Question

Find using distributive property.
 $ 728 \times 101 $

Answer 1

Hint: The distributive property helps us to rewrite the term in the parentheses as a sum of two different terms or we can also say that the term in the parentheses is distributed into two terms. We use the distributive property to make the calculations easier so that bigger terms can be multiplied with each other easily.

Complete step-by-step answer:
There are four main types of properties of numbers – Commutative property, Associative property, Identity property and Distributive property.
According to the commutative property, the numbers on which we perform mathematical operations have the same result irrespective of the order of arrangement of terms, associative property is similar to the commutative property, when three or more than three terms are added (or multiplied) the result is the same irrespective of the grouping of numbers. Identity property is followed by a number which after undergoing a mathematical operation gives its own value as the answer.
We have to find $ 728 \times 101 $ by the distributive property, so the statement can be rewritten as –
 $ 728 \times 101 = 728(100 + 1) $
Now, we multiply $ 728 $ individually with both the terms in the bracket that is $ 100 $ and $ 1 $
 $ 728(100 + 1) = 728 \times 100 + 728 \times 1 = 72800 + 728 $
Adding the two obtained terms we get –
 $ 728 \times 101 = 73528 $
Hence $ 73528 $ is the correct answer.
So, the correct answer is “ $ 73528 $ ”.

Note: 101 can be distributed in several ways but we know that multiplying a number with a multiple of 10 is the easiest so we rewrite the number keeping this thing in mind. As 100 is a multiple of 10 so we split the number 101 into the sum of 100 and 1. Thus the calculation has become very simple as the result of a number multiplied with one is the number itself and the sum of obtained terms can be found out easily.