Elementary Algebra

$= \frac{-177}{10}$
Follow the acronym PEDMAS: P: arenthesis E: ponents D:ivision M:ultiplication A:ddition S:ubtraction This is used to determine order of operations, starting with parenthesis and ending with subtraction. For example, you would complete the division of two numbers before the addition of another two numbers. In this case, we consider the parenthesis, then the exponents, then multiply, and then add: $\frac{-4(2-5)^{2}}{5} + \frac{3(-1-6)}{2}$ $= \frac{-4(-3)^{2}}{5} + \frac{3(-7)}{2}$ $= \frac{-4(9)}{5} + \frac{3(-7)}{2}$ $= \frac{-36}{5} + \frac{-21}{2}$ (Note, the numerator and the denominator are treated like separate expressions. We completely simplify both before simplifying further). 2. Find a common denominator by multiplying the first fraction by $2$ and the second fraction by $5$. $= \frac{-36(2)}{10} + \frac{-21(5)}{10}$ $= \frac{-72}{10} + \frac{-105}{10}$ $= \frac{-72-105}{10}$ $= \frac{-177}{10}$