Question

How do you solve x in $\dfrac{x}{8}=\dfrac{4.5}{12}$ ?

Answer 1

Hint: We need to solve the problem by the method of cross-multiplication. Let us consider the four numbers to be a, b, c and d respectively. We have the question in the form \[\dfrac{a}{b}=\dfrac{c}{d}\] (we have to always keep in mind that b and d are always non-zero), so after cross multiplication, it becomes as $a\times d=b\times c$ . Now to obtain a, we can rearrange as \[a=\dfrac{b\times c} {d}\] and hence obtain our final answer.

Complete step by step solution:
We have an equation and we have to find the values of x. We will do so by using the cross-multiplication method. In cross-multiplication method, we basically multiply the numerator of the first fraction with the denominator of the second and the denominator of the first is multiplied to the second.
We have the given equation as:
$\dfrac{x}{8}=\dfrac{4.5}{12}$
We can notice that it is of the form \[\dfrac{a}{b}=\dfrac{c}{d}\], where a=x, b=8, c=4.5 and d=12.
Now applying the formula $ a=\dfrac{b\times c}{d}$ to obtain x, we get
 $x=\dfrac{4.5\times 8}{12}$
To make the calculations simpler, we will remove the decimal point by converting it into fraction which is dividing it by 10 in this case.
$ \begin{align}
  & \Rightarrow x=\dfrac{45\times 8}{120} \\
 & \Rightarrow x=\dfrac{360}{120} \\
\end{align}$
$\Rightarrow x=3$
$\therefore $ The value of x is $3$ .

Note: The method of cross multiplication is also referred to as the Butterfly method. It is easy to subtract or add unlike fraction using cross multiplication. To change decimal into fraction we remove the point from the decimal and write the fraction numerator is the number without the decimal and denominator is $10^{n}$ where n is the number of digits before the decimal in the decimal number given. Example: 4.55 in fraction is = $\dfrac{455}{100}$