Question

What are the equivalent fractions to \[\dfrac{3}{7}\] ?.

Answer 1

Hint: These types of problems can be solved efficiently once we understand the underlying concepts behind the question. To solve this problem, we need to have a basic knowledge and idea of fractions and ratio and proportions. We first of all need to understand the problem statement very carefully. Here we need to write down some of the possible fractions that can be formed, which is equivalent to the fraction \[\dfrac{3}{7}\] . This can be done by multiplying any real number on the numerator as well as on the denominator and this will result in the given fraction.

Complete step by step answer:
Now we start off with the solution to the given problem by writing that, any real number multiplied on the numerator and the denominator of the fraction \[\dfrac{3}{7}\] will result to a fraction which is equivalent to \[\dfrac{3}{7}\] . This is because when we cancel out the common terms, both the terms from the numerator and the denominator gets cancelled and we are only left with the fraction \[\dfrac{3}{7}\] . So some of the examples that we can create from the fraction \[\dfrac{3}{7}\] are,
\[\begin{align}
  & \dfrac{3\times 2}{7\times 2}=\dfrac{6}{14} \\
 & \dfrac{3\times 3}{7\times 3}=\dfrac{9}{21} \\
 & \dfrac{3\times 1.2}{7\times 1.2}=\dfrac{3.6}{8.4} \\
\end{align}\]
And so on…

Note: For solving such problems we need to have a thorough idea of fractions and ways of representing a fraction. We must note down that any possible real number multiplied both on the numerator and the denominator will give us our required answer. We must also be careful about not converting the fraction to decimal form or else it may lead to an error in the solution to the problem. We should also take care while multiplying the numbers, as a small error may lead to not being able to revert back to the original fraction.