Question

First guess the answer and then check it by calculating - \[42\times 23=?\]

Answer 1

Hint: In this question, we have to multiply a two-digit number with another two-digit number. So, firstly we separate each number in multiple of $10$, and then by multiplying each other, we will add all multiplications. The obtained addition is our multiplication answer.

Complete step-by-step solution:
According to the question, we have to multiply $42$ with $23$. So we will separate $42$ and $23$ in multiple of $10$. Doing this will result in,
$\begin{align}
  & 42=40+2 \\
 & 23=20+3 \\
\end{align}$
Now, for multiplication, we will consider the below table

Now, let us understand the explanation of multiplication performed in the above table.
(i) At first, multiplication of $20$ and $40$ - we will take all zeroes separately and multiply $2$ and $4$, then all zeroes will be added at last.
Last digits of $20\times 40\Rightarrow 00$
Multiplying $2$ and $4$ $\Rightarrow 2\times 4=8$
And then zeroes will be added, so finally we have $20\times 40=800$
(ii) Multiplication of $20$ and $2$ - separate zeroes and multiply $2\times 2$, then add zero.
Last digit of $20\times 2\Rightarrow 0$ and $2\times 2=4$
So, we have the result as $20\times 2=40$
(iii) Similarly, multiplication of $3$ and $40$
We get the last digit of $3\times 40\Rightarrow 0$ and $3\times 4=12$
So, we have the final answer as $3\times 40=120$
(iv) Multiplication of $3$ and $2$
$3\times 2=6$
Now, adding all multiplications, we have
$42\times 23=800+40+120+6=966$
So, the final answer is $42\times 23=966$.

Note: This question can also be solved by following method –
We will multiply one number with each digit of another number separately, and then add by keeping in mind that multiplication of number with unit digit will start one unit earlier with respect to multiplication of number with next digit in addition.
$\begin{align}
  & ~~~42 \\
 & \times 23 \\
 & \overline{\begin{align}
  & ~~~126 \\
 & +84\times \\
 & \overline{~~~966} \\
\end{align}} \\
\end{align}$ $\begin{align}
  & \Rightarrow 42 \\
 & ~~~~~\times 3 \\
 & ~~~~\overline{126} \\
\end{align}$ and \[\begin{align}
  & 42 \\
 & \times 2 \\
 & \overline{~84} \\
\end{align}\]
So, $42\times 23=966$.
(ii) Students should take care of addition at last in the question. There can be mistakes here and the answer will be wrong.