How do you simplify -7 1/2 +5 1/3?

Jan 14, 2017

See entire simplification process below:

Explanation:

First, take each mixed fraction and convert it into an improper fraction:

$- \left(\left(\frac{2}{2} \times 7\right) + \frac{1}{2}\right) + \left(\left(\frac{3}{3} \times 5\right) + \frac{1}{3}\right)$

$- \left(\frac{14}{2} + \frac{1}{2}\right) + \left(\frac{15}{3} + \frac{1}{3}\right)$

$- \frac{15}{2} + \frac{16}{3}$

Next, we need to get each fraction over a common denominator (in this case $6$) so we can add the fractions. We do this by multiplying each fraction by the appropriate form of $1$:

$\left(- \frac{15}{2} \times \frac{3}{3}\right) + \left(\frac{16}{3} \times \frac{2}{2}\right)$

$- \frac{45}{6} + \frac{32}{6}$

Now, we can add the fractions:

$\frac{- 45 + 32}{6}$

$- \frac{13}{6}$

Or

$- 2 \frac{1}{6}$