Question

The value of $x$, for which the two rational numbers $\dfrac{3}{7}$, $\dfrac{x}{{42}}$ are equivalent, is:

Answer 1

Hint: Rational numbers are the numbers that can be expressed in the form of a fraction whose denominator is not equal to zero. For solving such numerical, we use cross-multiplication method wherein we multiply numerator of fraction A with denominator of fraction B and equate it to numerator of fraction B multiplied with denominator of fraction B. After equating both of them, we can easily find the value of $x$ .

Complete step by step answer:
The two rational numbers are equivalent, which means that the two numbers are equal.Therefore, we can write:
$\dfrac{3}{7} = \dfrac{x}{{42}}$
We know that 42 is a multiple of 7, we can simplify the equation, after which it becomes:
$\dfrac{3}{1} = \dfrac{x}{6}$
After cross-multiplication, the equation becomes:
$3 \times 6 = x$
$\therefore x = 18$

Therefore, the value of $x$ is 18.

Note: The common mistake while doing the simplification is, we write $\dfrac{3}{7} = \dfrac{x}{6}$ instead of $\dfrac{3}{1} = \dfrac{x}{6}$ which changes the entire answer. We need to be careful. Cross-multiplication has a very wide range of usage especially in solving complex questions. This question can also be solved by directly multiplying $42 \times \dfrac{3}{7}$ and finding the value of $x$.