Which of these rational numbers is ALREADY in standard form?

Class 7Rational NumbersRational Numbers

A $\frac{7}{9}$
B $\frac{15}{20}$
C $\frac{6}{- 11}$
D $\frac{- 8}{- 3}$

Step-by-Step Solution

\frac{7}{9}

: the denominator is positive and GCD(7, 9) = 1, so it is in standard form.

\frac{15}{20}

still has the common factor 5.

\frac{6}{- 11}

and

\frac{- 8}{- 3}

both fail the positive-denominator condition, even though nothing can be cancelled in either — being in lowest terms alone is not enough.

Answer: A)

\frac{7}{9}

Key idea: Recognising rationals

If you can write a number as **integer over non-zero integer**, it is rational. So:

- All integers are rational: 5 = 5/1, 0 = 0/1, −9 = −9/1.
- All fractions with integer numerator and denominator are rational: 3/4, −2/7, 11/3.
- Any decimal that terminates or repeats is rational: 0.25 = 1/4, 0.333… = 1/3.

Numbers that cannot be written as p/q (like √2 or π) are NOT rational — they're irrational. You'll meet those in Class 9.

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