Writing Large Numbers|Writing Numbers in Word
Practice the questions given in the worksheet on reading and writing large numbers to group place values into periods in hundred, thousand, million and billion. The questions are related to writing
Worksheet on Estimation | Estimate the Product |Nearest Tens, Hundreds
Practice the questions given in the worksheet on estimation. The questions are based on estimating the sum, difference, product and quotient to the nearest tens, hundreds and thousands.
Properties of Adding Integers | Closure |Commutative | Associative ...
The properties of adding integers are discussed here along with the examples. 1. The addition (sum) of any two integers is always an integer. For example: (i) 5 + 9 = 14 ∈ Z (ii) (-5) + 9 = 4 ∈ Z
Subtracting Integers | Subtraction of Integers |Fundamental Operations
Subtracting integers is the second operations on integers, among the four fundamental operations on integers. Change the sign of the integer to be subtracted and then add.
6th Grade Page
From Estimating Sum and Difference to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Multiplication by Ten, Hundred and Thousand |Multiply by 10, 100 &1000
May 01, 25 11:57 PM
To multiply a number by 10, 100, or 1000 we need to count the number of zeroes in the multiplier and write the same number of zeroes to the right of the multiplicand. Rules for the multiplication by 1… -
Adding and Subtracting Large Decimals | Examples | Worksheet | Answers
May 01, 25 03:01 PM
Here we will learn adding and subtracting large decimals. We have already learnt how to add and subtract smaller decimals. Now we will consider some examples involving larger decimals. -
Converting Fractions to Decimals | Solved Examples | Free Worksheet
Apr 28, 25 01:43 AM
In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps: -
Expanded Form of a Number | Writing Numbers in Expanded Form | Values
Apr 27, 25 10:13 AM
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… -
Converting Decimals to Fractions | Solved Examples | Free Worksheet
Apr 26, 25 04:56 PM
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.