Question

How do you solve the volume formula \[G = cd\], for \[d\]?

Answer 1

Hint: In the given question, we have been asked to solve the formula for\[d\]. In order to proceed with the following question we need to use the technique of transposing the terms. Transposing the term means moving terms from one side of the equation to another side of the equation, while keeping in mind the operations and their inverse operations. “ $ = $ ” acts as a balancing point between both the sides of the equation. Also, all the equations have two sides – LHS (Left Hand Side) and RHS ( Right Hand Side).

Complete step by step solution:
We are given,
\[G = cd\]
We need to find the formula for d, so we’ll perform inverse operation.
We’ll divide both the sides by c.
 $ \Rightarrow \dfrac{G}{c} = \dfrac{{c \times d}}{c} $
 $ \Rightarrow \dfrac{G}{c} = d $
This is the required formula
So, the correct answer is “ $ \dfrac{G}{c} = d $ ”.

Note: When a term is transposed from one side to another its operation changes to the inverse operation.
Four important rules are –
I.Inverse operation of addition is subtraction.
II.Inverse operation of subtraction is addition.
III.Inverse operation of multiplication is division.
IV.Inverse operation of division is multiplication.
V.Inverse operation of exponent is root
VI.Inverse operation of root is exponent.
Also, when we look at the signs of the terms-
Positive sign becomes negative after transposing it to the other side.
Negative sign becomes positive after transposing it to the other side.
This method helps us to avoid double writing of terms on both the sides and keeps the equation balanced.