Question

What fraction is equivalent to $\dfrac{1}{3}$?

Answer 1

Hint: Now we know that if we multiply a constant to the numerator and denominator of a fraction then the value of fraction will not change. Hence we can form equivalent fractions by just multiplying numerator and denominator of the fractions by a constant number.

Complete step by step solution:
Now let us first understand the concept fractions.
Fractions are nothing but numbers which represent parts of the whole.
A fraction is generally written as $\dfrac{p}{q}$ where p and q are integers such that q is not equal to 0. Now let us take an example of fractions. Suppose is a cake which is cut in 7 equal parts. Now we take 2 parts of the cake. Then this can be represented as $\dfrac{2}{7}$ . Hence we took ${{\dfrac{2}{7}}^{th}}$ of cake available.
Now let us say we multiply a number k to the numerator and denominator of the fraction. Then still we say the value of fraction is the same. Hence $\dfrac{2}{7}$ is the same as $\dfrac{2\times 2}{7\times 2}=\dfrac{4}{14}$ . Now using this concept we can say that we can create infinite fractions of the same value by just multiplying it to a constant term. Hence we get equivalent fractions.
Now let us consider the example $\dfrac{1}{3}$ .
We want to write the fraction equivalent to the given fraction.
Let us say we multiply 2 to the numerator and denominator of the fraction. We know that the value of the fraction will not change. Hence we get, $\dfrac{1\times 2}{3\times 2}=\dfrac{2}{6}$ . Hence one of the fraction equivalent to $\dfrac{1}{3}$ is $\dfrac{2}{6}$ .
Similarly we can make many other equivalent fractions of the same value.

Note: Now note that the numerator and denominator of the fractions can also be divided by the same value. Hence if we have $\dfrac{2}{6}$ on dividing the numerator and denominator by 2 we get the fraction as $\dfrac{1}{3}$ . Also when we have numerator and denominator such that it has no common factors then the fraction is said to be in simplest form.