Question

What are three equivalent fractions for $\dfrac{3}{4}$?

Answer 1

Hint: Now we are given with the fraction $\dfrac{3}{4}$ . Now we know that if we multiply a constant term to the numerator and denominator then the value of the fraction does not change. Hence we will form new fractions by multiplying the constants to numerator and denominator.

Complete step-by-step solution:
Now first let us understand the concept of fraction. Fractions are rational numbers of the form $\dfrac{p}{q}$ where p and q are any integers such that q is not equal to 0. Now for a fraction of the form $\dfrac{p}{q}$ p represents the numerator and q represents the denominator. Now let us understand what a fraction represents. The fraction $\dfrac{p}{q}$ represents p parts of q. Hence a fraction in general represents parts of the whole.
Now consider the given fraction $\dfrac{3}{4}$ .
Now we know that the value of fraction does not change if we multiply numerator and denominator by the same number. Hence we will find the equivalent fractions by multiplying numerator and denominator by the same constant.
Hence if we multiply the numerator and denominator by 2, 3 and 4 respectively we get,
$\Rightarrow \dfrac{3\times 2}{4\times 2},\dfrac{3\times 3}{4\times 3},\dfrac{3\times 4}{4\times 4}$
Hence we get the fractions as $\dfrac{6}{8},\dfrac{9}{12},\dfrac{12}{16}$
Hence we get the equivalent fractions of $\dfrac{4}{3}$.

Note: Now note that on multiplying or dividing the numerator and denominator by the same number the value of fraction does not change. But if we add or subtract the numerator and denominator by the same number then the value of fraction changes. That is $\dfrac{p}{q}\ne \dfrac{p\pm k}{q\pm k}$