State whether the following statement is true or false:
To find an equivalent fraction of a given fraction, we may add or subtract the same (non-zero) number to its numerator and denominator.
Correct option is B. False
We know that, an equivalent fraction is a fraction that reduces to the same simplest fraction as the original fraction.
For example, $$\dfrac{2}{6}$$ and $$\dfrac{10}{30}$$ are equivalent fractions as they both reduce to the same simplest form $$\dfrac13$$.
To obtain an equivalent fraction of a given fraction, we multiply or divide the numerator and the denominator of the fraction with the same non-zero number.
For example, for obtaining an equivalent fraction of $$\dfrac28$$, we can:
Either multiply both $$2$$ and $$8$$ with $$3$$ for getting $$\dfrac{6}{24}$$.
or divide both $$2$$ and $$8$$ by $$2$$ for getting $$\dfrac{1}{4}$$.
Here, in both cases, the fractions obtained are the equivalent fraction of the original fraction.
Hence, the given statement is false.