Chapter - 2 Whole Numbers

Q&A -Ask Doubts and Get Answers

Q
Whole Number

Question:

1. Which of the following will not represent zero:

(a) 1 + 0    (b) 0 × 0    (c) frac{0}{2}    (d) frac{10 - 10}{2}

 

Solution: (a) 1 + 0 = 1

It does not represents zero.

 

(b) 0 × 0 = 0

It represents zero.

 

(c) {color{Blue} frac{0}{2} = 0}

It represents zero.

 

(d) {color{Blue} frac{10 - 10}{2} = frac{0}{2} = 0}

It represents zero.

 

Hence, only (a) does not represent zero.

 

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

 

Solution: Yes.

If the product of two whole numbers is zero, one number definitely will be zero.

Example: 1 x 0 = 0

If the product of two whole numbers is zero, both numbers can be zero itself.

Example: 0 x 0 = 0.

Yes,  if the product of two whole numbers is zero, we can say that one or both of them will be zero.

 

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.

 

Solution: No.

If the product of two whole numbers is 1, both the number should be equal to 1.

Example: 1 x 1 = 1.

If the product of two whole numbers is 1, it is not possible that one number is other than 1.

Example: 1 x 2 = 2.

The product of two whole numbers is 1 only in the case when both the numbers are 1.

 

4. Find using distributive property :

(a) 728 × 101     (b) 5437 × 1001     (c) 824 × 25     (d) 4275 × 125     (e) 504 × 35

 

Solution: (a) 728 × 101 

= 728 × (100 + 1)

= 728 × 100 + 728 × 1

= 72800 + 728

= 73528

 

(b) 5437 × 1001

= 5437 x (1000 + 1)

= 5437 × 1000 + 5437 × I

= 5437000 + 5437

= 5442437

 

(c) 824 x 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 x 125

= 500000 + 25000+ 12500 - 3125

= 534375

 

(e) 504 × 35

= (500 + 4) x 35

= 500 x 35 + 4 × 35

= 17500 + 140

= 17640

 

5. Study the pattern :

1 × 8 + 1 = 9                1234 × 8 + 4 = 9876

12 × 8 + 2 = 98            12345 × 8 + 5 = 98765

123 × 8 + 3 = 987

Write the next two steps. Can you say how the pattern works?

(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

 

Solution: The next two steps are:

Step 1: 123456 x 8 + 6 = 987654

Step 2: 1234567 x 8 + 7 = 9876543

Here the pattern work in this way, 

(1) x 8 + 1 = 9

(12) x 8 + 2 = 98

(123) x 8 + 3 = 987

(1234) x 8 + 4 = 9876

(12345) x 8 + 5 = 98765

 

Answer:


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