# How do you subtract -1\frac { 9} { 10} - 4\frac { 2} { 5}?

Jul 21, 2017

See a solution process below:

#### Explanation:

To subtract these two numbers we first need to convert the mixed numbers into improper fractions:

$- 1 \frac{9}{10} - 4 \frac{2}{5} \implies - \left(1 + \frac{9}{10}\right) - \left(4 + \frac{2}{5}\right) \implies$

$- \left(\left[\frac{10}{10} \times 1\right] + \frac{9}{10}\right) - \left(\left[\frac{5}{5} \times 4\right] + \frac{2}{5}\right) \implies$

$- \left(\frac{10}{10} + \frac{9}{10}\right) - \left(\frac{20}{5} + \frac{2}{5}\right) \implies$

$- \frac{19}{10} - \frac{22}{5}$

Next, we need each fraction over a common denominator. We will multiply the fraction on the right by the appropriate form of $1$:

$- \frac{19}{10} - \left(\frac{2}{2} \times \frac{22}{5}\right) \implies$

$- \frac{19}{10} - \frac{44}{10}$

Then, we can subtract the numerators over the common denominator:

$- \frac{19}{10} - \frac{44}{10} \implies \frac{- 19 - 44}{10} \implies$

$- \frac{63}{10}$

Now, if necessary, we can convert the improper fraction into a mixed number:

$- \frac{63}{10} \implies - \frac{60 + 3}{10} \implies - \left(\frac{60}{10} + \frac{3}{10}\right) \implies - \left(6 + \frac{3}{10}\right) \implies$

$- 6 \frac{3}{10}$