10. Add as indicated. (z)/(3)+(1)/(2) (z)/(3)+(1)/(2)=square (Simplify your answer.) the equation.

To add the fractions \(\frac{z}{3}\) and \(\frac{1}{2}\), we need to find a common denominator. The least common multiple of 3 and 2 is 6.<br /><br />First, rewrite each fraction with the common denominator of 6:<br /><br />\[<br />\frac{z}{3} = \frac{z \cdot 2}{3 \cdot 2} = \frac{2z}{6}<br />\]<br /><br />\[<br />\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}<br />\]<br /><br />Now, add the fractions:<br /><br />\[<br />\frac{2z}{6} + \frac{3}{6} = \frac{2z + 3}{6}<br />\]<br /><br />So, the simplified answer is:<br /><br />\[<br />\frac{z}{3} + \frac{1}{2} = \frac{2z + 3}{6}<br />\]