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Rational Numbers in Standard Form

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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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