## Precalculus: Mathematics for Calculus, 7th Edition

a.) 3 b.) $\frac{13}{20}$
a.) $\frac{2}{3}$(6- $\frac{3}{2}$) Use the Distributive Property $\frac{2}{3}$$\times$$\frac{6}{1}$ - $\frac{2}{3}$$\times$$\frac{3}{2}$ Simplify $\frac{12}{3}$ - $\frac{1}{1}$ 4 - 1 = 3 b.) (3 + $\frac{1}{4}$)(1 - $\frac{4}{5}$) Use the Distributive Property 1(3 + $\frac{1}{4}$) - $\frac{4}{5}$(3 +$\frac{1}{4}$) Use Distributive Property again (1$\times$3 + 1$\times$$\frac{1}{4}) - (\frac{4}{5}$$\times$$\frac{3}{1} + \frac{4}{5}$$\times$$\frac{1}{4}$) Simplify 3 + $\frac{1}{4}$ - ($\frac{12}{5}$ + $\frac{4}{20}$) The Least Common Denominator of 1, 4, 5, and 20 = 20. Apply the minus sign (-1) to all variables in the parenthesis. $\frac{60}{20}$ + $\frac{5}{20}$ - $\frac{48}{20}$ - $\frac{4}{20}$ = $\frac{13}{20}$