# Division of Rational Numbers

## Key Questions

• Your question should be more specific but i will give you answer which i think you are looking for

Suppose we are give something like this;

Divide $\frac{36}{5}$ by $3 x$

First things first take the MI of $3 x$ that is $\frac{1}{3} x$

so now multiply both the terms $\frac{36}{5} \cdot \frac{1}{3} x$

Which is nothing but $\frac{12 x}{5}$

if u want to break it into a decimal $2.4 x$

So id you meant anything other than this plz comment i will come up with a different answer

• The reciprocal of a number, $a$, is a number, $b$ such that
$a \times b = 1$

For Real numbers, other than 0, the reciprocal of $a$ is $\frac{1}{a}$.

(The number $0$ does not have a reciprocal because $0 \times b = 1$ has no solution. $0 \times n = 0$ for all real and complex $n$.)

• If the numbers have the same sign (both positive or both negative), then the answer is positive.
If the numbers have opposite signs (one is positive and the other is negative), then the answer is negative.

One way of explaining this:

The rule for dividing is the as same rule for multiplying positive and negative numbers.
The rule is the same because division is multiplying by the reciprocal.

The reciprocal of a positive number is positive and the reciprocal of a negative number is negative.

The reciprocal of $\frac{p}{q}$ is $\frac{1}{\frac{p}{q}}$ which is the same as $\frac{q}{p}$.

The reciprocal of a number is the number you have to multiply by to get $1$.

Not every number has a reciprocal. $0$ does not have a reciprocal (because $0$ times any number is $0$).

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