Order of Operations - SSAT Upper Level Quantitative

1. If $x = 2$ and $y = 3$, what is the value of $2x^2 - 3(x + y) + \frac{18}{y}$?
   Answer: $-1$ Substitute x = 2 and y = 3, then follow the order of operations. The exponent first: 2x² = 2(2)² = 2(4) = 8. Then the parentheses and multiplication: 3(x + y) = 3(5) = 15. Then the division: 18/y = 18/3 = 6. Finally, combine from left to right: 8 − 15 = −7, and −7 + 6 = −1. An answer of 5 comes from distributing the 3 to x only, so 3(x + y) becomes 3x + y = 9, and 8 − 9 + 6 = 5. An answer of 8 multiplies 3 by x alone and forgets y: 8 − 6 + 6 = 8. An answer of 11 forgets to divide 18 by y: 8 − 15 + 18 = 11.
2. What is the value of $4 + 2[3^2 - 2(5 - 3)]$?
   Answer: $14$ Work from the innermost grouping outward. First, the parentheses: $5 - 3 = 2$, so $2(5 - 3) = 2 \times 2 = 4$. Next, the exponent: $3^2 = 9$. Inside the brackets: $9 - 4 = 5$. Multiply by the 2 in front of the brackets: $2 \times 5 = 10$. Finally, add: $4 + 10 = 14$. An answer of 20 comes from multiplying the 4 by the bracket value ($4 \times 5$) instead of adding 4 to $2 \times 5$. Answers of 16 and 24 come from slips inside the brackets: they need the bracket to equal 6 or 10 instead of $9 - 4 = 5$, which happens when the term $2(5 - 3)$ is not fully worked out before subtracting. Remember the order: grouping symbols, exponents, multiplication, then addition, and never add a number to the factor beside it before multiplying.
3. What is the value of $2 + 3 \cdot 4^2 - 5 \cdot (6 - 4) \div 2$?
   Answer: $45$ Follow the order of operations. Parentheses first: 6 − 4 = 2. Exponents next: 4² = 16. Then multiplication and division from left to right: 3 × 16 = 48, and 5 × 2 ÷ 2 = 10 ÷ 2 = 5. Finally, add and subtract from left to right: 2 + 48 = 50, and 50 − 5 = 45. An answer of 43 drops the leading 2 and computes only 48 − 5. An answer of 47 treats 5 · (6 − 4) as 5 − 2 = 3 and subtracts 3 instead of 5. An answer of 49 ignores the factor of 5 and subtracts only (6 − 4) ÷ 2 = 1.
4. What is the value of $(-3)^2 \cdot 2 - 4 \cdot 3 + \frac{24}{-6 + 2}$?
   Answer: $0$ 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.

Start this quiz