Question

What is the RHS part of the equation: $36\left( {8 - 3} \right) = \_\_\_$?
A) $38 - 36$
B) $\left( {36 \times 8} \right) \times \left( {36 - 3} \right)$
C) $\left( {36 \times 8} \right) - \left( {36 \times 3} \right)$
D) $\left( {36 \times 8} \right) - 3$

Answer 1

Hint: In this question, we are given an LHS part of the equation and we have been asked the RHS part of the equation. Expand the given equation using the distributive law of multiplication which says that $a\left( {b + c} \right)$ can be expanded as $ab + ac$ and then choose the correct option.

Complete step-by-step answer:
We are given an LHS part of the equation and we have been asked the RHS part of the equation. The concept used here is – Distributive property of multiplication.
It tells us how an equation of the form $a\left( {b + c} \right)$ can be solved. If we follow BODMAS rule, first the brackets will be solved and then a will be multiplied to $d\left( {d = b + c} \right)$. But as per distributive property, we first multiply the number outside the brackets with the number in brackets first then, we will add or subtract it from the product of the number outside the brackets with the second number in brackets. It will be shown as below:
$ \Rightarrow a\left( {b + c} \right)$
$ \Rightarrow ab + ac$
Now, let us solve the question options wise:
Option (A): $38 - 36$
This option will be discarded as there is no sign of multiplication.
Option (B): $\left( {36 \times 8} \right) \times \left( {36 - 3} \right)$
The first term of this equation is correct but the second part has wrong sign and both the parts are connected by the sign of multiplication rather than the sign of subtraction.
Option (C) $\left( {36 \times 8} \right) - \left( {36 \times 3} \right)$
This option is the correct option as it follows the rule of distributive property.
Option (D) $\left( {36 \times 8} \right) - 3$
This option is completely wrong as the second term of the question has not been multiplied with the outside number.

Hence, our correct answer is option (C).

Note: If we had been asked to expand the equation, we could have used the rule of BODMAS as well. But in this question, options are given as per distributive property and hence, we will use the property instead of BODMAS rule.
BODMAS is a useful acronym that tells you the order in which you solve mathematical problems. It’s important that you follow the rules of BODMAS, because without it your answers can be wrong,
The BODMAS acronym for:
Brackets (parts of a calculation inside brackets always come first).
Orders (numbers involving powers or square roots).
Division
Multiplication
Addition
Subtraction