Question

Which of the following expressions is equal to $83 \times 5$?
A. $8 \times \left( {3 + 5} \right)$
B. $5 \times (8 + 3)$
C. $5 \times (80 + 3)$
D. $80 \times (3 + 5)$

Answer 1

Hint: Here we need to split the term such that after multiplication within the brackets we get the same number as we get after multiplication of the given quantity in the question. There is no need to apply the BODMAS rule here for solving. We can easily do it by simple observation.

Complete step by step answer:
In the above solution, we have to find which expression from the given options is the same as $83 \times 5$. We can also write it as $83 \times 5 = \left( {80 + 3} \right) \times 5$. We need to use distributive property in this question. so, first we should know what the distributive property is. According to the distributive property of multiplication, when we multiply a number with the sum of two or more addends, we get a result that is equal to the result that is obtained when we multiply each addend separately by the number. The distributive property of multiplication applies to the sum and the difference of two more numbers.

So, let’s check each option one by one to get to the final answer.In option (A) we have,
$8 \times \left( {3 + 5} \right)$
Here we can easily see that we are getting a small number as required in the given question.Therefore, option (A) is incorrect.

In option (B)
We have,
$5 \times (8 + 3)$
Here we can easily see that we are getting a small number as required in the given question.Therefore, option (B) is incorrect.

In option (C)
We have,
$5 \times (80 + 3)$
Also, in our question we have given $83 \times 5$. We can apply distributive property here.
If we apply distributive property in it, we can also split it as $\left( {80 + 3} \right) \times 5$ and it is the same as given in this option. Therefore, option (C) is correct.

In option (D)
We have,
$80 \times (3 + 5)$
We can also write it as
$ \Rightarrow \left( {80 \times 3} \right) + \left( {80 \times 5} \right)$
In the given question, we have
$83 \times 5 = \left( {80 + 3} \right) \times 5 = \left( {80 \times 5} \right) + \left( {3 \times 5} \right)$
Here we can easily see that we are getting a very large number as required in the given question. Therefore, option (D) is incorrect.

Therefore, option (C) is correct.

Note:There is an alternative to this question. We can solve this question by simply solving the quantity in the given question and then solving each option in the same manner and then we can check with which option our given quantity is matching. For example - $83 \times 5 = 415$is our required answer. In option (A) we are getting $8 \times \left( {3 + 5} \right) = 8 \times 8 = 64$, in option (B) we are getting $5 \times (8 + 3) = 5 \times 11 = 55$, in option (C) we are getting $5 \times (80 + 3) = 5 \times 83 = 415$ and in option (D) we are getting $80 \times (3 + 5) = 80 \times 8 = 640$.