2 Mark Question

Question 12 Marks

Find the following products, using distributive laws:
439 × 997

Answer

439 × 997= 439 × (1000 - 3)
= 439 × 1000 - 439 × 3 (Using distributive law of multiplication over addition)
= 439000 - 1317
= 437683

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Question 22 Marks

Find the value of the following using various properties:
569 × 17 + 569 × 13 + 569 × 70

Answer

559 × 17 + 569 ×13 + 569 × 70= 569 × (17 + 13 + 70)
= 569 ×100
= 569000 (By using distributive property)

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Question 32 Marks

Find the following products, using distributive laws:
245 × 1008

Answer

245 × 1008= 245 × (1000 + 8)
= 245 × 1000 + 245 × 8 (Using distributive law of multiplication over addition)
= 245000 + 1960
=246960

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Question 42 Marks

Determine the sums given below using suitable rearrangement.
15409 + 278 + 691 + 422

Answer

15409 + 278 + 691 + 422
(15409 + 278) + (691 + 422) (Using associative property of addition)
= 15687 + 1113
= 16800

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Question 52 Marks

Find a whole number n such that $n \div n = n$.

Answer

Given: $n \div n = n$
$\Rightarrow n n n n=n$
$\Rightarrow n=n^2$
i.e., the whole number $n$ is equal to $n^2$.
$\therefore$ The given whole number must be 1 .

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Question 62 Marks

Determine the following products by suitable rearrangements :
2 × 1658 × 50

Answer

2 × 16858 × 50= (2 × 50) × 1658
= 100 × 1658
= 165800

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Question 72 Marks

Determine the sums given below using suitable rearrangement.
3259 + 10001 + 2641 + 9999

Answer

3259 + 10001 + 2641 + 9999
(3259 + 10001) + (2641 + 9999) (Using associative property of addition)
= 13260 + 12640
= 25900

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Question 82 Marks

Find the following products, using distributive laws:
740 × 105

Answer

740 × 105= 740 × (100 + 5)
= 740 × 100 + 740 × 5 (Using distributive law of multiplication over addition)
= 74000 + 3700
= 77700

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Question 92 Marks

Add the following numbers and check by revershing the order of the addends:
19753 + 2867

Answer

19753 + 2867 = 22620
By reversing the order of the addends, we get:
2867 + 19753 = 22620
$\therefore$ 19753 + 2867 = 2867 + 19753

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Question 102 Marks

Use distributive law to find the value of:
1063 × 128 - 1063 × 28.

Answer

Using distributive law, we have:
1063 × 128 - 1063 × 28
= 1063 × (128 - 28)
= 1063 × 100
= 106300

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Question 112 Marks

Determine the sums given below using suitable rearrangement.
953 + 707 + 647

Answer

953 + 707 + 647
953 + (707 + 647) (Using associative property of addition)
= 953 + 1354
= 2307

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Question 122 Marks

There are six sections of Class VI in a school and there are 45 students in each section. If the monthly charges from each student be Rs. 1650, find the total monthly collection from Class VI.

Answer

Number of students in 1 section = 45
Number of students in 6 sections = 45 × 6 = 270
Monthly charges from 1 student = Rs. 1650
Therefore, Total monthly collection from class VI = Rs. 1650 × 270 = Rs. 4,45,500

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Question 132 Marks

Find the following products, using distributive laws:
996 × 367

Answer

996 × 367= 367 × (1000 - 4)
= 367 × 1000 - 367 × 4 (Using distributive law of multiplication over addition)
= 367000 × 1468
= 365532

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Question 142 Marks

Find the value of the following using various properties:
9870 × 561 - 9870 × 461

Answer

9870 × 561 - 9870 × 461= 9870 × (561 - 461)
= 9870 × 100
= 987000 (By using distributive property)

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Question 152 Marks

Add the following numbers and check by revershing the order of the addends:
16509 + 114

Answer

16509 + 114 = 16623
By reversing the order of the addends, we get:
114 + 16509 = 16623
$\therefore$ 16509 + 114 = 114 + 16509

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Question 162 Marks

Complete one of the following magic squares by supplying the missing numbers:

Answer

In a magic square, the sum of each row is equal to the sum of each column and the sum of each main diagonal. By using this concept, we have:

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Question 172 Marks

Determine the following products by suitable rearrangements :
4 × 927 × 25

Answer

4 × 927 × 25= (4 × 25) × 927
= 100 × 927
= 92700

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Question 182 Marks

Find the following products, using distributive laws:
947 × 96

Answer

947 × 96= 947 × (100 - 4)
= 947 × 100 - 947 × 4 (Using distributive law of multiplication over addition)
= 94700 - 3788
= 90912

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Question 192 Marks

Find the following products, using distributive laws:
2437 × 999

Answer

Distributive property of multiplication over addition states that a(b + c) = ab + acDistributive property of multiplication over subtraction states that a(b - c) = ab - ac
2437 × 999
= 2437 × (1000 - 1)
= 2437 × 1000 - 2437 × 1
= 2437000 - 2437
= 2434563

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Question 202 Marks

Find the following products, using distributive laws:
1553 × 198

Answer

1553 × 198= 1553 × (200 - 2)
= 1553 × 200 - 1553 × 2 (Using distributive law of multiplication over addition)
= 310600 - 3106
= 307494

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Question 212 Marks

Find the following products, using distributive laws:
847 × 99

Answer

Distributive property of multiplication over addition states that a(b + c) = ab + acDistributive property of multiplication over subtraction states that a(b - c) = ab - ac
847 × 99
= 847 × (100 - 1)
= 847 × 100 - 847 × 1
= 84700 - 847
= 83853

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Question 222 Marks

Find the sum: (1546 + 498) + 3589.
Also, find the sum: 1546 + (498 + 3589).
Are the two sums equal?
State the property satisfied.

Answer

We have:
(1546 + 498) + 3589 = 2044 + 3589 = 5633
Also, 1546 + (498 + 3589) = 1546 + 4087 = 5633
Yes, the two sums are equal.
The associative property of addition is satisfied.

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Question 232 Marks

Determine the following products by suitable rearrangements :
250 × 60 × 50 × 8

Answer

250 × 60 × 50 × 8= (250 × 8) × (60 × 50)
= 2000 × 3000
= 6000000

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Question 242 Marks

Add the following numbers and check by revershing the order of the addends:
2359 + 548

Answer

2359 + 548 = 2907
By reversing the order of the addends, we get:
548 + 2359 = 2907
$\therefore$ 2359 + 548 = 548 + 2359

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Question 252 Marks

How many whole numbers are there between 1032 and 1209?

Answer

Number of whole numbers between 1032 and 1209 = (1209 - 1032) - 1
= 177 - 1
= 176

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Question 262 Marks

Find the following products, using distributive laws:
472 × 1097

Answer

472 × 1097= 472 × (1000 + 97)
= 472 × 1000 + 472 × 97 (Using distributive law of
multiplication over addition)
= 472000 + 45784
= 517784

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Question 272 Marks

Determine the sums given below using suitable rearrangement.
2 + 3 + 4 + 5 + 45 + 46 + 47 + 48

Answer

2 + 3 + 4 + 5 + 45 + 46 + 47 + 48
(2 + 3 + 4 + 5) + (45 + 46 + 47 + 48) (Using associative property of addition)
= 14 + 186
= 200

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Question 282 Marks

Find the following products, using distributive laws:
3576 × 9

Answer

Distributive property of multiplication over addition states that a(b + c) = ab + acDistributive property of multiplication over subtraction states that a(b - c) = ab - ac
3476 × 9
= 3576 × (10 - 1)
= 3576 × 10 - 3576 × 1
= 35760 - 3576
= 32184

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Question 292 Marks

Complete one of the following magic squares by supplying the missing numbers:

Answer

In a magic square, the sum of each row is equal to the sum of each column and the sum of each main diagonal. By using this concept, we have:

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Question 302 Marks

Determine the following products by suitable rearrangements :
625 × 20 × 8 × 50

Answer

625 × 20 × 8 × 50= (20 × 50) × 8 × 625
= 1000 × 8 × 625
= 8000 × 625
= 5000000

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Question 312 Marks

Find the sum by short method:
6784 + 9999

Answer

6784 + 9999
= 6784 + (10000 - 1)
= (6784 + 10000) - 1 (Using associative property of addition)
= 16784 - 1
= 16783

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Question 322 Marks

Determine the following products by suitable rearrangements :
8 × 125 × 40 × 25

Answer

8 × 125 × 40 × 25= (8 × 125) × (40 × 25)
= 1000 × 1000
= 1000000

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Question 332 Marks

Complete one of the following magic squares by supplying the missing numbers:

Answer

In a magic square, the sum of each row is equal to the sum of each column and the sum of each main diagonal. By using this concept, we have:

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Question 342 Marks

Determine the following products by suitable rearrangements :
574 × 625 × 16

Answer

574 × 625 × 16= 574 × (625 × 16)
= 574 × 10000
= 5740000

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Question 352 Marks

Determine the sums given below using suitable rearrangement.
1983 + 647 + 217 + 353

Answer

1983 + 647 + 217 + 353
(1983 + 647) + (217 +353) (Using associative property of addition)
= 2630 + 570
= 3200

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Question 362 Marks

Determine the sums given below using suitable rearrangement.
1 + 2 + 3 + 4 + 96 + 97 + 98 + 99

Answer

1 + 2 + 3 + 4 + 96 + 97 + 98 + 99
(1 + 2 + 3 + 4) + (96 + 97 + 98 + 99) (Using associative property of addition)
= (10) + (390)
= 400

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Question 372 Marks

The product of two whole number is zero. What do you conclude?

Answer

If the product of two whole number is zero, then one of them is definitely zero.
Example: 0 × 2 = 0 and 0 × 15 = 0
If the product of whole number is zero, then both of them may be zero.
I.e. 0 × 0 = 0
Now, 2 × 5 = 10. Here, the product will be non-zero because the numbers to be multiplied are not equal to zero.

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Question 382 Marks

Complete one of the following magic squares by supplying the missing numbers:

Answer

In a magic square, the sum of each row is equal to the sum of each column and the sum of each main diagonal. By using this concept, we have:

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Question 392 Marks

Find the sum by short method:
10578 + 99999

Answer

10578 + 99999
= 10578 + (100000 - 1)
= (10578 + 100000) - 1 (Using associative property of addition)
= 110578 - 1
= 110577

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Question 402 Marks

Find the value of the following using various properties:
8759 × 94 + 8759 × 6

Answer

8759 × 94 + 8759 × 6= 8759 × (94 + 6)
= 8759 × 100
= 875900 (By using distributive property)

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Question 412 Marks

Write the three whole numbers occurring just before 10001.

Answer

Three whole numbers occurring just before 10001 are as follows:
10001 - 1 = 10000
10000 - 1 = 9999
9999 - 1 = 9998
$\therefore$ The three whole numbers just before 10001 are 10000, 9999 and 9998.

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Question 422 Marks

Find the value of the following using various properties:
16825 × 16825 - 16825 × 6825

Answer

16825 × 16825 - 16825 - 6825= 16825 × (16825 - 6825)
= 16825 × 10000
= 168250000 (By using distributive property)

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Question 432 Marks

For any whole numbers a, b, c, is it true that (a + b) + c = a + (c + b)? Give reasons.

Answer

For any whole numbers a, b and c, we have:
(a + b) + c = a + (b + c)
Let a = 2, b = 3 and c = 4 [we can take any values for a, b and c]
L.H.S. = (a + b) + c
= (2 + 3) + 4
= 5 + 4
= 9
R.H.S. = a + (c + b)
= a + (b + c) [$\because $ Whole numbers follow the commutative law]
= 2 + (3 + 4)
= 2 + 7
= 9
$\therefore$ This shows that associativity (in addition) is one of the properties of whole numbers.

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Question 442 Marks

Find the following products, using distributive laws:
580 × 64

Answer

580 × 64= 580 × (60 + 4)
= 580 × 60 + 580 × 4 (Using distributive law of multiplication over addition)
= 34800 + 2320
= 37120

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Question 452 Marks

Find the value of the following using various properties:
7459 × 999 + 7459

Answer

7459 × 999 + 7459= 7459 × (999 + 1)
= 7459 × 1000
= 7459000 (By using distributive property)

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Question 462 Marks