# How do you find the reciprocal of -5 1/3?

Feb 11, 2017

The reciprocal is $- \frac{3}{16}$.

#### Explanation:

To find the reciprocal of a mixed fraction, we need to first convert it into an improper fraction. This is done by multiplying the whole number with the denominator of the fraction, adding the product to the numerator of the fraction and placing it above the same denominator while retaining the sign. In the above case:

$- 5 \frac{1}{3} = - \frac{16}{3}$

Now, a reciprocal is a number which when multiplied by the original number, results in $1$. In the case of a fraction, this is determined simply by reversing the fraction and retaining the sign; i.e. by making the numerator the denominator and vice versa.

$\therefore - \frac{16}{3}$ becomes $- \frac{3}{16}$

We can check this out by multiplying the two.

$- \frac{16}{3} \times - \frac{3}{16}$

Since the product of two negatives is a positive, we can drop the negative signs.

$\frac{16}{3} \times \frac{3}{16}$

$\frac{1 \cancel{16}}{1 \cancel{3}} \times \frac{1 \cancel{3}}{1 \cancel{16}}$

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

Therefore the reciprocal of $- 5 \frac{1}{3}$ is $- \frac{3}{16}$