# What is 10 2/3- 5 9/10?

Jan 13, 2017

$\frac{143}{30}$

or

$4 \frac{23}{30}$

#### Explanation:

First, we need to convert these mixed numbers to improper fractions. To convert a mixed number to an improper fraction you multiply the integer portion by the correct form of $1$ and then add it to the fraction portion:

$\left(\left(10 \times \frac{3}{3}\right) + \frac{2}{3}\right) - \left(\left(5 \times \frac{10}{10}\right) + \frac{9}{10}\right)$

$\left(\frac{30}{3} + \frac{2}{3}\right) - \left(\frac{50}{10} + \frac{9}{10}\right)$

$\frac{30 + 2}{3} - \frac{50 + 9}{10}$

$\frac{32}{3} - \frac{59}{10}$

Next, to add or subtract fractions they need to be over common denominators, in this case $30$. We need to multiple each fraction by the appropriate form of $1$ to make the denominator $30$:

$\left(\frac{10}{10} \times \frac{32}{3}\right) - \left(\frac{3}{3} \times \frac{59}{10}\right)$

$\frac{10 \times 32}{10 \times 3} - \frac{3 \times 59}{3 \times 10}$

$\frac{320}{30} - \frac{177}{30}$

$\frac{320 - 177}{30}$

$\frac{143}{30}$

or

$143 \div 30 = 4$ with a remainder of $23 =$

$4 + \frac{23}{30} = 4 \frac{23}{30}$