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7th Grade Math Quiz

7th Grade Math Quiz: Understand Additive Inverses

Practice Understand Additive Inverses in 7th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

Question 1 / 20

0 of 20 answered

An elevator starts at the ground floor (Floor 0). It goes up 777 floors, then down 444 floors, then up 111111 floors, then down 141414 floors. At this point, the elevator is at Floor 0 again. A passenger observes that the elevator's movement demonstrates additive inverses. Which explanation best describes what the passenger noticed?

Select an answer to continue

What this quiz covers

This quiz focuses on Understand Additive Inverses, giving you a quick way to practice the rules, question types, and explanations that matter most for 7th Grade Math.

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

An elevator starts at the ground floor (Floor 0). It goes up 777 floors, then down 444 floors, then up 111111 floors, then down 141414 floors. At this point, the elevator is at Floor 0 again. A passenger observes that the elevator's movement demonstrates additive inverses. Which explanation best describes what the passenger noticed?

  1. Going up 777 floors and down 777 floors are additive inverses, as are other equal up-down pairs
  2. The total upward movement and total downward movement are equal and opposite, making them additive inverses (correct answer)
  3. The net displacement of 000 floors shows that all movements combined equal the additive inverse of the starting position
  4. Each upward movement has a corresponding downward movement that serves as its additive inverse

Explanation: Up movements: +7 + 11 = +18 floors. Down movements: -4 + (-14) = -18 floors. The total up (+18) and total down (-18) are additive inverses because they sum to zero. Choice A incorrectly pairs movements that aren't equal. Choice C misuses the concept - the starting position is 0, and its additive inverse is also 0. Choice D is incorrect because the movements don't pair up as described (7 up, 4 down, 11 up, 14 down).

Question 2

Which number must be added to 12\frac{1}{2}21​ to make 000?

  1. −12-\frac{1}{2}−21​ (correct answer)
  2. −2-2−2
  3. 222
  4. 12\frac{1}{2}21​

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, the number 1/2 has an inverse of -1/2 since 1/2 + (-1/2) = 0. The number that must be added to 1/2 to make 0 is -1/2, as it is the additive inverse. A common error is confusing it with the reciprocal 2 (multiplicative inverse: 1/2 × 2 = 1), or wrongly picking -2 by inverting incorrectly, but additive inverses sum to zero, not multiply to 1. Finding the additive inverse involves flipping the sign (1/2→-1/2), and verifying means checking if they sum to zero (1/2 + (-1/2) = 0, yes). Mistakes include claiming the sum is not zero or using the wrong operation.

Question 3

A submarine's depth changes are recorded as: dives 454545 feet, rises 202020 feet, dives 353535 feet, rises 151515 feet, then dives 252525 feet. After these movements, the submarine is 707070 feet below its starting depth. The captain wants to return to the starting depth in one movement. This situation illustrates additive inverses in which way?

  1. The total diving distance and total rising distance are additive inverses of each other
  2. Each dive and rise movement has an additive inverse that cancels its effect completely
  3. The required movement (+70+70+70 feet) is the additive inverse of the current displacement (−70-70−70 feet) (correct answer)
  4. The starting depth and ending depth are additive inverses that sum to the required movement

Explanation: When you see problems involving opposite movements and returning to a starting point, you're working with additive inverses - numbers that add up to zero and cancel each other out. Let's track the submarine's movements. Diving means going down (negative), and rising means going up (positive): −45+20−35+15−25=−70-45 + 20 - 35 + 15 - 25 = -70−45+20−35+15−25=−70 feet. The submarine is now 70 feet below its starting depth, which we represent as −70-70−70 feet. To return to the starting depth, the submarine needs to move up 70 feet, or +70+70+70 feet. Notice that −70+70=0-70 + 70 = 0−70+70=0, which brings the submarine back to its starting point (zero displacement). This demonstrates additive inverses perfectly: the current displacement (−70-70−70) and the required movement (+70+70+70) are opposites that sum to zero. Answer A is incorrect because the total diving distance (105 feet) and total rising distance (35 feet) don't add to zero - they're not additive inverses. Answer B misunderstands the concept; individual movements don't have inverses within this problem. Answer D incorrectly suggests that depths themselves are additive inverses, when actually it's the displacement and correction movement that form the additive inverse pair. Remember: additive inverses always sum to zero. When you need to "undo" a displacement or return to a starting point, look for the number that, when added to your current position, gives you zero change overall.

Question 4

Sarah's science experiment involves adding chemicals to a solution. She adds 2.52.52.5 mL of acid, then 1.81.81.8 mL of base, then 3.23.23.2 mL of acid, then some amount of base. After all additions, the solution has the same acidity level as when she started. If acids and bases neutralize each other in a 1:11:11:1 ratio, how much base did she add in the final step?

  1. 3.93.93.9 mL, because this amount makes the total acid equal the total base added (correct answer)
  2. 5.75.75.7 mL, because this creates additive inverses with the total acid amount
  3. 1.81.81.8 mL, because this balances the 3.23.23.2 mL of acid added in the third step
  4. 2.52.52.5 mL, because this balances the 2.52.52.5 mL of acid added in the first step

Explanation: Total acid added: 2.5 + 3.2 = 5.7 mL. Base already added: 1.8 mL. To neutralize all acid, total base needed: 5.7 mL. Additional base needed: 5.7 - 1.8 = 3.9 mL. The total acid (5.7 mL) and total base (5.7 mL) are additive inverses in terms of their effect on acidity. Choice B confuses the final amount with the total. Choices C and D only consider partial neutralization rather than complete neutralization.

Question 5

What is the additive inverse (opposite) of −12-12−12?

  1. 000
  2. 121212 (correct answer)
  3. 112\frac{1}{12}121​
  4. −12-12−12

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, the number -12 has an inverse of 12 since -12 + 12 = 0. The correct inverse here is 12, as it flips the sign of -12 to make the sum zero. A common error is claiming the inverse of -12 is still -12 (not flipping the sign), or confusing it with the reciprocal 1/12, which is the multiplicative inverse where -12 × (1/-12) = 1, not additive. Finding the additive inverse involves flipping the sign (-12→12), and verifying means checking if they sum to zero (-12 + 12 = 0, yes). Properties include the inverse being unique (only 12 adds with -12 to give 0), and avoiding mistakes like claiming the sum is not zero.

Question 6

A thermometer shows a temperature increase of 8∘8^\circ8∘C in the morning and a decrease of 8∘8^\circ8∘C in the afternoon. What is the total change in temperature for the day?

  1. 0∘0^\circ0∘C (correct answer)
  2. −16∘-16^\circ−16∘C
  3. 8∘8^\circ8∘C
  4. 16∘16^\circ16∘C

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, a temperature rise of 8°C is +8, a fall of 8°C is -8, and combined: 8 + (-8) = 0 net change (back to starting temperature). The total change is 0°C because the increase and decrease are additive inverses that cancel. A common error might be adding absolute values to get 16°C or halving to 8°C, or wrongly claiming -16°C by doubling the negative, but opposites sum to zero. Finding the additive inverse involves flipping the sign (+8→-8), and verifying means checking if they sum to zero (8 + (-8) = 0, yes). In contexts like weather, opposite changes neutralize, and the property is commutative: +8 + (-8) = (-8) + 8 = 0.

Question 7

A student deposits 35intoaschoolstoreaccountandlaterwithdraws35 into a school store account and later withdraws 35intoaschoolstoreaccountandlaterwithdraws35. What is the net change in the account balance?

  1. $-35
  2. $35
  3. $0 (correct answer)
  4. $70

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like a deposit of 50andwithdrawalof50 and withdrawal of 50andwithdrawalof50 summing to 0netchange(oppositetransactionscancel),temperaturerising8°andfalling8°giving0°netchange(oppositechangescancel),orgaining15yardsandlosing15yardsresultingin0netyards(oppositedirectionscancel);everynumberhasanadditiveinverse:5→−5,−3→3(flipthesign),2.5→−2.5,even0→0(zeroisitsowninverse).Forexample,adepositof0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip the sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, a deposit of 0netchange(oppositetransactionscancel),temperaturerising8°andfalling8°giving0°netchange(oppositechangescancel),orgaining15yardsandlosing15yardsresultingin0netyards(oppositedirectionscancel);everynumberhasanadditiveinverse:5→−5,−3→3(flipthesign),2.5→−2.5,even0→0(zeroisitsowninverse).Forexample,adepositof35 is modeled as +35, and a withdrawal of 35as−35,combined:35+(−35)=0net(backtostartingbalance).Inthiscase,thenetchangeintheaccountbalanceis35 as -35, combined: 35 + (-35) = 0 net (back to starting balance). In this case, the net change in the account balance is 35as−35,combined:35+(−35)=0net(backtostartingbalance).Inthiscase,thenetchangeintheaccountbalanceis0, as the deposit and withdrawal are additive inverses that cancel each other out. A common error might be thinking the net is 70byaddingtheabsolutevaluesorclaiming−35,confusingthewithdrawalasthefinalbalance.Tofindtheadditiveinverse,simplyflipthesign(5→−5,−3→3,0→0),andverifybycheckingifa+b=0(if7+(−7)=0,yesinverses;if7+5=12≠0,notinverses).Inreal−worldcontextslikebankaccounts,adepositof70 by adding the absolute values or claiming -35, confusing the withdrawal as the final balance. To find the additive inverse, simply flip the sign (5→-5, -3→3, 0→0), and verify by checking if a + b = 0 (if 7 + (-7) = 0, yes inverses; if 7 + 5 = 12 ≠ 0, not inverses). In real-world contexts like bank accounts, a deposit of 70byaddingtheabsolutevaluesorclaiming−35,confusingthewithdrawalasthefinalbalance.Tofindtheadditiveinverse,simplyflipthesign(5→−5,−3→3,0→0),andverifybycheckingifa+b=0(if7+(−7)=0,yesinverses;if7+5=12=0,notinverses).Inreal−worldcontextslikebankaccounts,adepositof100 and withdrawal of $100 leave the balance unchanged (opposites neutralize), and remember the property that the inverse is unique (only one number adds with 35 to give 0: must be -35).

Question 8

A student deposits \25intoaschoolstoreaccountandlaterwithdrawsinto a school store account and later withdrawsintoaschoolstoreaccountandlaterwithdraws$25$. What is the net change in the account balance? (Think of withdrawal as a negative change.)

  1. 252525
  2. −25-25−25
  3. 000 (correct answer)
  4. 505050

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like a deposit of 50andwithdrawalof50 and withdrawal of 50andwithdrawalof50 summing to 0netchange(oppositetransactionscancel),temperaturerising8°andfalling8°giving0°netchange(oppositechangescancel),orgaining15yardsandlosing15yardsresultingin0netyards(oppositedirectionscancel);everynumberhasanadditiveinverse:5→−5,−3→3(flipsign),2.5→−2.5,even0→0(zeroisitsowninverse).Forexample,adepositof0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, a deposit of 0netchange(oppositetransactionscancel),temperaturerising8°andfalling8°giving0°netchange(oppositechangescancel),orgaining15yardsandlosing15yardsresultingin0netyards(oppositedirectionscancel);everynumberhasanadditiveinverse:5→−5,−3→3(flipsign),2.5→−2.5,even0→0(zeroisitsowninverse).Forexample,adepositof25 is modeled as +25, and a withdrawal of 25as−25,combined:25+(−25)=0net(backtostartingbalance).Inthiscase,thenetchangeis25 as -25, combined: 25 + (-25) = 0 net (back to starting balance). In this case, the net change is 25as−25,combined:25+(−25)=0net(backtostartingbalance).Inthiscase,thenetchangeis0, as the deposit and withdrawal are additive inverses that cancel each other out. A common error is thinking the net is $50 by adding magnitudes without signs (25 + 25 = 50) or confusing with multiplication, but actually, opposites sum to zero. To find an additive inverse, flip the sign (like 25 → -25). You can verify by checking if they sum to zero: 25 + (-25) = 0, confirming they are inverses; in real-world contexts like bank accounts, a deposit and equal withdrawal leave the balance unchanged.

Question 9

A hiker climbs 200200200 meters up a trail and then goes 200200200 meters back down to the starting elevation. Which expression shows the net change in elevation?

  1. 200+(−200)=0200 + (-200) = 0200+(−200)=0 (correct answer)
  2. −200+(−200)=−400-200 + (-200) = -400−200+(−200)=−400
  3. 200+200=400200 + 200 = 400200+200=400
  4. 200×(−200)=−40,000200 \times (-200) = -40{,}000200×(−200)=−40,000

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, climbing +200 m and descending -200 m: 200 + (-200) = 0 net change (back to start). The correct expression is 200 + (-200) = 0, showing the net elevation change as zero due to additive inverses. A common error is using multiplication like 200 × (-200) = -40,000 (confusing operations) or adding positives to 400 (ignoring signs), but additive inverses involve addition to zero. Finding the additive inverse involves flipping the sign (200→-200), and verifying means checking if they sum to zero (200 + (-200) = 0, yes). In hiking contexts, up and down are opposites that cancel when equal.

Question 10

A student deposits 30intoaschoolstoreaccountandlaterwithdraws30 into a school store account and later withdraws 30intoaschoolstoreaccountandlaterwithdraws30. What is the net change in the account balance?

  1. $30
  2. $60
  3. $0 (correct answer)
  4. $-60

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to 0netchange(oppositetransactionscancel),temperaturerising8°andfalling8°giving0°netchange(oppositechangescancel),orgaining15yardsandlosing15yardsresultingin0netyards(oppositedirectionscancel);everynumberhasanadditiveinverse:5→−5,−3→3(flipsign),2.5→−2.5,even0→0(zeroisitsowninverse).Forexample,adepositof0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, a deposit of 0netchange(oppositetransactionscancel),temperaturerising8°andfalling8°giving0°netchange(oppositechangescancel),orgaining15yardsandlosing15yardsresultingin0netyards(oppositedirectionscancel);everynumberhasanadditiveinverse:5→−5,−3→3(flipsign),2.5→−2.5,even0→0(zeroisitsowninverse).Forexample,adepositof30 is modeled as +30, a withdrawal of 30as−30,andcombined:30+(−30)=0net(backtostartingbalance).Inthiscase,thenetchangeis30 as -30, and combined: 30+(-30)=0 net (back to starting balance). In this case, the net change is 30as−30,andcombined:30+(−30)=0net(backtostartingbalance).Inthiscase,thenetchangeis0 because the deposit and withdrawal are additive inverses that cancel each other out. A common error might be thinking the net is 60byaddingtheabsolutevalueswithoutconsideringsigns,orconfusingitwith60 by adding the absolute values without considering signs, or confusing it with 60byaddingtheabsolutevalueswithoutconsideringsigns,orconfusingitwith30 by halving, but actually, opposites cancel to zero. Finding the additive inverse involves flipping the sign (like +30→-30), and verifying means checking if they sum to zero (30 + (-30) = 0, yes). In real-world contexts, such as bank accounts, a deposit and equal withdrawal leave the balance unchanged, demonstrating how opposites neutralize each other.

Question 11

What is the value of −(−9)-(-9)−(−9)?

  1. −18-18−18
  2. 000
  3. 999 (correct answer)
  4. −9-9−9

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, the additive inverse of 9 is -9, so -(-9) applies the negative sign to -9, flipping it back to 9, since -(-9) = 9. The value is 9, as taking the negative of a negative number gives the positive (the additive inverse of -9 is 9). A common error is keeping it negative like -9 (not flipping) or doubling to -18 (confusing with multiplication), or claiming 0 (misunderstanding), but -(-a) = a. Finding the additive inverse involves flipping the sign (-9→9), and verifying means checking if -9 + 9 = 0, yes. Properties include the inverse being unique, and this shows double negation returns the original.

Question 12

Are −9-9−9 and 999 additive inverses? (In other words, do they add to 000?)

  1. Yes, because −9-9−9 is the reciprocal of 999.
  2. Yes, because −9+9=0-9 + 9 = 0−9+9=0. (correct answer)
  3. No, because −9+9=18-9 + 9 = 18−9+9=18.
  4. No, because −9×9=−1-9 \times 9 = -1−9×9=−1.

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like a deposit of 50andwithdrawalof50 and withdrawal of 50andwithdrawalof50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip the sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, -9 and 9 sum to -9 + 9 = 0, so they are additive inverses. Yes, -9 and 9 are additive inverses because -9 + 9 = 0. A common error is confusing with multiplication like -9 × 9 = -81 or claiming the sum is 18 by adding absolutes, or mixing with reciprocal where 1/9 × 9 = 1. To find the additive inverse, simply flip the sign (5→-5, -3→3, 0→0), and verify by checking if a + b = 0 (if -9 + 9 = 0, yes inverses; if -9 + (-9) = -18 ≠ 0, not). Avoid mistakes like confusing additive and multiplicative inverses (a + (-a) = 0 vs. a × (1/a) = 1 are different), or claiming the sum is non-zero.

Question 13

Which number must be added to 34\dfrac{3}{4}43​ to make 000?

  1. −34-\dfrac{3}{4}−43​ (correct answer)
  2. −43-\dfrac{4}{3}−34​
  3. 43\dfrac{4}{3}34​
  4. 34\dfrac{3}{4}43​

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like a deposit of 50andwithdrawalof50 and withdrawal of 50andwithdrawalof50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip the sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, the number 3/4 has an inverse of -3/4 since 3/4 + (-3/4) = 0. The number that must be added to 3/4 to make 0 is -3/4, as it is the additive inverse. A common error is confusing with the reciprocal 4/3, which is the multiplicative inverse (3/4 × 4/3 = 1), not additive, or claiming 3/4 itself where the sum is not zero. To find the additive inverse, simply flip the sign (5→-5, -3→3, 0→0), and verify by checking if a + b = 0 (if 3/4 + (-3/4) = 0, yes; if 3/4 + 4/3 ≠ 0, not). Properties include commutativity (3/4 + (-3/4) = (-3/4) + 3/4 = 0), and avoid claiming the sum is non-zero or using the wrong sign.

Question 14

Which statement about additive inverses is true?

  1. Every number has an additive inverse, and a+(−a)=0a + (-a) = 0a+(−a)=0. (correct answer)
  2. Additive inverses multiply to 000.
  3. Only positive numbers have additive inverses.
  4. The additive inverse of −3-3−3 is −3-3−3.

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like a deposit of 50andwithdrawalof50 and withdrawal of 50andwithdrawalof50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, every number like -3 has an inverse of 3, since -3 + 3 = 0. The true statement is that every number has an additive inverse, and a + (-a) = 0. A common error is thinking inverses multiply to 0 or that only positives have them, but they add to 0 and all numbers do. To find an additive inverse, flip the sign. Verifying: check sum to zero; mistakes confuse with multiplicative inverses.

Question 15

A submarine moves down 505050 meters (represented by −50-50−50) and then moves up 505050 meters (represented by +50+50+50). What is the total change in its position?

  1. −50-50−50 meters
  2. −100-100−100 meters
  3. 000 meters (correct answer)
  4. 100100100 meters

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, moving down -50 m and up +50 m: -50 + 50 = 0 net change (back to start). The total change is 0 meters because the movements are additive inverses that cancel. A common error might be subtracting to -100 (adding negatives) or halving to -50, or claiming +100 (ignoring signs), but they sum to zero. Finding the additive inverse involves flipping the sign (-50→+50), and verifying means checking if they sum to zero (-50 + 50 = 0, yes). In contexts like submarines, down and up are opposites that neutralize when equal.

Question 16

Are 777 and −7-7−7 additive inverses? (In other words, do they add to 000?)

  1. Yes, because 7+(−7)=−147 + (-7) = -147+(−7)=−14
  2. Yes, because 7+(−7)=07 + (-7) = 07+(−7)=0 (correct answer)
  3. No, because 7+(−7)=147 + (-7) = 147+(−7)=14
  4. No, because 7×(−7)=−17 \times (-7) = -17×(−7)=−1

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, the number 7 has an inverse of -7 since 7 + (-7) = 0. Yes, 7 and -7 are additive inverses because 7 + (-7) = 0. A common error is confusing with multiplication (7 × (-7) = -49, not -1 as stated, but irrelevant) or miscalculating the sum as 14 or -14 (adding wrong). Finding the additive inverse involves flipping the sign (7→-7), and verifying means checking if a + b = 0 (7 + (-7) = 0, yes; 7 + 5 = 12 ≠ 0, no). Properties include commutativity: 7 + (-7) = (-7) + 7 = 0, and avoiding mixing with multiplicative inverses.

Question 17

A football team gains 151515 yards on one play and loses 151515 yards on the next play. What is the net change in yardage?

  1. 151515 yards
  2. −30-30−30 yards
  3. 303030 yards
  4. 000 yards (correct answer)

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, gaining 15 yards is +15, losing 15 yards is -15, and combined: 15 + (-15) = 0 net yards. The net change is 0 yards because the gain and loss are additive inverses that cancel. A common error might be adding to 30 yards (ignoring signs) or halving to 15, or claiming -30 by doubling negative, but opposites sum to zero. Finding the additive inverse involves flipping the sign (+15→-15), and verifying means checking if they sum to zero (15 + (-15) = 0, yes). In sports like football, gains and losses are opposites that neutralize when equal.

Question 18

Which statement correctly defines an additive inverse?

  1. The additive inverse of aaa is the number that makes a+(inverse)=0a + (\text{inverse}) = 0a+(inverse)=0. (correct answer)
  2. The additive inverse of aaa is the number that makes a×(inverse)=1a \times (\text{inverse}) = 1a×(inverse)=1.
  3. Only 000 has an additive inverse.
  4. The additive inverse of aaa is always ∣a∣|a|∣a∣.

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like depositing 50andwithdrawing50 and withdrawing 50andwithdrawing50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, for any a, its inverse b satisfies a + b = 0, so b = -a. The correct statement is that the additive inverse of a is the number that makes a + (inverse) = 0. A common error is confusing it with multiplicative inverse (a × inverse = 1) or wrongly saying only 0 has one (all numbers do), or claiming it's |a| (which is positive and doesn't work for positives). Finding the additive inverse involves flipping the sign (5→-5), and verifying means checking if a + b = 0. Mistakes include using the wrong operation or limiting inverses incorrectly.

Question 19

During a science experiment, the temperature rises by 8∘C8^\circ\text{C}8∘C and later falls by 8∘C8^\circ\text{C}8∘C. What is the total change in temperature?

  1. 16∘C16^\circ\text{C}16∘C
  2. 0∘C0^\circ\text{C}0∘C (correct answer)
  3. −16∘C-16^\circ\text{C}−16∘C
  4. −8∘C-8^\circ\text{C}−8∘C

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like a deposit of 50andwithdrawalof50 and withdrawal of 50andwithdrawalof50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip the sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, a temperature rise of 8°C is +8, and a fall of 8°C is -8, combined: 8 + (-8) = 0 net change (back to starting temperature). The total change in temperature is 0°C, as the rise and fall are additive inverses that cancel each other. A common error might be adding the absolute values to get 16°C or claiming -16°C by doubling the fall incorrectly. To find the additive inverse, simply flip the sign (5→-5, -3→3, 0→0), and verify by checking if a + b = 0 (if 8 + (-8) = 0, yes inverses; if 8 + 8 = 16 ≠ 0, not inverses). In contexts like temperature changes, identify opposites (rise ↔ fall), and they combine to zero net effect; remember zero is special as its own inverse.

Question 20

A hiker climbs 200200200 meters up a trail and then walks 200200200 meters back down. What is the hiker’s net change in elevation?

  1. 000 meters (correct answer)
  2. −200-200−200 meters
  3. 200200200 meters
  4. 400400400 meters

Explanation: This question tests understanding of additive inverses: opposite quantities (a and -a) that combine to zero (a+(-a)=0), occurring when opposite transactions, changes, or directions cancel. The additive inverse of a is -a: a number with the opposite sign that sums to zero (7 and -7: 7+(-7)=0, mutually inverse); in contexts like a deposit of 50andwithdrawalof50 and withdrawal of 50andwithdrawalof50 summing to $0 net change (opposite transactions cancel), temperature rising 8° and falling 8° giving 0° net change (opposite changes cancel), or gaining 15 yards and losing 15 yards resulting in 0 net yards (opposite directions cancel); every number has an additive inverse: 5→-5, -3→3 (flip the sign), 2.5→-2.5, even 0→0 (zero is its own inverse). For example, climbing +200 m and descending -200 m: 200 + (-200) = 0 net change (back to start). The hiker’s net change in elevation is 0 meters, as the up and down movements are additive inverses that cancel. A common error might be adding to 400 meters or claiming 200 meters by ignoring the direction. To find the additive inverse, simply flip the sign (5→-5, -3→3, 0→0), and verify by checking if a + b = 0 (if 200 + (-200) = 0, yes inverses; if 200 + 200 = 400 ≠ 0, not). In contexts like elevation, identify opposites (up ↔ down), and they combine to zero net effect; the inverse is unique (only -200 adds with 200 to 0).