Order of Operations - ISEE Lower Level Mathematics Achievement

1. What is the value of $\frac{1}{2} \times 12 + 3$?

   $9$. Multiplication precedes addition: compute $\frac{1}{2} \times 12$ first, then add 3.

2. What is the value of $(36 \div 3)^2$?

   $144$. Parentheses prioritize the division, then square the result.

3. What is the value of $36 \div 3^2$?

   $4$. Exponents precede division: compute $3^2$ first, then divide 36 by that.

4. What is the value of $4 \times (2^3 - 5)$?

   $12$. Parentheses require evaluating the exponent and subtraction inside first, then multiplying by 4.

5. What is the value of $6 + \frac{8}{4} \times 3$?

   $12$. Division and multiplication precede addition and are done left to right: $\frac{8}{4} \times 3$, then add to 6.

6. What does it mean to evaluate $+$ and $-$ from left to right in an expression?

   Do $+$ and $-$ in the order they appear, moving left to right. Addition and subtraction share precedence and are evaluated in sequence from left to right as they occur in the expression.

7. What is the correct order of operations for $+,-,\times,\div$, parentheses, and exponents?

   Parentheses, exponents, multiply/divide left to right, add/subtract left to right. Follows the PEMDAS rule: parentheses first, then exponents, multiplication and division from left to right, and addition and subtraction from left to right.

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

   $11$. Multiplication precedes addition, so compute $4 \times 2$ first, then add 3.

9. What is the value of $4^3 \div 8$?

   $8$. Exponents precede division: compute $4^3$ first, then divide by 8.

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

    $3$. Parentheses require multiplying inside first, then dividing 18 by that result.

11. What is the value of $24 \div 6 + 2 \times 3$?

    $10$. Division and multiplication precede addition and are done left to right: $24 \div 6$ and $2 \times 3$, then add the results.

12. What is the value of $\frac{1}{2} \times (12 + 3)$?

    $\frac{15}{2}$. Parentheses take priority: add inside first, then multiply by $\frac{1}{2}$.

13. What is the value of $10 - 2 \times (3 + 1)$?

    $2$. Parentheses are evaluated first, then multiplication, followed by subtraction.

14. What is the value of $3 + 2[5 - (1 + 1)]$?

    $9$. Innermost parentheses first, then brackets as implied multiplication, followed by addition.

15. What is the value of $2(7 + 3)$?

    $20$. Parentheses are evaluated first, followed by the implied multiplication.

16. What is the value of $24 \div (6 + 2) \times 3$?

    $9$. Parentheses are evaluated first, then division, followed by multiplication left to right.

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

    $14$. Parentheses take priority, so add inside first, then multiply by 2.

18. What is the value of $10 - 2 \times 3 + 1$?

    $5$. Multiplication precedes addition and subtraction: compute $2 \times 3$ first, then 10 minus that plus 1 left to right.

19. What is the value of $2 \cdot 7 + 3$?

    $17$. Multiplication precedes addition, so compute $2 \cdot 7$ first, then add 3.

20. What does it mean to evaluate $\times$ and $\div$ from left to right in an expression?

    Do $\times$ and $\div$ in the order they appear, moving left to right. Multiplication and division share precedence and are evaluated in sequence from left to right as they occur in the expression.

21. What is the value of $5^2 - 3 \times 4$?

    $13$. Exponents precede multiplication and subtraction: compute $5^2$ first, then $3 \times 4$, and subtract from 25.

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

    $12$. Division and multiplication are performed left to right: divide 18 by 3 first, then multiply by 2.

23. What is the value of $(5^2 - 3) \times 4$?

    $88$. Parentheses prioritize the subtraction after the exponent, then multiply the result by 4.

24. What is the value of $(6 + \frac{8}{4}) \times 3$?

    $24$. Parentheses prioritize the addition after division, then multiply the result by 3.

25. What is the value of $8 - 3^2 + 4$?

    $3$. Exponents precede addition and subtraction: compute $3^2$ first, then perform 8 minus that plus 4 left to right.

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