Question

What is the value of $6\times 7\times 8$?

• A. $42$
• B. $56$
• C. $336$
• D. None of the above

Answer 1

The correct option is C $336$

To calculate $6\times 7\times 8$, we can follow one of the two following options:

1. First multiply $7$ and $8$, and then with the result multiply $6$, i.e., $6\times 7\times 8=6\times (7\times 8)$.
2. First multiply $6$ and $7$, and then with the result multiply $8$, i.e., $6\times 7\times 8=(6\times 7)\times 8$.

$\underset{–}{\text{Note:}}$ Multiplication is associative, i.e., here, $6\times 7\times 8=6\times (7\times 8)=(6\times 7)\times 8$.

In option $2$, after first multiplication, we get $42\times 8$, whereas, in option $1$, we get $6\times 56$. As $42$ is less than $56$, it might be easier to handle the further multiplication through option $2$.

Hence,
$6\times 7\times 8$
$=(6\times 7)\times 8$
$=42\times 8$
$=(40+2)\times 8$

Now, we use the box method to find out $(40+2)\times 8$.

	$40$	$2$
$8$	$8\times 40$ $=8\times 4\times 10$ $=32\times 10$ $=320$	$8\times 2$ $=16$

$\therefore (40+2)\times 8=320+16=336$

Hence, the value of $6\times 7\times 8$ is $336$, i.e., option (c.) is the correct one.