Question

State whether the statements given are True or False

If $$\dfrac{p}{q}$$ is a rational number and m is a non-zero common divisor of p and q, then $$\dfrac{p}{q}=\dfrac{pm}{qm}$$.

Answer 1

Correct option is A. True
Let $$m=1,2...$$
When $$m=1,$$
$$\Rightarrow \dfrac{p}{q}=\dfrac{p÷1}{1÷q}$$
$$=\dfrac{p}{1}\times \dfrac{1}{q}=\dfrac{p}{q}$$
When $$m=2$$
$$\Rightarrow \dfrac{p}{q}=\dfrac{p÷2}{2÷q}$$
$$=\dfrac{p}{2}\times \dfrac{2}{q}=\dfrac{p}{q}$$
Hence, $$\dfrac{p}{q}=\dfrac{p÷m}{q÷m}$$