Question

To reduce a rational number to its standard form, we divide its numerator and denominator by their :
a) LCM
b) HCF
c) Product
d) Multiple.

Answer 1

Hint: For these kinds of questions, we should initially know the concept of rational numbers. Rational numbers are a form of real numbers which can be expressed in $\dfrac{p}{q}$ where $p,q$ are integers and $q$ is not equal to $0$. Standard form of a number is the basic form. It cannot be reduced less than that. So we should divide both numerator and denominator of a rational number such that it should be reduced to it’s lowest form.

Complete step by step solution:

Let us take an example to understand better. We have a rational number $\dfrac{27}{81}$ . Both are divisible by $3$. So this rational number is not it’s lowest form.

Let us divide the numerator and denominator by $3$. 

Upon doing so, we get the following :

$\Rightarrow \dfrac{27}{81}=\dfrac{9}{27}$ 

$\dfrac{9}{27}$ is still divisible by $3$. So this rational number is also not in it’s lowest. 

Let us divide the numerator and denominator by $3$. 

Upon doing so, we get the following :

$\Rightarrow \dfrac{9}{27}=\dfrac{3}{9}$ 

$\dfrac{3}{9}$ is still divisible by $3$. So this rational number is also not in it’s lowest. 

Let us divide the numerator and denominator by $3$. 

Upon doing so, we get the following :

$\Rightarrow \dfrac{3}{9}=\dfrac{1}{3}$ 

$\dfrac{1}{3}$ is not divisible by $3$. The numerator and denominator are not divisible by the same number anymore. So this is the lowest form or the standard form of the rational number $\dfrac{27}{81}$.

So we divided this rational by $3$ three times or we divided this rational by $27=3\times 3\times 3$ .

HCF of $27$ and $81$ is $27$. As we observed, we divided the numerator and denominator with $27$

$\therefore $ Hence, to reduce a rational number to its standard form, we divide its numerator and denominator by their HCF. So, the correct answer is “Option B”.

Note: We should be aware of all the definitions of all these. We should also know how to find the least common multiple of LCM and highest common factor or HCF of two or more numbers. We should be careful while solving since there is a lot of scope for calculation errors. These questions alone would not be asked in the examination. But these would be helpful in simplifying a question further so as to get the answer. So a lot of practice is required to be able to do them quickly.