Question

Given the formula \[D = ABC\] , what is the formula for \[C\] ?

Answer 1

Hint: In this question, given the formula \[D=ABC\] and we need to find the formula of \[C\] with the help of the given formula . An expression is nothing but it is built up with integers, constants, variables. Mathematically, a symbol (letter) which doesn’t have a value is called a variable. Similarly when it has a fixed value it is called constant. We can find the formula of \[C\] by keeping \[C\] as stable and moving \[A\], \[B\] to the other side.

Complete step by step solution:
Given, \[D=ABC\]
The formula of \[D\] is given by the product of the three values \[A\], \[B\] and \[C\]. We need to find the formula of \[C\]. The formula of \[C\] can be found if it is drawn from the given formula by keeping \[C\] on one side and moving other terms to the opposite side.
\[D=ABC \]
First we need switch their sides,
\[\Rightarrow \ ABC=D \]
By keeping \[C\] as stable and moving \[A\],\[B\] to other side ,
We get, \[C = \dfrac{D}{{AB}}\]
Thus we get the formula of \[C\]
The formula of \[C\] is \[D\] divided by the product of \[A\] and \[B\].
The formula of \[C = \dfrac{D}{{AB}}\]

Note:
Mathematically, many expressions include variables. Variables are classified into free variables and bounded variables. A simple example of algebraic expression is \[3x+2\] , here \[x\] is the variable, \[3\] is the coefficient of \[x\] and \[2\] is the constant which also has a definite value. There are three types of expression namely monomial expression, binomial expression and polynomial expression.
Alternative solution :
We can also find the formula of \[C\] by division method.
Given,
\[D=ABC\]
We need to divide both sides by \[AB\] to find the formula of \[C\] by keeping the given expression balanced.
\[\Rightarrow \dfrac{D}{{AB}} = \dfrac{{ABC}}{{AB}}\]
[On the right side, \[A\] and \[B\] at both numerator and denominator get cancel out ]
By dividing,
We get,
\[\Rightarrow \dfrac{D}{{AB}} = C\]
Thus we get the formula of \[C\].