# How do you evaluate: One minus a negative one-third?

Feb 20, 2017

$1 - \left(- \frac{1}{3}\right) = \frac{4}{3}$

#### Explanation:

Subtracting a negative quantity is the same as adding the corresponding positive quantity.

So:

$1 - \left(- \frac{1}{3}\right) = 1 + \frac{1}{3} = \frac{4}{3}$

Feb 20, 2017

Writing this in mathematical terms gives the expression:

$1 - \left(- \frac{1}{3}\right)$

To solve, we first need to make the $1$ a fraction by multiplying by the appropriate form of $1$ so it has the same denominator as the fraction:

$\left(\frac{3}{3} \times 1\right) - \left(- \frac{1}{3}\right) \to$

$\frac{3}{3} - \left(- \frac{1}{3}\right)$

Knowing minus a minus is a plus we can rewrite this as:

$\frac{3}{3} + \frac{1}{3}$

Now we can solve by adding the numerators over the common denominator:

$\frac{3 + 1}{3}$

$\frac{4}{3}$