Question

What is the product of 8 and 54?

Answer 1

Hint: We can solve this problem by using the algebraic identities to make the calculations easy.
We use the distributive property in algebra which is given as,
$a\left( b\pm c \right)=ab\pm ac$
We divide the bigger number as a sum of two numbers such that the calculations become easy.

Complete step by step answer:
We are asked to find the value of products 8 and 54.
Let us assume that the required value of the product as $'x'$ then we get,
$\Rightarrow x=8\times 54$
Here, we can see that finding the product of the above equation is a bit difficult.
So, let us divide the bigger number that is 54 as the sum of two numbers so that the calculations can be made easy and also we can use the distributive property.
Let us divide the number 54 as sum of two numbers then we get,
$\Rightarrow x=8\times \left( 50+4 \right)$
We know that the distributive property in algebra which is given as,
$a\left( b\pm c \right)=ab\pm ac$
By using the distributive property to above equation then we get,
$\Rightarrow x=\left( 8\times 50 \right)+\left( 8\times 4 \right)$
Here, we can see that the value of the first bracket is 400 and the value of the second bracket is 32.
By substituting the required values in above equation then we get,
$\begin{align}
  & \Rightarrow x=400+32 \\
 & \Rightarrow x=432 \\
\end{align}$
Therefore, we can conclude that the value of product of 8 and 54 is 432 that is,
$\therefore 8\times 54=432$

Note: Here we can see that the number 54 is divided as sum of two numbers as,
$\Rightarrow 54=50+4$
But, we know that the number 54 can be divided as sum of two numbers in so many ways like,
$\begin{align}
  & \Rightarrow 54=49+5 \\
 & \Rightarrow 54=45+9.......\text{so on} \\
\end{align}$
Here, we can see that there are many possibilities but we need to choose the combination that gives the easy calculations.
So dividing 54 as a sum of 50 and 4 is the best way to solve this problem.