Apply Order Of Operations - International Brotherhood of Electrical Workers Exam IBEW

1. What is the value of $8-3\times 2$?

   $2$. Multiplication precedes subtraction, so compute $3\times 2=6$ first, then $8-6$.

2. What is the value of $4\left[2+(3-1)^2\right]$?

   $24$. Brackets and parentheses are grouping symbols, so evaluate innermost $3-1=2$, then $2^2=4$, add $2$ to get $6$, and multiply by $4$.

3. What is the value of $(8-3)\times 2$?

   $10$. Parentheses take precedence, so evaluate $8-3=5$ first, then multiply by $2$.

4. What is the value of $2(3+4)^2$?

   $98$. Parentheses precede the exponent, which precedes implied multiplication, so evaluate $3+4=7$, then $7^2=49$, and multiply by $2$.

5. What is the value of $(14-6)\div 3$?

   $\frac{8}{3}$. Parentheses take precedence, so evaluate $14-6=8$ first, then divide by $3$.

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

   $3$. The fraction bar groups the denominator, so compute $3\times 2=6$ first, divide $12$ by $6$ to get $2$, then add $1$.

7. What is the value of $36\div 6+2\times 3$?

   $12$. Division and multiplication precede addition and are evaluated left to right, so compute $36\div 6=6$ and $2\times 3=6$, then add.

8. What is the value of $14-6\div 3$?

   $12$. Division precedes subtraction, so compute $6\div 3=2$ first, then subtract from $14$.

9. What is the value of $5+4\times (7-5)$?

   $13$. Parentheses precede multiplication, which precedes addition, so evaluate $7-5=2$, then $4\times 2=8$, and add $5$.

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

    $64$. Parentheses group the inner exponent, so compute $2^3=8$ first, then raise to the power of $2$.

11. What is the value of $\frac{3+5}{2}$?

    $4$. The fraction bar acts as grouping, so add $3+5=8$ in the numerator first, then divide by $2$.

12. 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 equal precedence and are evaluated from left to right, so division precedes multiplication here.

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

    $3$. Parentheses take precedence, so compute $3\times 2=6$ first, then divide $18$ by $6$.

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

    $24$. Exponents precede multiplication, so evaluate $2^3=8$ first, then multiply by $3$.

15. What is the value of $(5+4)\times (7-5)$?

    $18$. Parentheses take precedence, so evaluate $5+4=9$ and $7-5=2$ first, then multiply.

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

    $7$. Parentheses group the fraction, so multiply $\frac{1}{2}\times 8=4$ first, then add $3$.

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

    $-9$. Parentheses take precedence for the inner exponent, then apply the outer negative sign to the result.

18. What is the value of $-3^2$ (no parentheses)?

    $-9$. Exponents precede unary negation, so compute $3^2=9$ first, then apply the negative sign.

19. What is the value of $6-2(4-1)$?

    $0$. Parentheses precede implied multiplication, which precedes subtraction, so evaluate $4-1=3$, then $2\times 3=6$, and subtract from $6$.

20. What is the value of $2^{(3^2)}$?

    $512$. Exponents are right-associative, so evaluate $3^2=9$ first, then $2^9$.

21. What does it mean to evaluate addition and subtraction left to right in $10-3+2$?

    Compute $10-3$ first, then add $2$. Addition and subtraction have equal precedence and are evaluated from left to right, so subtraction precedes addition here.

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

    $12$. Division and multiplication are evaluated left to right, so divide $18\div 3=6$ first, then multiply by $2$.

23. What is the value of $3+\frac{5}{2}$?

    $\frac{11}{2}$. Division precedes addition, so compute $\frac{5}{2}$ first, then add to $3$.

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

    $9$. Parentheses group the negative base, so square $-3$ to get a positive result.

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