To estimate sums and differences in number, we use the rounded numbers for estimates to the nearest tens, hundreds, and thousands.
Estimated sums:
In many practical calculations, only an approximation rather than an exact answer is required. For this purpose, numbers are rounded to a given place value of ten, hundred, thousand …
Example for estimating sums:
1. There are 74 coconut biscuits and 48 chocolate biscuits in one glass. Estimate the total number of cookies.
Round the numbers to the nearest ten and add up.
On TENS. rounded
There are around 120 cookies.
The actual number of cookies is 122.
The estimate deviates from the actual one by 2. from.
2. There are 275 students in the 4th grade and 238 students in the 5th grade. Estimate the total number of students in the two classes.
We can round up the numbers to either the nearest ten or the nearest hundred and add them up to get an estimate.
On TENS. rounded
There are about 520 students.
The estimate differs from the actual one by 7.
Rounded to HUNDREDS
There are about 500 students.
The estimate differs from the actual one by 13.
Estimating the difference:
Example for estimating the difference:
The school library has 284 natural science and 268 social science books.
Estimate the difference in the number of books.
On TENS. rounded
The difference is about 20 books.
The estimate differs from the actual number by 4.
Rounded to HUNDREDS
In this case, rounding up to hundreds does not make sense because the difference is 0.
Examples of estimating sums and differences in numbers:
1. The number of students in grades III, IV, and V is 154,129 and 118, respectively. Estimate the total number of students in the three grades.
Solution:
The rounded numbers are used for estimation.
154 ⇒ 200 is more than 150
129 ⇒ 100 is less than 150
118 100 less than 150. be
400 So the total estimated is 400
[Note: Actual number is 401, which is one more than 400]
Answer: 400
2. There are 479 girls and 729 boys in a school. Estimate the total number of students in the school.
Solution:
To estimate, the numbers can be rounded 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 Class IV math book and 196 pages in the English book of the same class. Estimate the difference in page numbers between the two books.
Solution:
We use the rounded numbers for estimation.
216 220
– 196 ⇒ 200
20th ⇒ 20th
The estimated difference in the number of pages is 20.
The actual difference is also 20.
4th Round up the numbers 324 and 777 to the nearest ten. Find the estimated and actual difference.
Solution:
Round off the numbers to the nearest ten
324 → 320 777 → 780
Therefore 780 – 320 = 460 is the estimated difference.
Actual difference
777 – 324 = 453 is the actual difference.
5. Round the numbers 423 and 885 up to the nearest 100. Find the estimated and actual difference.
Solution:
Round off the numbers to the nearest 100
885 → 900 423 → 400
Therefore 900 – 400 = 500 is the estimated difference.
Actual difference
885 – 423 = 462 is the actual difference.
Questions and answers about estimating sums and differences:
I. Find the estimated and exact difference for each of the items. The first is done for you.
II. Different types of toys are manufactured in a toy factory. Below is the number of different types of toys made in a month. Observe the data and answer the following questions.
Kind of toy Dolls cars Soft toy Superhero 
Quantity produced 6731 5974 6585 6842 
(i) What is the difference between the number of dolls and cars made in a month? Give your answer to the next 10 and 100.
Doll cars
(a) Next 10s: ____________ ____________
(b) Next 100s: ____________ ____________
(ii) If 1,600 superheroes are sold in the market, how many are there left for sale?
(iii) How many more soft toys should the factory make to make the number 7000?
Reply:
(i) (a) 6730; 5970
(b) 6700; 6000
(ii) 5242
(iii) 415
III. Round the numbers shown to the nearest ten. Find the estimated difference and the actual difference.
Estimated difference 
Actual difference 

(i) 254 of 875 
__________ 
__________ 
(ii) 214 of 784 
__________ 
__________ 
(iii) 657 of 954 
__________ 
__________ 
(iv) 21 of 287 
__________ 
__________ 
Reply:
III. (i) 630, 621
(ii) 570, 570
(iii) 290, 297
(iv) 270, 266
IV. Round the numbers shown to the nearest 100s. Find the estimated difference and the actual difference.
Estimated difference 
Actual difference 

(i) 121 of 145 
__________ 
__________ 
(ii) 124 of 448 
__________ 
__________ 
(iii) 215 of 659 
__________ 
__________ 
(iv) 347 of 728 
__________ 
__________ 
Reply:
IV. (i) 0.24
(ii) 300, 324
(iii) 500, 444
(iv) 400, 381
Related concept
● additive
● Word problems adding
● subtraction
● Check for subtraction and addition
● Word problems with addition and subtraction
● Estimating sums and differences
● Find the missing digits
● Multiply a number by a twodigit number
● Multiplication of a number by a 3digit number
● Multiply a number
● Appreciating products
● Word problems with multiplication
● Multiplication and division
● Terms used in divisions
● Division of twodigit by onedigit numbers
● Division of fourdigit numbers by onedigit number
● Division by 10 and 100 and 1000
● Share numbers
● Estimating the quotient
● Division by twodigit numbers
● Word problems with the division
4th grade math activities
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