Question

Find the product using the suitable properties.
$854\times 102$

Answer 1

Hint: First we will write the definition of distributive We will break 102 into 100 + 2, and then we will use distributive property to solve the equation and that it will be easy to multiply small numbers like 2 and to multiply it by 100 is also easy.

Complete step-by-step answer:
Definition: The distributive property let us multiply a sum by multiplying each addend separately and then add the products.
Now we will use this definition to solve this question.
Let’s first write 102 = 100 + 2,
Now $854\times 102$,
$\begin{align}
  & =854\left( 100+2 \right) \\
 & =85400+854\times 2 \\
 & =85400+1708 \\
 & =87108 \\
\end{align}$
Hence, by using the distributive property we have easily solved the question.

Note: Here to solve this question we have used distributive property on 102 to solve this question. We can also solve this question by writing 854 as the sum of two numbers and then we can use distributive property to solve and we can see that the answer will be same, but the second way will take more amount of time and the calculation will also be a bit lengthy than the first method, so it is recommended to use the first method that have been shown in the solution.