## Elementary Algebra

$= \frac{29}{12}$
1. Follow the acronym PEDMAS: P: arenthesis E: ponents D:ivision M:ultiplication A:ddition S:ubtraction $=$ P.E.D.M.A.S This is used to determine which order of operations is completed first from top to bottom. For example, you would complete the division of two numbers before the addition of another two numbers. In this case, we divide and multiply before subtracting: Note, we never can divide by a fraction, so we must multiply by the reciprocal of that fracton: $\frac{4}{5} \div \frac{1}{5} \times \frac{2}{3} - \frac{1}{4}$ $= \frac{4}{5} \times \frac{5}{1} \times \frac{2}{3} - \frac{1}{4}$ $= \frac{20}{5} \times \frac{2}{3} - \frac{1}{4}$ $= \frac{40}{15} - \frac{1}{4}$ (Simplify the first fraction) $= \frac{8}{3} - \frac{1}{4}$ 2. Find a common denominator when subtracting: In order to obtain a common denominator of $12$, we only have to multiply the first fraction by $4/4$ and the second fraction by $3/3$. $= \frac{8(4)}{12} - \frac{1(3)}{12}$ $= \frac{32}{12} - \frac{3}{12}$ $= \frac{29}{12}$