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

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

The estimate differs from the actual one by 7.

Rounded to HUNDREDS

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]

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.

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?

(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 __________ __________

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 __________ __________

IV. (i) 0.24

(ii) 300, 324

(iii) 500, 444

(iv) 400, 381

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