Which rational numbers are their OWN reciprocal?

Class 7Rational NumbersRational Numbers

A1 and −1
B1 only
C0 and 1
DEvery rational number

Step-by-Step Solution

Flipping

\frac{1}{1}

gives

\frac{1}{1} = 1

, and flipping

\frac{- 1}{1}

gives

\frac{1}{- 1} = - 1

, so both are unchanged. 0 has NO reciprocal at all

(\frac{1}{0}

is not defined), which rules out "0 and 1". Every other rational changes when flipped, e.g.

\frac{2}{3}

becomes

\frac{3}{2}

Answer: A) 1 and −1

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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