Order of Operations - SSAT Middle Level Quantitative

1. What is the value of $\frac{1}{2} \times 8 + 3$?

   $7$. Multiplication precedes addition, so compute $\frac{1}{2} \times 8$ before adding 3.

2. What is the value of $(16 \div 2)^2$?

   $64$. Parentheses take precedence, so compute $16 \div 2$ before squaring the result.

3. What is the value of $2[(7 - 3) + 1]$?

   $10$. Parentheses and brackets take precedence, so evaluate innermost $7 - 3$ first, then add 1, and multiply by 2.

4. What is the value of $4[3 + 2]$?

   $20$. Brackets function like parentheses, so evaluate $3 + 2$ first before multiplying by 4.

5. What is the value of $12 - 4 + 3$?

   $11$. Addition and subtraction are performed left to right, so subtract 4 from 12 before adding 3.

6. What is the value of $2(7 - 3) + 1$?

   $9$. Parentheses take precedence, so compute $7 - 3$ first, then multiply by 2 before adding 1.

7. What is the correct order of operations for evaluating expressions?

   Parentheses, exponents, multiply/divide, add/subtract (left to right). The order of operations follows PEMDAS: parentheses first, then exponents, multiplication and division from left to right, and addition and subtraction from left to right.

8. What does it mean to evaluate addition and subtraction "left to right" in $10 - 3 + 4$?

   Compute $10 - 3$ first, then add $4$. Addition and subtraction have the same precedence and are evaluated from left to right, so perform subtraction before addition in this expression.

9. What is the value of $16 \div 2^2$?

   $4$. Exponents precede division, so compute $2^2$ before dividing 16 by the result.

10. What is the value of $5^2 - 3^2$?

    $16$. Exponents precede subtraction, so compute $5^2$ and $3^2$ before subtracting.

11. What is the value of $6 - 2^2 \times 3$?

    $-6$. Exponents precede multiplication, which precedes subtraction, so compute $2^2$ first, then multiply by 3, and subtract from 6.

12. What is the value of $12 - (4 + 3)$?

    $5$. Parentheses take precedence, so compute $4 + 3$ before subtracting from 12.

13. What is the value of $9 - 3 \times (2 + 1)$?

    $0$. Parentheses take precedence, so compute $2 + 1$ first, then multiply by 3 before subtracting from 9.

14. What is the value of $(2^3 + 1) \times 2$?

    $18$. Parentheses take precedence, so compute $2^3 + 1$ before multiplying by 2.

15. What is the value of $\frac{1}{2} \times (8 + 3)$?

    $\frac{11}{2}$. Parentheses take precedence, so compute $8 + 3$ before multiplying by $\frac{1}{2}$.

16. What does it mean to evaluate multiplication and division "left to right" in $24 \div 6 \times 2$?

    Compute $24 \div 6$ first, then multiply by $2$. Multiplication and division have the same precedence and are evaluated from left to right, so perform division before multiplication in this expression.

17. What is the value of $2^3 + 1$?

    $9$. Exponents precede addition, so evaluate $2^3$ before adding 1.

18. What is the value of $(3 + 4) \times 2$?

    $14$. Parentheses take precedence, so evaluate $3 + 4$ first before multiplying by 2.

19. What is the value of $3 + 4 \times 2$?

    $11$. Multiplication precedes addition in the order of operations, so compute $4 \times 2$ before adding 3.

20. What is the value of $20 \div 5 + 2 \times 3$?

    $10$. Multiplication and division are performed left to right before addition, so compute $20 \div 5$ and $2 \times 3$ separately, then add the results.

21. What is the value of $7 + 3 \times 0^2$?

    $7$. Exponents precede multiplication, which precedes addition, so compute $0^2$ first, then multiply by 3, and add to 7.

22. What is the value of $3 + 2 \times 5^1$?

    $13$. Exponents precede multiplication, which precedes addition, so compute $5^1$ first, then multiply by 2, and add to 3.

23. What is the value of $18 \div (3 \times 2)$?

    $3$. Parentheses take precedence, so compute $3 \times 2$ first before dividing 18 by the result.

24. What is the value of $(9 - 3) \times (2 + 1)$?

    $18$. Parentheses take precedence, so evaluate $9 - 3$ and $2 + 1$ separately before multiplying the results.

25. What is the value of $18 \div 3 \times 2$?

    $12$. Division and multiplication are performed left to right, so divide 18 by 3 before multiplying by 2.

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