Order of Operations and Algebraic Evaluation

Vocabulary and problem-based flashcards focusing on simplifying order of operations expressions and evaluating variable expressions based on Page 1 notes.

Order of Operations

The mathematical rules establishing the sequence for evaluating expressions: grouping symbols, exponents, multiplication and division from left to right, and addition and subtraction from left to right.

Simplifying $-6^2 + 2(8-5)^3 \div 3$

An expression simplified by evaluating inner parentheses $(8-5)^3 = 27$, applying exponents, performing multiplication and division $-36 + 54 \div 3 = -36 + 18$, and finishing addition.

Simplifying $9 - 1.5 - 5(4 + 3^3)$

An expression simplified by calculating inside parentheses $4 + 3^3 = 4 + 27 = 31$, followed by multiplication $5 \times 31 = 155$, yielding $9 - 1.5 - 155$.

Evaluating $-4x^2 + y^3 \div 5$ given $x = 2$ and $y = -5$

An algebraic evaluation computed by substituting the given values to obtain $-4(2)^2 + (-5)^3 \div 5 = -16 + (-125) \div 5 = -16 - 25 = -41$.

Evaluating $11 - 5y$ given $y = -5$

An algebraic evaluation computed by substituting $y = -5$ into the expression to obtain $11 - 5(-5) = 11 + 25 = 36$.

Evaluating $4(c + 5)$ given $c = -1$ and $f = 4$

An algebraic evaluation computed by substituting $c = -1$ into the expression to obtain $4(-1 + 5) = 4(4) = 16$.