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

The correct option is B

HCF

A rational number, in Mathematics, can be defined as any number which can be represented in the form of $\frac{p}{q}$ where $q\ne 0$. When the rational number is divided, the result will be in decimal form, which may be either terminating decimal or repeating decimal. The set of rational numerals include positive, negative numbers, and zero.

A standard form of a rational number

A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than $1$.

Conversion of rational numbers into standard form

A rational number is made up of a numerator and a denominator. A rational number is said to be in standard form if the Highest Common Factor or the H.C.F. of numerator and denominator is $1$.

• Whenever we have a rational number, first, we find the H.C.F. of numerator and denominator, if it is $1$ i.e. if the numerator and denominator of the rational number are coprime numbers, then the given rational number is in its standard form.
• If the numerator and denominator are not co-prime, then we start dividing both the numerator and denominator by the common factor of both. We keep on dividing the numerator and denominator with the common factors unless we get a numerator and denominator with H.C.F. equal to $1$.

Hence, option (B) is correct.