Order of Operations
Help Questions
SSAT Upper Level: Quantitative › Order of Operations
If $$x = 2$$ and $$y = 3$$, what is the value of $$2x^2 - 3(x + y) + \frac{18}{y}$$?
$$11$$
$$2$$
$$5$$
$$8$$
Explanation
Following order of operations: First, substitute x = 2 and y = 3. Then evaluate exponents: 2(2)² = 2(4) = 8. Next, evaluate inside parentheses: (x + y) = (2 + 3) = 5. Then multiplication and division from left to right: 3(5) = 15 and 18/3 = 6. Finally, combine: 8 - 15 + 6 = 5. Choice A results from incorrectly calculating 2x² as 2(2) = 4. Choice C results from forgetting the subtraction sign. Choice D results from evaluating addition before multiplication.
What is the value of $$2 + 3 \cdot 4^2 - 5 \cdot(6 - 4) \div 2$$?
$$49$$
$$45$$
$$47$$
$$43$$
Explanation
Following order of operations: First, evaluate parentheses: (6 - 4) = 2. Next, evaluate exponents: 4² = 16. Then, perform multiplication and division from left to right: 3 × 16 = 48, and 5 × 2 ÷ 2 = 5. Finally, perform addition and subtraction from left to right: 2 + 48 - 5 = 47. Choice A results from incorrectly calculating 3 × 4² as 3 × 4 × 2. Choice B results from calculation errors in the final step. Choice D results from not performing the final subtraction.
What is the value of $$(-3)^2 \cdot 2 - 4 \cdot 3 + \frac{24}{-6 + 2}$$?
$$12$$
$$0$$
$$18$$
$$6$$
Explanation
Following order of operations: First, evaluate exponents and operations in denominators: (-3)² = 9 and (-6 + 2) = -4. Next, perform multiplication and division: 9 × 2 = 18, 4 × 3 = 12, and 24 ÷ (-4) = -6. Finally, combine from left to right: 18 - 12 + (-6) = 6 - 6 = 0. Choice B results from forgetting the final addition of -6. Choice C results from incorrectly calculating the division as positive 6. Choice D results from not performing any subtraction.
What is the value of $$4 + 23^2 - 2(5 - 3)$$?
$$14$$
$$16$$
$$24$$
$$20$$
Explanation
Following order of operations: Start with the innermost parentheses: (5 - 3) = 2. Next, work outward: 2(2) = 4. Then evaluate the exponent: 3² = 9. Inside the brackets: 9 - 4 = 5. Next, multiply: 2[5] = 10. Finally: 4 + 10 = 20. Choice A results from incorrectly calculating 3² as 6. Choice B results from errors in handling the brackets. Choice D results from adding instead of subtracting within the brackets.