Question

How do you solve $\dfrac{6}{18}=\dfrac{x}{36}$ ?

Answer 1

Hint: In this question we will use the geometric cross formula and rearrange both the sides of the expression, and then simplify terms on both the side of the expression by multiplying and dividing the terms to find the required value of $x$.

Complete step-by-step solution:
We have the expression as $\dfrac{6}{18}=\dfrac{x}{36}$
On cross multiplying the terms in the expression, we get:
 $\Rightarrow 6\times 36=x\times 18$
On dividing both the sides by $18$, we get:
 \[\Rightarrow \dfrac{6\times 36}{18}=\dfrac{x\times 18}{18}\]
On simplifying the terms, we get:
\[\Rightarrow 6\times 2=x\]
On rearranging the expression, we get:
\[\Rightarrow x=6\times 2\]
On multiplying the terms, we get:
\[\Rightarrow x=12\], which is the required final answer.

Note: The cross formula is used to simplify the terms because an equation which has two fractions, their value won’t be changed if they are multiplied or divided by the name number.
The main reason for using cross multiplication is to compare the fractions, it tells us which fraction is greater and which one is smaller. It is useful when working with large fractions which are complex to reduce.
It is to be remembered that while cross multiplying when a term which is multiplication and division will change into division and multiplication respectively.
Similarly, when a term which is positive or negative when transferred across the $=$ sign will become negative or positive respectively.
The cross formula is also used to find out the missing value of a term by considering it to be $x$.
It is to be remembered that the denominator of a fraction cannot be zero because division by zero is unacceptable in mathematics.
It is not compulsory that both the sides will have fractions, a number with no denominator always has as the denominator.