Order of Operations - ISEE Middle Level Mathematics Achievement

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

   $7$. Multiplication is performed before addition, so multiply $\frac{1}{2}$ by 8 first, then add 3.

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

   $13$. Exponents are evaluated before addition, so compute $2^3$ first, then add 5.

3. What is the value of $7 + 2(4 - 1)$?

   $13$. Evaluate parentheses first, then implied multiplication by 2, and finally add to 7.

4. What is the value of $30 \div 5 \div 2$?

   $3$. Divisions are performed left to right, so divide 30 by 5 first, then divide the result by 2.

5. What is the value of $12 - 3(2 + 1)$?

   $3$. Evaluate parentheses first, then multiplication by 3, and finally subtract from 12.

6. What is the value of $(-3)^2$?

   $9$. The parentheses include the negative sign, so square -3 directly.

7. What does the order of operations require you to do first in $4^2 + 3$?

   Evaluate the exponent: $4^2$. According to the order of operations (PEMDAS), exponents are evaluated before addition.

8. What is the value of $(8 - 3)^2 - 5$?

   $20$. Evaluate parentheses first, then the exponent, and finally subtract 5.

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

   $9$. Evaluate parentheses first, then implied multiplication by 2, and finally subtract 3.

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

    $14$. Evaluate parentheses first, then the exponent, followed by multiplication, and finally addition.

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

    $2$. Exponents are evaluated before subtraction, so compute $2^2$ first, then subtract from 6.

12. What is the value of $9 + 6 \div 3 \times 2$?

    $13$. Division and multiplication are performed left to right, so divide 6 by 3, multiply by 2, then add to 9.

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

    $14$. Parentheses are evaluated first, so add 3 and 4 before multiplying by 2.

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

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

15. What operation is performed first in $10 - 6 + 2$?

    Subtraction, because $-$ and $+$ go left to right. Addition and subtraction are performed left to right after multiplication and division.

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

    $6$. The fraction $\frac{3}{4}$ multiplies directly with 8, as there are no other operations requiring precedence.

17. What is the value of $5^2 - 4^2$?

    $9$. Exponents are evaluated before subtraction, so compute $5^2$ and $4^2$ first, then subtract.

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

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

19. What operation is performed first in $6 \div 2 \times 3$?

    Division, because $\div$ and $\times$ go left to right. Multiplication and division are performed left to right after parentheses and exponents.

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

    $-9$. Exponents are evaluated before the negative sign, so compute $3^2$ and then apply the unary minus.

21. What is the value of $24 \div 3 + 2$?

    $10$. Division is performed before addition, so divide 24 by 3 first, then add 2.

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

    $\frac{24}{5}$. Parentheses are evaluated first, so add 3 and 2 before dividing 24 by the result.

23. What does the order of operations require you to do first in $8 - 3(2 + 1)$?

    Evaluate the parentheses: $(2 + 1)$. According to the order of operations (PEMDAS), parentheses are evaluated before multiplication and subtraction.

24. What is the value of $16 - 4 \times 2^2$?

    $0$. Evaluate the exponent first, then multiplication, and finally subtraction.

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

    $3$. Parentheses are evaluated first, so multiply 3 by 2 before dividing 18 by the result.

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