## Chapter 2 Whole Numbers Exercise 2.3

**Question 1: Which of the following will not represent zero:**

a) 1 + 0

b) 0 × 0

c) 0/2

d) 10 - 10/2

Answer:

a) 1 + 0

b) 0 × 0

c) 0/2

d) 10 - 10/2

Answer:

a) 1 + 0 = 1

Therefore, it does not represent zero

b) 0 × 0 = 0

Therefore, it represents zero

c) 0/2 = 0

Therefore, it represents zero

d) 10 - 10/2 = 0/2 = 0

Therefore, it represents zero

**Question 2: If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.**

Answer:If product of two whole numbers is zero, definitely one of them is zero. Example: 0 × 5 = 0 and 1560 × 0 = 0. If product of two whole numbers is zero, both of them may be zero. Example: 0 × 0 = 0. Yes, if the product of two whole numbers is zero, then both of them will be zero

Answer:

**Question 3: If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.**

Answer:If the product of two whole numbers is 1, both the numbers should be equal to 1. Example: 1 × 1 = 1 but 1 × 15048 = 15048. Therefore, it’s clear that the product of two whole numbers will be 1, only in situation when both numbers to be multiplied are 1.

Answer:

**Question 4: Find using distributive property:**

a) 728 × 101

b) 5437 × 1001

c) 824 × 25

d) 4275 × 125

e) 504 × 35

Answer:

a) 728 × 101

b) 5437 × 1001

c) 824 × 25

d) 4275 × 125

e) 504 × 35

Answer:

a)

= 728 × 101

= 728 × (100 + 1)

= 728 × 100 + 728 × 1

= 72800 + 728

= 73528

b)

= 5437 × 1001

= 5437 × (1000 + 1)

= 5437 × 1000 + 5437 × 1

= 5437000 + 5437

= 5442437

c)

= 824 × 25

= (800 + 24) × 25

= (800 + 25 - 1) × 25

= 800 × 25 + 25 × 25 - 1 × 25

= 20000 + 625 - 25

= 20000 + 600

= 20600

d)

= 4275 × 125

= (4000 + 200 + 100 - 25) × 125

= (4000 × 125 + 200 × 125 + 100 × 125 - 25 × 125)

= 500000 + 25000 + 12500 – 3125

= 534375

e)

= 504 × 35

= (500 + 4) × 35

= 500 × 35 + 4 × 35

= 17500 + 140

= 17640

**Question 5: Study the pattern:**

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

Write the next two steps. Can you say how the pattern works? (Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

Answer:

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

Write the next two steps. Can you say how the pattern works? (Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

Answer:

123456 × 8 + 6 = 987654

1234567 × 8 + 7 = 9876543

123456 = (111111 + 11111 + 1111 + 111 + 11 + 1)

123456 × 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) × 8

= 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8

= 888888 + 88888 + 8888 + 888 + 88 + 8

= 987648

123456 × 8 + 6 = 987648 + 6

= 987654

Yes, here the pattern works.

1234567 × 8 + 7 = 9876543

Given 1234567 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1)

1234567 × 8 = (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8

= 1111111 × 8 + 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8

= 8888888 + 888888 + 88888 + 8888 + 888 + 88 + 8

= 9876536

1234567 × 8 + 7 = 9876536 + 7

= 9876543

Yes, here the pattern works.

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