Exercise 2.3 - Chapter 2- Whole numbers - Ncert Solutions class 6 - Maths

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Question 1:
Which of the following will not represent zero:
(a) $1+0$
(b) $0 \times 0$
(c) $\frac{0}{2}$
(d) $\frac{10-10}{2}$

Answer 1:
(a) $[1+0$ is equal to 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.

Answer 2:
Yes, if we multiply any number with zero the resultant product will be zero.
Example: $\quad 2 \times 0=0,5 \times 0=0,9 \times 0=0$
If both numbers are zero, then the result also be zero.

$0 \times 0=0$

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

Answer 3:
If only one number be 1 then the product cannot be 1 .
Examples: $\quad 5 \times 1=5,4 \times 1=4,8 \times 1=8$
If both number are 1 , then the product is 1
$1 \times 1=1$

Question 4:
Find using distributive property:
(a) $728 \times 101$
(b) $5437 \times 1001$
(c) $824 \times 25$
(d) $4275 \times 125$
(e) $504 \times 35$

Answer 4:
(a)

$
\begin{aligned}
& 728 \times 101 \\
& =728 \times(100+1) \\
& =728 \times 100+728 \times 1 \\
& =72800+728 \\
& =73528
\end{aligned}
$

(c)

$
\begin{aligned}
& 824 \times 25 \\
& =824 \times(20+5) \\
& =824 \times 20+824 \times 5 \\
& =16480+4120 \\
& =20600
\end{aligned}
$

$
\text { (d) } \begin{aligned}
& 4275 \times 125 \\
& =4275 \times(100+20+5) \\
& =4275 \times 100+4275 \times 20+4275 \times 5 \\
& =427500+85500+21375 \\
& =534375
\end{aligned}
$

(e)

$
\begin{aligned}
& 504 \times 35 \\
& =(500+4) \times 35 \\
& =500 \times 35+4 \times 35 \\
& =17500+140 \\
& =17640
\end{aligned}
$

Question 5:
Study the pattern: 

$
\begin{array}{lll}
1 \times 8+1=9 ; & 12 \times 8+2=98 ; & 123 \times 8+3=987 \\
1234 \times 8+4=9876 ; & 12345 \times 8+5=98765 &
\end{array}
$
Write the next two steps. Can you say how the pattern works?
Answer 5:

$
\begin{aligned}
& 123456 \times 8+6=987654 \\
& 1234567 \times 8+7=9876543
\end{aligned}
$
Pattern works like this:

$
\begin{aligned}
1 \times 8+1 & =9 \\
12 \times 8+2 & =98 \\
123 \times 8+3 & =987 \\
1234 \times 8+4 & =9876 \\
12345 \times 8+5 & =98765 \\
123456 \times 8+6 & =987654 \\
1234567 \times 8+7 & =9875643
\end{aligned}
$