Question

Fill in the blanks:
\[8\times \left[ \left( -4 \right)\times 5 \right]=\left[ 8\times ...... \right]\times 5\]
(a) 8
(b) 6
(c) 4
(d) 5

Answer 1

Hint:Given expression in the problem is
\[8\times \left[ \left( -4 \right)\times 5 \right]=\left[ 8\times ...?... \right]\times 5\] \[\to \] (1)
As, we know rules of multiplications of signs are given as
Product of \[+\]and \[+=+\]
Product of \[-\]and \[+=-\]
Product of \[+\]and \[-=-\]
Product of \[-\]and \[-=+\]
Using this we solve the given question.

Complete step-by-step answer:
Let us solve the left hand side of the equation (1). As numbers\[-4\] and 5 are in multiplication. So, we can get products of them as\[-20\] because product of 4 and 5 is 20 and of \[-\] and \[+\]sign is \['-'\].
Hence, we can write the equation (1) as
\[8\times \left( -20 \right)=\left[ 8\times ? \right]\times 5\]
Now, we can get multiplication of 8 and\[-20\]as\[-160\]. So, we get
\[-160=\left[ 8\times ? \right]\times 5\]
On dividing the whole equation by 8 and 5, we get
\[\dfrac{-160}{8\times 5}=\dfrac{\left[ 8\times ? \right]\times 5}{8\times 5}\]
\[\dfrac{-160}{8\times 5}=?\]
\[\dfrac{-160}{40}=?\]
Now, we can divide 160 by 40 and hence get the result as 4. So, we get
\[\begin{align}
 & -4=? \\
 & ?=-4 \\
\end{align}\]
Hence, we need to fill the blank by \['-4'\].
So, option (c) is the correct answer.

Note: Don’t get confused with the multiplication of signs. As one may put the product of \[-4\] and 5 as 20, which is wrong. So, taking care of signs is a must while doing these kinds of questions and similarly with division of positive and negative numbers. It follows the same rule, which is followed by the multiplication of signs.