Order of Operations Practice Problems

Vocabulary practice flashcards evaluating arithmetic expressions involving exponents, multiplication, division, addition, and subtraction following the order of operations.

$$7 - (-8)^2 \div 4 \times (-4)$$

$71$ (Evaluating by order of operations: first calculate the exponent $(-8)^2 = 64$, then divide $64 \div 4 = 16$, then multiply $16 \times (-4) = -64$, and finally subtract $7 - (-64) = 71$)

$$7 + (-7)^2 \times (-2) - 3$$

$-94$ (Evaluating by order of operations: first calculate the exponent $(-7)^2 = 49$, then multiply $49 \times (-2) = -98$, then add $7 + (-98) = -91$, and finally subtract $-91 - 3 = -94$)

$$6 - 7 \times 3^2 \div 2$$

$-25.5$ or $-\frac{51}{2}$ (Evaluating by order of operations: first calculate the exponent $3^2 = 9$, then multiply $7 \times 9 = 63$, then divide $63 \div 2 = 31.5$, and finally subtract $6 - 31.5 = -25.5$)

$$7 - (-8)^2 \div 4 \times (-4)$$

A numerical expression that evaluates to $71$ by applying the order of operations: evaluate the exponent $(-8)^2 = 64$, compute division and multiplication from left to right ($64 \div 4 = 16$, then $16 \times (-4) = -64$), and subtract to obtain $7 - (-64) = 71$.

$$7 + (-7)^2 \times (-2) - 3$$

A numerical expression that evaluates to $-94$ by applying the order of operations: evaluate the exponent $(-7)^2 = 49$, multiply $49 \times (-2) = -98$, add $7 + (-98) = -91$, and subtract $3$ to obtain $-94$.

$$6 - 7 \times 3^2 \div 2$$

A numerical expression that evaluates to $-25.5$ (or $-\frac{51}{2}$) by applying the order of operations: evaluate the exponent $3^2 = 9$, compute multiplication and division from left to right ($7 \times 9 = 63$, then $63 \div 2 = 31.5$), and subtract to obtain $6 - 31.5 = -25.5$.