IBEW: Electrical Training Alliance Aptitude Test Quiz: Apply Order Of Operations
20 questions · exam conditions
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Apply Order Of OperationsQuestion 1 of 20

Calculate the value of 7×3−2imes5+17 \times 3 - 2 imes 5 + 1.

6
10
12
96
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IBEW: Electrical Training Alliance Aptitude Test Quiz

IBEW: Electrical Training Alliance Aptitude Test Quiz: Apply Order Of Operations

Practice Apply Order Of Operations in IBEW: Electrical Training Alliance Aptitude Test with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Apply Order Of Operations, giving you a quick way to practice the rules, question types, and explanations that matter most for IBEW: Electrical Training Alliance Aptitude Test.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Calculate the value of 7×3−2imes5+17 \times 3 - 2 imes 5 + 1.

  1. 6
  2. 10
  3. 12 (correct answer)
  4. 96
Explanation: When you encounter mathematical 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 essential for electrical calculations involving power, voltage, and current formulas. Let's work through 7×3−2×5+17 \times 3 - 2 \times 5 + 1 step by step. According to order of operations, multiplication and division come before addition and subtraction, working from left to right: First, perform the multiplications:
  • 7×3=217 \times 3 = 21
  • 2×5=102 \times 5 = 10
Now the expression becomes: 21−10+121 - 10 + 1 Next, work left to right with addition and subtraction:
  • 21−10=1121 - 10 = 11
  • 11+1=1211 + 1 = 12
The answer is 12, which is choice C. Let's examine why the other answers are wrong: Choice A (6) likely comes from incorrectly calculating left to right without following order of operations: 7×3=217 \times 3 = 21, then 21−2=1921 - 2 = 19, then 19×5=9519 \times 5 = 95, then 95+1=9695 + 1 = 96 - but this shows complete disregard for proper sequencing. Choice B (10) might result from only calculating 2×5=102 \times 5 = 10 and ignoring the rest, or from some other computational error. Choice D (96) comes from working strictly left to right: ((7×3)−2)×5+1=(21−2)×5+1=19×5+1=95+1=96((7 \times 3) - 2) \times 5 + 1 = (21 - 2) \times 5 + 1 = 19 \times 5 + 1 = 95 + 1 = 96. Remember: Always apply PEMDAS consistently in electrical formulas. Whether calculating power (P=I2RP = I^2R) or complex circuit analysis, order of operations mistakes lead to dangerous miscalculations in real electrical work.

Question 2

Evaluate 5−[3−(2−7)]25 - [3 - (2 - 7)]^2 $.

  1. -11
  2. -59 (correct answer)
  3. 59
  4. -69
Explanation: When you encounter nested expressions with brackets and exponents, you must work systematically from the innermost grouping symbols outward, following the order of operations (PEMDAS/BODMAS). Let's evaluate 5−[3−(2−7)]25 - [3 - (2 - 7)]^2 step by step. Start with the innermost parentheses: (2−7)=−5(2 - 7) = -5. Now the expression becomes 5−[3−(−5)]25 - [3 - (-5)]^2. Next, work inside the brackets: 3−(−5)=3+5=83 - (-5) = 3 + 5 = 8. This gives us 5−[8]25 - [8]^2. Calculate the exponent: 82=648^2 = 64. Finally, perform the subtraction: 5−64=−595 - 64 = -59. Choice A (-11) likely results from incorrectly calculating 2−7=52 - 7 = 5 instead of −5-5, which would lead to 3−5=−23 - 5 = -2, then (−2)2=4(-2)^2 = 4, and 5−4=15 - 4 = 1, though this still doesn't directly give -11. Choice C (59) represents forgetting the negative sign in the final subtraction, calculating 5−645 - 64 as 64−5=5964 - 5 = 59 instead. Choice D (-69) might occur from adding instead of subtracting in the final step: 5+64=695 + 64 = 69, then incorrectly applying a negative sign. For order of operations problems on the IBEW exam, always work methodically from the inside out. Write down each step clearly to avoid sign errors, which are the most common mistakes in these calculations. Double-check your work by ensuring each grouping symbol is properly resolved before moving to the next level.

Question 3

Evaluate the expression: −4(5−8)-4(5 - 8)

  1. 12 (correct answer)
  2. -12
  3. -28
  4. -52
Explanation: 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)-4(5 - 8), you must follow the order of operations (PEMDAS). First, solve what's inside the parentheses: 5−8=−35 - 8 = -3. Now you have −4(−3)-4(-3). When multiplying two negative numbers, the result is positive: −4×(−3)=+12-4 \times (-3) = +12. Looking at the wrong answers: Answer B (-12) represents the common error of treating the multiplication as −4×3=−12-4 \times 3 = -12, which happens when students forget that 5−85 - 8 equals −3-3, not +3+3. Answer C (-28) likely comes from incorrectly distributing first: −4×5−(−4)×8=−20+32=12-4 \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=135 + 8 = 13), then multiplying: −4×13=−52-4 \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.

Question 4

Evaluate the expression: 5+23×35 + 2^3 \times 3

  1. 21
  2. 29 (correct answer)
  3. 39
  4. 59
Explanation: 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+23×35 + 2^3 \times 3 step by step. First, handle the exponent: 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8. Next, perform the multiplication: 8×3=248 \times 3 = 24. Finally, add: 5+24=295 + 24 = 29. The correct answer is B) 29. Looking at the wrong answers reveals common mistakes. Choice A) 21 likely comes from incorrectly calculating 232^3 as 6 instead of 8, then computing 5+6×3=5+18=235 + 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=75 + 2 = 7), then calculating 73×37^3 \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+33(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 I2RI^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.

Question 5

Evaluate the expression: 5×[10+(6−2)]5 \times [10 + (6 - 2)]

  1. 54
  2. 60
  3. 70 (correct answer)
  4. 78
Explanation: When you encounter expressions with multiple operations and grouping symbols, you must follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets first, then Exponents/Orders, then Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). Let's work through 5×[10+(6−2)]5 \times [10 + (6 - 2)] step by step. Start with the innermost parentheses: (6−2)=4(6 - 2) = 4. Now the expression becomes 5×[10+4]5 \times [10 + 4]. Next, handle the brackets: 10+4=1410 + 4 = 14. Finally, perform the multiplication: 5×14=705 \times 14 = 70. Looking at the wrong answers, choice A (54) likely results from incorrectly calculating 5×[10+(6−2)]5 \times [10 + (6 - 2)] as 5×10+6−2=545 \times 10 + 6 - 2 = 54 by ignoring the grouping symbols entirely. Choice B (60) could come from miscalculating the inner parentheses as (6−2)=2(6 - 2) = 2, giving 5×[10+2]=5×12=605 \times [10 + 2] = 5 \times 12 = 60. Choice D (78) might result from adding instead of subtracting in the parentheses: (6+2)=8(6 + 2) = 8, leading to 5×[10+8]=5×18=905 \times [10 + 8] = 5 \times 18 = 90, though this doesn't match exactly—it could involve other calculation errors. The correct answer is C (70). For IBEW math problems, always write out each step of the order of operations. Electrical calculations often involve complex expressions with multiple operations, so developing systematic habits with basic arithmetic will serve you well in more advanced circuit analysis and power calculations.

Question 6

Evaluate the expression: 10+6×4−16÷210 + 6 \times 4 - 16 \div 2

  1. 24
  2. -26
  3. 26 (correct answer)
  4. 56
Explanation: When you encounter mathematical expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS) to get the correct result. This fundamental concept ensures everyone solves expressions the same way, which is crucial for electrical calculations in the field. Let's work through 10+6×4−16÷210 + 6 \times 4 - 16 \div 2 step by step. First, perform multiplication and division from left to right: 6×4=246 \times 4 = 24 and 16÷2=816 \div 2 = 8. This gives us 10+24−810 + 24 - 8. Then perform addition and subtraction from left to right: 10+24=3410 + 24 = 34, then 34−8=2634 - 8 = 26. Answer A (24) represents the mistake of only calculating 6×46 \times 4 and ignoring the rest of the expression. Answer B (-26) occurs when you incorrectly calculate the final subtraction, perhaps computing 8−34=−268 - 34 = -26 instead of 34−8=2634 - 8 = 26. Answer D (56) results from adding all the numbers together (10+6+4+16+2=5610 + 6 + 4 + 16 + 2 = 56) while completely ignoring the operations—a common error when rushing through problems. The correct answer is C (26). For electrical work, mathematical precision is non-negotiable—incorrect calculations can lead to dangerous situations or equipment damage. Always write out each step of the order of operations, especially under test pressure. Remember: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Taking an extra few seconds to follow PEMDAS systematically will prevent costly calculation errors.

Question 7

Evaluate the expression: 3×22−(10−5)÷53 \times 2^2 - (10 - 5) \div 5

  1. 1
  2. 3
  3. 11 (correct answer)
  4. 35
Explanation: When you encounter 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 3×22−(10−5)÷53 \times 2^2 - (10 - 5) \div 5 step by step: First, handle what's inside parentheses: (10−5)=5(10 - 5) = 5 Next, calculate the exponent: 22=42^2 = 4 Now the expression becomes: 3×4−5÷53 \times 4 - 5 \div 5 Then perform multiplication and division from left to right:
  • 3×4=123 \times 4 = 12
  • 5÷5=15 \div 5 = 1
Finally, subtract: 12−1=1112 - 1 = 11 Answer C (11) is correct because it follows the proper order of operations. Answer A (1) likely results from incorrectly doing subtraction before multiplication, getting 3×22−10+5÷5=12−10+1=33 \times 2^2 - 10 + 5 \div 5 = 12 - 10 + 1 = 3, then making another error. Answer B (3) comes from the error above: calculating 12−10+1=312 - 10 + 1 = 3 instead of properly grouping the parentheses first. Answer D (35) probably results from ignoring the order of operations entirely and calculating left to right: 3×2=63 \times 2 = 6, then 62=366^2 = 36, then some variation of the remaining operations. For IBEW math problems, always write out each step of the order of operations. Don't try to do multiple steps mentally—electrical calculations require precision, and developing systematic problem-solving habits now will serve you well in field calculations involving voltage, current, and resistance.

Question 8

Evaluate the expression: 100÷10×2−5100 \div 10 \times 2 - 5

  1. 0
  2. -3
  3. 5
  4. 15 (correct answer)
Explanation: Order of operations is crucial for electrical calculations you'll encounter on the job, from computing power loads to determining voltage drops across multiple components. When you see an expression with multiple operations, you must follow PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's work through 100÷10×2−5100 \div 10 \times 2 - 5 step by step. Since there are no parentheses or exponents, we start with multiplication and division, working from left to right: First: 100÷10=10100 \div 10 = 10 Next: 10×2=2010 \times 2 = 20 Finally: 20−5=1520 - 5 = 15 So the answer is D) 15. The wrong answers represent common order of operations mistakes. Choice A) 0 likely comes from incorrectly grouping operations, perhaps calculating 100÷(10×2)−5=100÷20−5=5−5=0100 \div (10 \times 2) - 5 = 100 \div 20 - 5 = 5 - 5 = 0. Choice B) -3 might result from performing subtraction before division and multiplication, getting something like 100÷10×(2−5)=10×(−3)=−30100 \div 10 \times (2-5) = 10 \times (-3) = -30, then making another error. Choice C) 5 could come from calculating 100÷(10×2)=5100 \div (10 \times 2) = 5 and ignoring the subtraction entirely. Remember: multiplication and division have equal priority and are performed left to right, not multiplication first. This principle applies directly to electrical formulas where you'll calculate power, current, and resistance values—getting the order wrong can lead to dangerous miscalculations on the job.

Question 9

Evaluate 8−2(32−5)8 - 2(3^2 - 5) $.

  1. 0 (correct answer)
  2. 4
  3. 8
  4. -8
Explanation: 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(32−5)8 - 2(3^2 - 5) step by step. First, handle the parentheses by evaluating what's inside: 32−5=9−5=43^2 - 5 = 9 - 5 = 4. Now the expression becomes 8−2(4)8 - 2(4). Next, perform the multiplication: 2(4)=82(4) = 8. Finally, subtract: 8−8=08 - 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=02(4) - 8 = 0 instead of 8−2(4)=08 - 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.

Question 10

Evaluate the expression: 25−10+5−225 - 10 + 5 - 2

  1. 8
  2. 12
  3. 18 (correct answer)
  4. 22
Explanation: 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+5−225 - 10 + 5 - 2 step by step: First: 25−10=1525 - 10 = 15 Next: 15+5=2015 + 5 = 20 Finally: 20−2=1820 - 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=825 - (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=1225 - 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=2225 - 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.

Question 11

What is the value of 6×0+4÷26 \times 0 + 4 \div 2?

  1. 0
  2. 2 (correct answer)
  3. 5
  4. 12
Explanation: When you encounter an expression with multiple operations like this, you must follow the order of operations (PEMDAS/BODMAS). This means you perform multiplication and division from left to right before addition and subtraction. Let's work through 6×0+4÷26 \times 0 + 4 \div 2 step by step. First, handle the multiplication: 6×0=06 \times 0 = 0. Next, handle the division: 4÷2=24 \div 2 = 2. Finally, add the results: 0+2=20 + 2 = 2. Looking at the wrong answers: Choice A) 0 represents the trap of thinking that since 6×0=06 \times 0 = 0, the entire expression equals zero. This ignores the addition of 4÷24 \div 2. Choice C) 5 suggests you might have incorrectly calculated 4÷2=34 \div 2 = 3 and then added 0+3+2=50 + 3 + 2 = 5, or made some other computational error. Choice D) 12 could result from ignoring the order of operations entirely and working left to right: 6×0=06 \times 0 = 0, then 0+4=40 + 4 = 4, then 4÷2=24 \div 2 = 2, but this doesn't actually yield 12 either—this might catch students who panic and guess. The correct answer is B) 2. For IBEW electrical calculations, always remember that mathematical precision follows the same order of operations you'll use in electrical formulas. Whether you're calculating power, voltage, or current using complex expressions, applying PEMDAS correctly is essential. Practice breaking down multi-step problems systematically—this skill transfers directly to electrical circuit analysis.

Question 12

What is the value of −52+10-5^2 + 10?

  1. 15
  2. -15 (correct answer)
  3. -20
  4. 35
Explanation: This question tests your understanding of the order of operations and how negative signs interact with exponents—a critical skill for electrical calculations involving power and resistance formulas. When evaluating −52+10-5^2 + 10, you must carefully apply the order of operations. The exponent 525^2 is calculated first, giving you 25. The negative sign in front is then applied, making it −25-25. Finally, you add 10: −25+10=−15-25 + 10 = -15. The key insight is that −52-5^2 means "the opposite of 5 squared," not "negative 5, squared." If the problem intended the latter, it would be written as (−5)2(-5)^2, which equals positive 25. Choice A (15) represents the error of treating −52-5^2 as (−5)2=25(-5)^2 = 25, then adding 10 to get 35, but somehow arriving at 15—likely from calculation confusion. Choice C (-20) comes from incorrectly calculating −52-5^2 as −30-30 (perhaps confusing it with −5×6-5 \times 6) then adding 10. Choice D (35) results from the common mistake of treating −52-5^2 as (−5)2=25(-5)^2 = 25, then adding 10. For IBEW exam success, always remember that exponents take precedence over the negative sign unless parentheses indicate otherwise. When you see expressions like −a2-a^2, mentally insert parentheses around the exponent: −(a2)-(a^2). This distinction appears frequently in electrical formulas involving power calculations where sign errors can lead to serious miscalculations.

Question 13

Evaluate the expression: 4×(9−3)+24 \times (9 - 3) + 2

  1. 24
  2. 26 (correct answer)
  3. 32
  4. 35
Explanation: 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×(9−3)+24 \times (9 - 3) + 2 step by step: First, solve what's in parentheses: (9−3)=6(9 - 3) = 6 Next, perform the multiplication: 4×6=244 \times 6 = 24 Finally, add: 24+2=2624 + 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 4×64 \times 6. Choice C) 32 results from incorrectly applying order of operations—specifically, if you add first (3+2=53 + 2 = 5), then calculate 4×(9−5)=4×4=164 \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: 4×9=364 \times 9 = 36, then 36−3=3336 - 3 = 33, then 33+2=3533 + 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.

Question 14

Evaluate: 2×52−(10+5)2 \times 5^2 - (10 + 5)

  1. 15
  2. 35 (correct answer)
  3. 85
  4. 90
Explanation: This question tests your ability to apply the correct order of operations (PEMDAS/BODMAS) when evaluating mathematical expressions - a fundamental skill you'll use regularly in electrical calculations. Let's work through 2×52−(10+5)2 \times 5^2 - (10 + 5) step by step. First, handle operations inside parentheses: (10+5)=15(10 + 5) = 15. Next, calculate the exponent: 52=255^2 = 25. Then perform multiplication: 2×25=502 \times 25 = 50. Finally, subtract: 50−15=3550 - 15 = 35. Looking at the wrong answers reveals common order-of-operations mistakes. Choice A (15) occurs if you incorrectly calculate 2×5=102 \times 5 = 10, then 102=10010^2 = 100, subtract 85, getting confused in the process. Choice C (85) happens if you work left to right without following proper order: 2×5=102 \times 5 = 10, then 102=10010^2 = 100, subtract 1515 to get 8585. Choice D (90) results from adding instead of subtracting at the end: 2×25+15=652 \times 25 + 15 = 65 (though this doesn't quite match either, suggesting multiple errors). The correct answer is B (35). Study tip: Always write out PEMDAS when tackling complex expressions: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). In electrical work, you'll encounter formulas with multiple operations - like power calculations with squared terms - so mastering order of operations now will prevent costly errors in real-world applications.

Question 15

An electrician needs to calculate the total resistance of a circuit section. The formula is given by the expression 15+123×2215 + \frac{12}{3} \times 2^2.

What is the total resistance in ohms based on the given expression?

  1. 19 ohms
  2. 31 ohms (correct answer)
  3. 32 ohms
  4. 81 ohms
Explanation: 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+123×2215 + \frac{12}{3} \times 2^2, you must follow the order of operations strictly. First, handle the exponent: 22=42^2 = 4. Next, perform the division: 123=4\frac{12}{3} = 4. Then multiply: 4×4=164 \times 4 = 16. Finally, add: 15+16=3115 + 16 = 31 ohms. Answer A (19 ohms) results from incorrectly adding first: (15+12)÷3×4=27÷3×4=36(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+22=15+4+4=2315 + 12 ÷ 3 + 2^2 = 15 + 4 + 4 = 23, then making an arithmetic error, or from 15+12+3+2=3215 + 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=322(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.

Question 16

Calculate the value of the expression: 10+62×4\frac{10 + 6}{2 \times 4}

  1. 2 (correct answer)
  2. 22
  3. 26
  4. 32
Explanation: When you encounter mathematical expressions with multiple operations, the order of operations (PEMDAS/BODMAS) is crucial. This fundamental concept appears regularly on electrical calculations, so mastering it now will serve you well throughout the IBEW exam. Let's work through 10+62×4\frac{10 + 6}{2 \times 4} step by step. First, you must evaluate the numerator and denominator separately before dividing. In the numerator: 10+6=1610 + 6 = 16 In the denominator: 2×4=82 \times 4 = 8 (multiplication comes before addition in order of operations) Now you can divide: 168=2\frac{16}{8} = 2 Looking at the wrong answers reveals common mistakes. Choice B (22) likely comes from incorrectly calculating 10+6+2×4=10+6+8=2410 + 6 + 2 \times 4 = 10 + 6 + 8 = 24, then making an arithmetic error. Choice C (26) probably results from adding all numbers without respecting the fraction structure: 10+6+2+4+4=2610 + 6 + 2 + 4 + 4 = 26. Choice D (32) might come from incorrectly multiplying the numerator and denominator: (10+6)×(2×4)=16×2=32(10 + 6) \times (2 \times 4) = 16 \times 2 = 32, forgetting this should be division, not multiplication. The key strategy is to always treat fractions as division problems where you complete all operations in the numerator first, then all operations in the denominator, then divide the results. Never mix operations between numerator and denominator until you're ready for that final division step.

Question 17

Calculate the value of 12÷(−2)2+512 \div (-2)^2 + 5.

  1. -1
  2. 2
  3. 8 (correct answer)
  4. 11
Explanation: This question tests your understanding of the order of operations (PEMDAS/BODMAS) and how to handle negative numbers with exponents. When you see mixed operations like this, you must follow the correct sequence to avoid common calculation errors. Let's work through 12÷(−2)2+512 \div (-2)^2 + 5 step by step. First, handle the exponent: (−2)2=(−2)×(−2)=4(-2)^2 = (-2) \times (-2) = 4. Remember that when you square a negative number, the result is always positive because you're multiplying two negative values. Next, perform the division: 12÷4=312 \div 4 = 3. Finally, add: 3+5=83 + 5 = 8. Looking at the wrong answers: Choice A (-1) likely comes from incorrectly calculating (−2)2(-2)^2 as −4-4 instead of positive 4, then getting 12÷(−4)+5=−3+5=212 \div (-4) + 5 = -3 + 5 = 2, but making an additional error. Choice B (2) results from the same mistake with the exponent (treating (−2)2(-2)^2 as −4-4), giving 12÷(−4)+5=−3+5=212 \div (-4) + 5 = -3 + 5 = 2. Choice D (11) comes from incorrectly applying the order of operations, perhaps calculating 12÷(−2)+512 \div (-2) + 5 first to get −6+5=−1-6 + 5 = -1, then squaring that result, or making other sequence errors. The key strategy here is to always remember that exponents come before division in the order of operations, and that squaring any real number (positive or negative) always yields a positive result. Write out each step clearly to avoid rushing through the calculation sequence.

Question 18

Evaluate the expression: 42−2×35\frac{4^2 - 2 \times 3}{5}

  1. 25\frac{2}{5}
  2. 145\frac{14}{5}
  3. 105\frac{10}{5} (correct answer)
  4. 103\frac{10}{3}
Explanation: When you encounter algebraic expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS) carefully. This means handling parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). Let's work through 42−2×35\frac{4^2 - 2 \times 3}{5} step by step. First, evaluate the exponent: 42=164^2 = 16. Next, handle the multiplication: 2×3=62 \times 3 = 6. Now the expression becomes 16−65\frac{16 - 6}{5}. Perform the subtraction in the numerator: 16−6=1016 - 6 = 10. Finally, you have 105=2\frac{10}{5} = 2, which equals 105\frac{10}{5} in fraction form. Looking at the wrong answers: Choice A (25\frac{2}{5}) likely results from incorrectly calculating the numerator as 2 instead of 10, perhaps by confusing the order of operations. Choice B (145\frac{14}{5}) suggests someone added instead of subtracting: 42+2×3=16+6=224^2 + 2 \times 3 = 16 + 6 = 22, but even then the arithmetic is off. Choice D (103\frac{10}{3}) gets the correct numerator (10) but uses 3 as the denominator instead of 5, possibly mixing up numbers from the original expression. The correct answer is C: 105\frac{10}{5}. For IBEW math problems, always write out each step of the order of operations. Electrical calculations often involve complex expressions, and skipping steps or rushing through the order of operations leads to costly errors in real-world applications.

Question 19

Evaluate the expression: 9+[24÷(3×2)]−19 + [24 \div (3 \times 2)] - 1

  1. 4
  2. 12 (correct answer)
  3. 15
  4. 20
Explanation: 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÷(3×2)]−19 + [24 \div (3 \times 2)] - 1 step by step. Start with the innermost parentheses: (3×2)=6(3 \times 2) = 6. Now the expression becomes 9+[24÷6]−19 + [24 \div 6] - 1. Next, handle the division inside the brackets: 24÷6=424 \div 6 = 4, giving us 9+4−19 + 4 - 1. Finally, work left to right with addition and subtraction: 9+4=139 + 4 = 13, then 13−1=1213 - 1 = 12. Choice A (4) likely comes from calculating only the bracketed portion [24÷(3×2)]=4[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=379 + 24 + 3 + 2 - 1 = 37, or perhaps 9+4+3−1=159 + 4 + 3 - 1 = 15 by mixing up intermediate steps. Choice D (20) might come from adding 9+24÷6−1=9+4−19 + 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.

Question 20

What is the value of 8−(−3)28 - (-3)^2?

  1. -1 (correct answer)
  2. 14
  3. 17
  4. 25
Explanation: When you encounter expressions with negative numbers and exponents, the order of operations and careful attention to parentheses becomes crucial. This question tests whether you understand how exponents interact with negative signs. Let's work through 8−(−3)28 - (-3)^2 step by step. First, you need to evaluate (−3)2(-3)^2. Since the negative sign is inside the parentheses, you're squaring the entire negative number: (−3)2=(−3)×(−3)=9(-3)^2 = (-3) \times (-3) = 9. Now the expression becomes 8−9=−18 - 9 = -1. Looking at the wrong answers reveals common mistakes. Answer B (14) likely comes from incorrectly treating the expression as 8+(−3)28 + (-3)^2, turning the subtraction into addition and getting 8+9=178 + 9 = 17. Wait, that would be answer C (17). Answer B (14) might result from misunderstanding the exponent entirely. Answer C (17) definitely comes from changing the subtraction to addition: 8+(−3)2=8+9=178 + (-3)^2 = 8 + 9 = 17. Answer D (25) probably results from incorrectly calculating (−3)2(-3)^2 as something other than 9, or from a completely different computational error. The key trap here is the order of operations with negative numbers. Remember that (−3)2=9(-3)^2 = 9, but −32=−9-3^2 = -9 because without parentheses, you'd square 3 first, then apply the negative sign. For IBEW math problems involving exponents and negative numbers, always identify what's inside parentheses first, handle exponents before other operations, and double-check your signs throughout each step.