Students can download Chapter 2 Whole Numbers Ex 2.3 KSEEB Solutions for Class 6 Maths helps you to revise the complete syllabus.

## Karnataka State Syllabus Class 6 Maths Chapter 2 Whole Numbers Ex 2.3

Question 1.

Which of the following will not represent zero:

a) 1 + 0

b) 0 × 0

c) \(\frac{0}{2}\)

d) \(\frac{10-10}{2}\)

a) 1 + 0 = 1 It does not represent zero

b) 0 × 0 = 0 It represent zero

c) \(\frac{0}{2}=0\) It represents zero

d) \(\frac{10-10}{2}=\frac{0}{2}=0\) It represent zero

Solution:

a) 1 + 0 = 1

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.

Solution:

If the product of 2 whole numbers is zero, then one of them is definitely zero,

For example, 0 × 2 =0 and 17 × 0 = 0

If the product of 2 whole numbers is zero them both of them may be zero 0 × 0 = 0

However, 2 × 3 = 6

(Since the number to be multiplied are not equal to zero, the result of the product will also be non-zero.

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?

Solution:

If the product of 2 numbers is, then both the numbers have to be equal to 1

For example, 1 × 1 = 1 However, 1 × 6 = 6

Clearly, the product of two whole numbers will be 1 in the situation when both numbers to be multiplied are 1.

Question 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 × (1000 + 1)

= 5437 × 1000 + 5437 × 1

= 5437000 + 5437 = 5442437

c) 824 × 25 = (800 + 024) × 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).

Solution

123456 × 8 + 6 = 987648 + 6 = 987654

1234567 × 8 + 7 = 9876536 + 7 = 9876543

Yes, the pattern works.

As 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