Question

How do you solve $\dfrac{6}{8} = \dfrac{{12}}{x}$?

Answer 1

Hint: Here first of all we will take the expression and will perform cross-multiplication. In cross multiplication the denominator of one side is multiplied with the numerator of the other side and vice-versa. Then will remove common factors from the numerator and the denominator and then will simplify for the resultant required value for “x”

Complete step by step solution:
Take the given expression: $\dfrac{6}{8} = \dfrac{{12}}{x}$
Perform cross multiplication in the above equation, where the numerator of one side is multiplied with the denominator of the opposite side and vice-versa.
$ \Rightarrow 6 \times x = 12 \times 8$
Now, the term multiplicative at one end goes to the denominator if moved to the opposite side.
 \[ \Rightarrow x = \dfrac{{12 \times 8}}{6}\]
Find the factors on the numerator of the above equation.
 \[ \Rightarrow x = \dfrac{{6 \times 2 \times 8}}{6}\]
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator of the above expression.
 \[ \Rightarrow x = 2 \times 8\]
Simplify the above equation finding the product of two terms.
 \[ \Rightarrow x = 16\]
This is the required solution.
So, the correct answer is “x = 16”.

Note: Be very careful while simplifying the given expression, first step should be converted in the simplified form and then start the solution. Do it wisely since the entire solution depends on it only. Be good in multiple and remember at least till twenty. Always remember common factors from the numerator and the denominator cancel each other. Be good in finding the factors at times for the big numbers you have to find the prime factors to remove common factors from the numerator and the denominator and it can be done by using the long division method or factor tree method.