# How do you find the reciprocal of 3?

Jun 12, 2018

The reciprocal of a number is another word for its multiplicative inverse, or the number which gives 1 when multiplied by the original number.

To find the reciprocal of any number, simply take 1 and divide it by that number. So, the reciprocal of $3$ is:

$1 \div 3 = \textcolor{red}{\frac{1}{3}}$

We can check that this is the multiplicative inverse of $\textcolor{\lim e g r e e n}{3}$ by multiplying those two numbers together and seeing if we get 1:

$\textcolor{\lim e g r e e n}{3} \cdot \textcolor{red}{\frac{1}{3}} = \cancel{3} \cdot \frac{1}{\cancel{3}} = 1$

Hope this helps!

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As a side note for future problems, you may want to remember that the number $0$ does not have a reciprocal. This is because there isn't any number you can multiply by zero to get $1$. Try it for yourself $-$ you always get zero!

Jun 12, 2018

The reciprocal of $\frac{3}{1}$ is $\frac{1}{3}$

#### Explanation:

The reciprocal of a number is the same as its multiplicative inverse.

(The multiplying opposite)

It is the number 'turned upside down'.

The product of a number and its reciprocal is always $1$

$\frac{a}{b} \times \frac{b}{a} = 1$

$\frac{5}{2} \times \frac{2}{5} = 1$

So in this case, we can write $3$ as: $\frac{3}{1}$

The reciprocal is $\frac{1}{3}$

$\frac{3}{1} \times \frac{1}{3} = 1$

Note that $0$ does not have a reciprocal because you cannot turn $\frac{0}{1}$ upside down and then divide by $0$