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

1. Simplify \dfrac{18 - 3^2\cdot2}{4 - 2(3 - 5)}.
   Answer: 0 When you encounter complex algebraic expressions like this, the key is following the order of operations (PEMDAS) systematically to avoid calculation errors that can lead you to incorrect answer choices. Let's work through this step-by-step. In the numerator: $18 - 3^2 \cdot 2$. First, handle the exponent: $3^2 = 9$. Then multiplication: $9 \cdot 2 = 18$. Finally, subtraction: $18 - 18 = 0$. For the denominator: $4 - 2(3 - 5)$. Start with parentheses: $3 - 5 = -2$. Then multiplication: $2(-2) = -4$. Finally, subtraction: $4 - (-4) = 4 + 4 = 8$. This gives us $\frac{0}{8} = 0$, confirming that (A) 0 is correct. Now let's see where the wrong answers come from. (B) 1 likely results from incorrectly calculating the numerator as something non-zero, then getting lucky with the denominator calculation. (C) -2 probably comes from making an order of operations error in the numerator, perhaps calculating $18 - 3^2 \cdot 2$ as $15^2 \cdot 2$ or similar mistakes. (D) Undefined would be correct if the denominator equaled zero, but this might tempt students who miscalculate $4 - 2(3 - 5)$ as $4 - 2(-2) = 4 - 2 + 2 = 4$ instead of properly distributing the multiplication. Study tip: Always write out each step of PEMDAS clearly. The most common errors on IBEW math problems come from rushing through order of operations, especially with negative numbers and parentheses.
2. Evaluate the expression: $5 + 3 \times 8$
   Answer: 29 When you encounter expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS). This fundamental rule determines which calculations to perform first, and it's critical for electrical calculations involving power, voltage, and current formulas. In the expression $5 + 3 \times 8$, multiplication takes precedence over addition. First, calculate $3 \times 8 = 24$. Then add: $5 + 24 = 29$. This gives us answer choice B. Let's examine why the other answers are incorrect. Choice A (16) results from incorrectly adding first: $5 + 3 = 8$, then multiplying $8 \times 8 = 64$. Wait, that's not 16 either—this might come from adding $5 + 3 = 8$ and then multiplying by 2 instead of 8, showing confusion about the order of operations. Choice C (39) could result from misreading the expression or making calculation errors. Choice D (64) comes from the partial error mentioned above: adding first to get 8, then multiplying $8 \times 8 = 64$. For IBEW exam success, master the order of operations since electrical formulas frequently combine addition, subtraction, multiplication, and division. Whether you're calculating power using $P = I^2R + P_{base}$ or working with complex impedance calculations, performing operations in the wrong sequence will give incorrect results that could affect safety and system performance. Always remember: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
3. Simplify $(-3)^2 - 4$\div$2 + 6$.
   Answer: 13 This problem tests your ability to apply the order of operations (PEMDAS/BODMAS) correctly, which is fundamental for electrical calculations involving power, voltage, and current formulas. When you see an expression with multiple operations, you must follow the correct sequence: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Let's work through $(-3)^2 - 4 \div 2 + 6$: First, handle the exponent: $(-3)^2 = (-3) \times (-3) = 9$ Next, perform division: $4 \div 2 = 2$ Now we have: $9 - 2 + 6$ Finally, work left to right: $9 - 2 = 7$, then $7 + 6 = 13$ The answer is C) 13. Let's examine why the other choices are wrong: A) −1 likely results from incorrectly calculating $(-3)^2$ as $-9$ instead of $+9$, then computing $-9 - 2 + 6 = -5$, or from other order of operations errors. B) 5 probably comes from making the exponent error above but following a different incorrect sequence, such as $-9 + 6 - 2 = -5$ or similar miscalculations. D) 17 might result from treating the expression as $(-3)^2 - (4 \div 2 + 6) = 9 - 8 = 1$ or from calculating $9 + 4 \div 2 + 6$ by ignoring the subtraction sign. Remember: negative numbers squared become positive, and always follow PEMDAS strictly. In electrical work, order of operations errors in power calculations can lead to dangerous miscalculations, so practice this systematically.
4. Evaluate $8 - 2(3^2 - 5)$$.
   Answer: 0 This question tests your ability to apply the order of operations (PEMDAS/BODMAS) correctly when evaluating algebraic expressions—a fundamental skill you'll use throughout electrical calculations. Let's work through $8 - 2(3^2 - 5)$ step by step. First, handle the parentheses by evaluating what's inside: $3^2 - 5 = 9 - 5 = 4$. Now the expression becomes $8 - 2(4)$. Next, perform the multiplication: $2(4) = 8$. Finally, subtract: $8 - 8 = 0$. Looking at the wrong answers, choice B (4) likely comes from stopping after evaluating the parentheses and forgetting to complete the full calculation. Choice C (8) probably results from either ignoring the subtraction entirely or making an error in the order of operations. Choice D (-8) suggests someone calculated $2(4) - 8 = 0$ instead of $8 - 2(4) = 0$, essentially flipping the subtraction order. The correct answer is A (0). For IBEW exam success, always work through order of operations systematically: handle parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. Write out each step rather than trying to do multiple operations mentally—this prevents the simple arithmetic errors that can cost you points on electrical calculations where precision is critical.
5. Evaluate $10 - 3\{2 + [4 - (6 $\div$ 3)]\}$$.
   Answer: −2 When you encounter complex expressions with multiple grouping symbols, you must follow the order of operations (PEMDAS) and work from the innermost groupings outward. Start with the innermost parentheses: $6 \div 3 = 2$. Now the expression becomes $10 - 3\{2 + [4 - 2]\}$. Next, solve the brackets: $4 - 2 = 2$. The expression is now $10 - 3\{2 + 2\}$. Solve inside the braces: $2 + 2 = 4$. This gives you $10 - 3\{4\}$. Multiply: $3 \times 4 = 12$. Finally: $10 - 12 = -2$. Answer A (−2) is correct because it follows the proper order of operations systematically. Answer B (2) likely comes from incorrectly calculating $10 - 12$ as positive 2, perhaps by subtracting the smaller number from the larger one regardless of order. Answer C (−14) probably results from making an error in the grouping calculations, possibly getting $10 - 3\{8\}$ instead of $10 - 3\{4\}$ and then calculating $10 - 24 = -14$. Answer D (14) could come from multiple errors, such as adding instead of subtracting at the final step, turning $10 - 12$ into $10 + 4 = 14$. For IBEW exam success, always work systematically through nested groupings from inside out, and double-check each step. Write out each intermediate step to avoid calculation errors, especially with negative results.
6. Evaluate $\left( \dfrac{5}{6} \right)^{−1} − \left( 2 − \dfrac{7}{3} \right)$.
   Answer: $\dfrac{23}{15}$ This problem tests your ability to work with negative exponents and order of operations with fractions—skills you'll use regularly in electrical calculations involving impedance and power formulas. Start by evaluating each part separately. For $\left(\frac{5}{6}\right)^{-1}$, remember that a negative exponent means "take the reciprocal." So $\left(\frac{5}{6}\right)^{-1} = \frac{6}{5}$. Next, evaluate $2 - \frac{7}{3}$. Convert 2 to thirds: $2 = \frac{6}{3}$, so $2 - \frac{7}{3} = \frac{6}{3} - \frac{7}{3} = -\frac{1}{3}$. Now substitute back into the original expression: $\frac{6}{5} - \left(-\frac{1}{3}\right) = \frac{6}{5} + \frac{1}{3}$. To add these fractions, find a common denominator of 15: $\frac{6}{5} = \frac{18}{15}$ and $\frac{1}{3} = \frac{5}{15}$. Therefore: $\frac{18}{15} + \frac{5}{15} = \frac{23}{15}$. Looking at the wrong answers: Choice B ($\frac{13}{15}$) results from incorrectly calculating $\frac{18}{15} - \frac{5}{15}$ instead of adding. Choice C (1) comes from computational errors in fraction arithmetic. Choice D ($\frac{29}{15}$) likely stems from mishandling the negative exponent or sign errors. The correct answer is A: $\frac{23}{15}$. Study tip: When you see negative exponents, immediately think "reciprocal," and always double-check your signs when subtracting negative terms—they become additions.
7. Compute $|4 − 9$\div$3| + (−2)^3$.
   Answer: −7 When you encounter complex expressions with multiple operations, you must follow the order of operations (PEMDAS) carefully: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Let's work through $|4 − 9 \div 3| + (−2)^3$ step by step. First, handle what's inside the absolute value bars: $4 − 9 \div 3$. Division comes before subtraction, so calculate $9 \div 3 = 3$, giving us $4 − 3 = 1$. The absolute value $|1| = 1$. Next, calculate the exponent: $(−2)^3 = (−2) × (−2) × (−2) = −8$. Notice that since we have an odd exponent, the result is negative. Finally, add the results: $1 + (−8) = 1 − 8 = −7$. Answer A (−5) likely comes from incorrectly calculating $(−2)^3$ as $−4$ instead of $−8$. Answer C (7) represents the error of treating $(−2)^3$ as positive 8, perhaps confusing it with $(-2)^2$ or misunderstanding how negative bases work with odd exponents. Answer D (9) might result from incorrectly doing the division last instead of following proper order of operations. For IBEW math problems, always write out each step of the order of operations. Pay special attention to negative numbers raised to powers—odd exponents keep the negative sign, while even exponents make the result positive. Double-check your arithmetic at each step to avoid cascading errors.
8. Evaluate the expression: $25 - 10 + 5 - 2$
   Answer: 18 When you encounter arithmetic expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS). However, this expression contains only addition and subtraction, which have equal precedence and are evaluated from left to right. Let's work through $25 - 10 + 5 - 2$ step by step: First: $25 - 10 = 15$ Next: $15 + 5 = 20$ Finally: $20 - 2 = 18$ The answer is 18, which is choice C. Now let's examine why the other options are incorrect: Choice A (8) likely results from incorrectly grouping operations, perhaps calculating $25 - (10 + 5 + 2) = 25 - 17 = 8$. This violates the left-to-right rule for equal-precedence operations. Choice B (12) might come from the error $25 - 10 - 5 + 2 = 12$, where someone mistakenly changed the addition to subtraction or miscalculated somewhere in the sequence. Choice D (22) could result from treating all operations as addition: $25 - 10 + 5 + 2 = 22$, incorrectly changing the final subtraction to addition. For IBEW exam success, remember that when you see expressions with only addition and subtraction, work strictly from left to right. Don't let the mix of positive and negative operations confuse you into grouping them incorrectly. Practice these step-by-step calculations until the left-to-right pattern becomes automatic—this precision is crucial for electrical calculations you'll encounter throughout the exam.
9. Evaluate the expression: $9 + [24 \div (3 \times 2)] - 1$
   Answer: 12 When you encounter expressions with multiple operations like this one, you need to apply the order of operations (PEMDAS/BODMAS) systematically. This means handling Parentheses/Brackets first, then Exponents, then Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). Let's work through $9 + [24 \div (3 \times 2)] - 1$ step by step. Start with the innermost parentheses: $(3 \times 2) = 6$. Now the expression becomes $9 + [24 \div 6] - 1$. Next, handle the division inside the brackets: $24 \div 6 = 4$, giving us $9 + 4 - 1$. Finally, work left to right with addition and subtraction: $9 + 4 = 13$, then $13 - 1 = 12$. Choice A (4) likely comes from calculating only the bracketed portion $[24 \div (3 \times 2)] = 4$ and forgetting to complete the full expression. Choice C (15) results from incorrectly adding all the numbers without following order of operations: $9 + 24 + 3 + 2 - 1 = 37$, or perhaps $9 + 4 + 3 - 1 = 15$ by mixing up intermediate steps. Choice D (20) might come from adding $9 + 24 \div 6 - 1 = 9 + 4 - 1$ but then making an arithmetic error. The correct answer is B (12). For IBEW math problems, always write out each step of the order of operations clearly. Electrical calculations often involve complex expressions with multiple operations, so developing this systematic approach will serve you well in both the exam and field work.
10. An electrician needs the value of $120 − 4($2^3$ + $3^2$) $\div$ 6$$ to determine a wire length in centimetres. What is the result?
    Answer: $\dfrac{326}{3}$ This problem tests your ability to apply the order of operations (PEMDAS/BODMAS) correctly when evaluating complex expressions - a skill essential for electrical calculations involving formulas with multiple operations. Let's work through $120 - 4(2^3 + 3^2) \div 6$ step by step. First, handle the exponents inside the parentheses: $2^3 = 8$ and $3^2 = 9$, so $(2^3 + 3^2) = 8 + 9 = 17$. Next, perform the multiplication: $4 \times 17 = 68$. Then the division: $68 \div 6 = \frac{68}{6} = \frac{34}{3}$. Finally, subtract from 120: $120 - \frac{34}{3} = \frac{360}{3} - \frac{34}{3} = \frac{326}{3}$. Choice A gives us $\frac{326}{3}$, which matches our calculation. Choice B ($\frac{292}{3}$) likely results from incorrectly calculating the exponents or making an arithmetic error in the subtraction. Choice C ($\frac{272}{3}$) suggests confusion with the order of operations, possibly doing subtraction before completing the multiplication and division. Choice D ($\frac{360}{3} = 120$) represents the common mistake of ignoring the entire second term and just using the initial value. When tackling order of operations problems on the IBEW exam, always write out each step clearly and double-check your exponent calculations. These problems appear frequently in electrical formulas, so mastering PEMDAS prevents costly errors in real-world applications.
11. Evaluate the expression: $4 \times (9 - 3) + 2$
    Answer: 26 When you encounter mathematical expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Let's work through $4 \times (9 - 3) + 2$ step by step: First, solve what's in parentheses: $(9 - 3) = 6$ Next, perform the multiplication: $4 \times 6 = 24$ Finally, add: $24 + 2 = 26$ Therefore, the answer is B) 26. Now let's see where the wrong answers come from. Choice A) 24 occurs if you forget the final addition step and stop after calculating $4 \times 6$. Choice C) 32 results from incorrectly applying order of operations—specifically, if you add first ($3 + 2 = 5$), then calculate $4 \times (9 - 5) = 4 \times 4 = 16$, then mistakenly add something else. Choice D) 35 comes from completely ignoring parentheses and working left to right: $4 \times 9 = 36$, then $36 - 3 = 33$, then $33 + 2 = 35$. Study tip: Always write out each step when solving order of operations problems. The most common errors on electrical exams occur when students rush through basic calculations or skip steps mentally. Take the extra few seconds to work methodically—it prevents costly arithmetic mistakes that can throw off circuit calculations and electrical formulas later.
12. What is the total resistance in ohms based on the given expression?
    Answer: 31 ohms This question tests your ability to apply the order of operations (PEMDAS/BODMAS) to electrical calculations, a fundamental skill for circuit analysis where mathematical precision directly impacts safety and functionality. To solve $15 + \frac{12}{3} \times 2^2$, you must follow the order of operations strictly. First, handle the exponent: $2^2 = 4$. Next, perform the division: $\frac{12}{3} = 4$. Then multiply: $4 \times 4 = 16$. Finally, add: $15 + 16 = 31$ ohms. Answer A (19 ohms) results from incorrectly adding first: $(15 + 12) ÷ 3 × 4 = 27 ÷ 3 × 4 = 36$, then somehow getting 19 through further errors. This violates the order of operations entirely. Answer C (32 ohms) comes from calculating $15 + 12 ÷ 3 + 2^2 = 15 + 4 + 4 = 23$, then making an arithmetic error, or from $15 + 12 + 3 + 2 = 32$ by ignoring all operations except addition. Answer D (81 ohms) likely results from adding everything first: $(15 + 12 + 3 + 2)^2 = 32^2$, but this completely misinterprets the expression structure. The correct answer is B (31 ohms). Study tip: In electrical calculations, always write out each step of PEMDAS separately. Mathematical errors in resistance calculations can lead to improper wire sizing, circuit protection failures, and safety hazards. Practice order of operations with electrical formulas until it becomes automatic—your safety and your customers' depend on mathematical precision.
13. What is the value of $(6 + 4) \times 10 \div 5$?
    Answer: 20 This question tests your understanding of the order of operations, a fundamental math skill you'll use constantly in electrical calculations involving voltage, current, and resistance. When solving $(6 + 4) \times 10 \div 5$, you must follow PEMDAS (Parentheses, Exponents, Multiplication/Division from left to right, Addition/Subtraction from left to right). Start with the parentheses: $6 + 4 = 10$. This gives you $10 \times 10 \div 5$. Next, work left to right with multiplication and division: $10 \times 10 = 100$, then $100 \div 5 = 20$. Answer A (5) represents a common error where someone incorrectly calculates the final division: $10 \div 5 = 2$, then mistakenly uses only part of the expression. Answer B (12) occurs when someone adds instead of multiplies in the second step: $10 + 10 \div 5 = 10 + 2 = 12$. Answer C (14) results from ignoring order of operations entirely and working strictly left to right: $6 + 4 = 10$, $10 \times 10 = 100$, but then making an arithmetic error or misapplying the division. The correct answer is D (20). For IBEW exam success, always write out each step of complex calculations, especially when dealing with power formulas like $P = I^2R$ or voltage divider circuits. Order of operations mistakes in electrical calculations can lead to dangerous errors in real-world applications. Practice PEMDAS until it becomes automatic—your safety and your electrical systems depend on accurate math.
14. What is the result of $3 + (9 - 2) \times 2^2$?
    Answer: 31 When you encounter mathematical expressions with multiple operations like this one, you must follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). Let's work through $3 + (9 - 2) \times 2^2$ step by step. First, solve what's in parentheses: $(9 - 2) = 7$. Next, handle the exponent: $2^2 = 4$. Now we have $3 + 7 \times 4$. Since multiplication comes before addition, calculate $7 \times 4 = 28$. Finally, add: $3 + 28 = 31$. Choice A (31) is correct following proper order of operations. Choice B (40) likely comes from adding first: $3 + 9 - 2 = 10$, then $10 \times 2^2 = 40$ - this ignores the parentheses and violates order of operations. Choice C (48) might result from calculating $(3 + 9 - 2) \times 2^2 = 10 \times 4 = 40$, then making an arithmetic error, or from $3 + 9 \times 2^2 + 2 = 3 + 36 + 9 = 48$ by misreading the expression. Choice D (144) could come from $(3 + 9) \times 2^2 \times 1.5 = 72$ through multiple errors, or $12^2 = 144$ by completely misinterpreting the problem. Remember: PEMDAS is non-negotiable in electrical calculations. Whether you're computing power formulas or circuit analysis, following the correct order of operations prevents costly mistakes. Always work parentheses first, then exponents, then multiplication/division, finally addition/subtraction.
15. Evaluate the expression: $-4(5 - 8)$
    Answer: 12 This question tests your understanding of the order of operations and working with negative numbers—fundamental skills you'll use constantly in electrical calculations. When evaluating $-4(5 - 8)$, you must follow the order of operations (PEMDAS). First, solve what's inside the parentheses: $5 - 8 = -3$. Now you have $-4(-3)$. When multiplying two negative numbers, the result is positive: $-4 \times (-3) = +12$. Looking at the wrong answers: Answer B (-12) represents the common error of treating the multiplication as $-4 \times 3 = -12$, which happens when students forget that $5 - 8$ equals $-3$, not $+3$. Answer C (-28) likely comes from incorrectly distributing first: $-4 \times 5 - (-4) \times 8 = -20 + 32 = 12$, then somehow getting the sign wrong. Answer D (-52) appears to come from adding instead of subtracting in the parentheses ($5 + 8 = 13$), then multiplying: $-4 \times 13 = -52$. The correct answer is A (12). Study tip: Always work inside parentheses first, and remember that multiplying two negatives gives a positive result. In electrical work, you'll encounter negative values frequently (like phase relationships), so mastering these sign rules now will serve you well. Practice problems with nested operations until the order becomes automatic.
16. What is the value of $5.5 + 0.5 \times 10$?
    Answer: 10.5 When you encounter arithmetic expressions with multiple operations, the order of operations (PEMDAS/BODMAS) determines how to solve them correctly. This fundamental math skill appears regularly on the IBEW exam, so mastering it is essential. Let's work through $5.5 + 0.5 \times 10$ step by step. According to order of operations, you must perform multiplication before addition. First, calculate $0.5 \times 10 = 5.0$. Then add this result to 5.5: $5.5 + 5.0 = 10.5$. Now let's examine why the other answers are incorrect. Choice A (10.0) results from a calculation error—possibly rounding 10.5 down or making an arithmetic mistake in the final addition. Choice C (55.5) comes from incorrectly adding first: if you mistakenly calculated $(5.5 + 0.5) \times 10 = 6.0 \times 10 = 60.0$, then somehow arrived at 55.5, this represents a double error in both order of operations and arithmetic. Choice D (60) is what you'd get if you violated order of operations by adding first: $(5.5 + 0.5) \times 10 = 6.0 \times 10 = 60$. The key strategy for IBEW math questions is to always apply PEMDAS religiously: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Write out each step to avoid mental calculation errors. Many wrong answers on electrical exams stem from rushing through basic math rather than electrical theory mistakes, so slow down and be methodical with arithmetic fundamentals.
17. What is the value of the expression $18 \div 3 \times 2 + 5$?
    Answer: 17 When you encounter mathematical expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS) to get the correct result. This fundamental skill appears regularly on technical exams because precise calculations are critical in electrical work. Let's work through $18 \div 3 \times 2 + 5$ step by step. According to the order of operations, you perform multiplication and division from left to right, then addition and subtraction from left to right. First, $18 \div 3 = 6$ Next, $6 \times 2 = 12$ Finally, $12 + 5 = 17$ The correct answer is D) 17. Now let's see where the wrong answers come from. Choice A) 8 likely results from incorrectly doing $18 \div (3 \times 2) + 5 = 18 \div 6 + 5 = 3 + 5 = 8$, which incorrectly groups the multiplication and division. Choice B) 11 probably comes from calculating $18 \div 3 + 5 = 6 + 5 = 11$ and completely ignoring the $\times 2$ operation. Choice C) 16 might result from doing $18 \div 3 \times 2 = 12$ correctly but then making an arithmetic error in the final addition. Remember that multiplication and division have equal priority and are performed left to right, not multiplication first. This is a common source of errors. When solving order of operations problems, work methodically from left to right within each priority level, and double-check your arithmetic at each step.
18. Evaluate the expression: $5 + 2^3 \times 3$
    Answer: 29 When you encounter mathematical expressions with multiple operations, the order of operations (PEMDAS/BODMAS) determines how to solve them correctly. This fundamental concept ensures consistent results regardless of who performs the calculation. Let's work through $5 + 2^3 \times 3$ step by step. First, handle the exponent: $2^3 = 2 \times 2 \times 2 = 8$. Next, perform the multiplication: $8 \times 3 = 24$. Finally, add: $5 + 24 = 29$. The correct answer is B) 29. Looking at the wrong answers reveals common mistakes. Choice A) 21 likely comes from incorrectly calculating $2^3$ as 6 instead of 8, then computing $5 + 6 \times 3 = 5 + 18 = 23$ — though this still doesn't quite match, suggesting multiple errors. Choice C) 39 might result from adding first ($5 + 2 = 7$), then calculating $7^3 \times 3$, but this would actually give a much larger number. Choice D) 59 could come from misapplying order of operations in various ways, such as treating the expression as $(5 + 2)^3 + 3^3$. Remember PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). On electrical exams, you'll frequently encounter formulas with multiple operations — like power calculations involving $I^2R$ or voltage dividers. Always handle exponents before multiplication, and multiplication before addition. Write out each step to avoid careless errors that could cost points on critical calculations.
19. What is the value of $48 \div 8 \times 3$?
    Answer: 18 When you encounter mathematical expressions with multiple operations, the order of operations (PEMDAS/BODMAS) determines how to solve them correctly. For expressions containing only multiplication and division, you work from left to right since these operations have equal precedence. Let's work through $48 \div 8 \times 3$ step by step. Moving from left to right: first, $48 \div 8 = 6$. Then, $6 \times 3 = 18$. Looking at the wrong answers reveals common misconceptions. Answer A (2) results from incorrectly treating the expression as $48 \div (8 \times 3)$, which would give $48 \div 24 = 2$. This error occurs when students mistakenly believe multiplication always comes before division, rather than working left to right. Answer C (24) comes from calculating $8 \times 3 = 24$ but then adding instead of dividing: $48 - 24 = 24$ or making another computational error. Answer D (128) likely results from multiplying all three numbers together: $48 \times 8 \times 3 = 1152$, or perhaps $48 + 8 \times 10 = 128$, showing complete disregard for the given operations. The correct answer is B (18). For IBEW exam success, remember that mathematical accuracy is crucial in electrical calculations. When you see division and multiplication together, always work left to right. A helpful memory device: "My Dear Aunt Sally" reminds you of the order (Multiplication/Division, Addition/Subtraction), but within each pair, go left to right. Practice these fundamental operations until they're automatic—electrical formulas build on this foundation.
20. What is the value of $4 \times 5 + (12 - 2^2) \div 4$?
    Answer: 22 This question tests your ability to apply the order of operations (PEMDAS/BODMAS), a fundamental skill you'll need for electrical calculations involving complex formulas with multiple operations. Let's work through $4 \times 5 + (12 - 2^2) \div 4$ step by step. First, handle what's inside the parentheses: $12 - 2^2$. Since exponents come before subtraction, calculate $2^2 = 4$, then $12 - 4 = 8$. Now you have $4 \times 5 + 8 \div 4$. Next, perform multiplication and division from left to right: $4 \times 5 = 20$ and $8 \div 4 = 2$. Finally, add: $20 + 2 = 22$. Answer A (7) likely results from incorrectly doing $4 + (12 - 2^2) \div 4 = 4 + 8 \div 4 = 4 + 2 = 6$ (close to 7), suggesting you missed the multiplication entirely or made an arithmetic error. Answer B (12) probably comes from calculating $(4 \times 5 + 12 - 2^2) \div 4$, incorrectly treating the entire expression as if it were in parentheses and divided by 4, giving you $(20 + 12 - 4) \div 4 = 28 \div 4 = 7$ (though this doesn't quite match either). Answer D (28) results from ignoring the division: $4 \times 5 + (12 - 2^2) = 20 + 8 = 28$. Remember PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). In electrical work, you'll frequently encounter complex formulas where order of operations determines whether your calculations for power, voltage, and current are correct.

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