Question

What are two equivalent fractions for $\dfrac{4}{7}$?

Answer 1

Hint: Now we know that the value of a fraction does not change if we multiply the numerator and denominator of the fraction by a common number. Hence we will find equivalent fractions of the given fractions by multiplying the numerator and denominator by common constant.

Complete step by step solution:
Now let us understand the concept of fractions.
Fractions are nothing but numbers which denote equal parts of the whole.
A fraction is generally written in the form $\dfrac{p}{q}$ where p and q both are integers such that q is not equal to 0. Here p is called the numerator of the fraction and q is called the denominator of the fraction.
Now let us understand the fraction with an example. Suppose we have cut a chocolate in 10 equal parts. Now suppose we take 4 parts out of 10 parts. Then the number can be represented as $\dfrac{4}{10}$ which means 4 parts out of 10 parts.
The value of fraction does not change if we multiply the numerator and denominator of the fraction by some constant.
Now consider the given fraction $\dfrac{4}{7}$ .
Now we can create equivalent fractions by multiplying the numerator and denominator of the fraction by the same number.
Let us say we multiply the numerator and denominator by 2 and 3. Hence we get the fractions as $\dfrac{8}{14}$ and $\dfrac{12}{21}$.
Hence the equivalent fractions of $\dfrac{4}{7}$ are $\dfrac{8}{14}$ and $\dfrac{12}{21}$ .

Note: Now note that we cannot add and subtract fractions generally. To add and subtract two fractions they must have the same denominator. Hence if we have different denominators we make them the same by writing their equivalent fractions such that we get a denominator of the fractions equal.