Students can Download Chapter 2 Whole Numbers Ex 2.3 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 6 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.
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
It the product of 2 whole numbers is zero them both of them may be zero 0 × 0 = 0
However, 2 × 3 = 6
(Since 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