Calculating a Fraction's Reciprocal

Question

Is there any way or equation that allows me to calculate the reciprocal of any fraction? I mean if i have 5/6 and i need it's reciprocal by using a formula or an equation to calculate it.

Is there or not? thanks all

$\left(\frac{x}{y}\right)^{-1} = \frac{y}{x} ;; x,y \neq 0$ – Daniel R Oct 31 '13 at 13:33 — Daniel R, Oct 31 '13 at 13:33
isn't it just f(x) = 1/x where x is that fraction? – kaine Oct 31 '13 at 13:33 — kaine, Oct 31 '13 at 13:33

score 3 · Accepted Answer · answered Oct 31 '13 at 13:34

3

Flip it, ${}{}{}{}{}{}{}$ (provided the numerator is not $0$.).

The reciprocal of $\;\dfrac xy,\;\; x, y \neq 0\;\;$ is given by $\;\dfrac 1{\left(\frac xy\right)} = \dfrac yx$.

So for your fraction, the reciprocal of $\dfrac 56$ is given by $ \dfrac 65$.

answered Oct 31 '13 at 13:34

amWhy

209,954

so there is no specific formula or equation to calculate it? just flipping it? – John Oct 31 '13 at 13:41
If you want an equation, then given the nonzero defined fraction $\frac xy$, it's reciprocal (also called its inverse) is given by $\left(\frac xy\right)^{-1} = \dfrac 1{\frac xy} = \frac yx$. This means whenever you multiply a fraction with its reciprocal, the answer will be $1$. The only rational number without a (mulitiplicative) inverse is $0$. You can also note that if we denote the reciprocal of $\dfrac xy$ as $r$, then we want $r$ such that $\frac xy \cdot r = 1 \iff r = \dfrac 1{\frac xy}$. – amWhy Oct 31 '13 at 13:44
@amWhy: Another TU 4 u +1 – Amzoti Nov 01 '13 at 12:08

Calculating a Fraction's Reciprocal

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