# Rational Numbers in Standard Form

## Notes

### Rational numbers in standard form:

• 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.

• Further, the negative sign occurs only in the numerator.

• The numbers (-1)/2, 3/7 etc. are in standard form.

• If a rational number is not in the standard form, then it can be reduced to the standard form.

• Thus, to reduce the rational number to its standard form, we divide its numerator and denominator by their HCF ignoring the negative sign, if any.

• If there is negative sign in the denominator, divide by ‘- HCF’.

## Example

Reduce (- 45)/30 to the standard form.

(- 45)/30 = (- 45 ÷ 3)/(30 ÷ 3) = (-15)/(10) = (- 15 ÷ 5)/(10 ÷ 5) = (-3)/2.

This could also be done as

(- 45)/30 = (- 45 ÷ 15)/(30 ÷ 15) = (-3)/2.

## Example

Reduce to standard form: 36/(−24)

The HCF of 36 and 24 is 12.

Thus, its standard form would be obtained by dividing by – 12.

36/(- 24) = (36  ÷  (- 12))/(- 24  ÷  (- 12)) = (- 3)/2.

## Example

Reduce to standard form: (- 3)/(- 15)

The HCF of 3 and 15 is 3.

Thus, (-3)/(- 15) = (-3  ÷  (- 2))/(- 15  ÷  (- 3)) = 1/5.

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Standard Form of Rational Numbers [00:14:47]
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