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Understand Additive Inverses - 7th Grade Math

  1. A submarine moves down 5050 meters (represented by −50-50) and then moves up 5050 meters (represented by +50+50). What is the total change in its position?
    Answer: 00 meters 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 $50 and withdrawing $50 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.
  2. A student deposits $30 into a school store account and later withdraws $30. What is the net change in the account balance?
    Answer: $0 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 $50 and withdrawing $50 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 deposit of $30 is modeled as +30, a withdrawal of $30 as -30, and combined: 30+(-30)=0 net (back to starting balance). In this case, the net change is $0 because the deposit and withdrawal are additive inverses that cancel each other out. A common error might be thinking the net is $60 by adding the absolute values without considering signs, or confusing it with $30 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.
  3. A hiker climbs 200200 meters up a trail and then walks 200200 meters back down. What is the hiker's net change in elevation?
    Answer: 00 meters 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 $50 and withdrawal of $50 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).
  4. In a football game, a team gains 1515 yards on one play and loses 1515 yards on the next play. What is the net change in yards?
    Answer: 00 yards 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 $50 and withdrawal of $50 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 and losing -15 yards: 15 + (-15) = 0 net. The net change in yards is 0, as gain and loss are additive inverses. A common error is adding to 30 yards or halving to 15, but opposites sum to zero net. To find an additive inverse, flip the sign (15 → -15). In sports contexts, opposite plays cancel; zero is special as its own inverse.
  5. A football team gains 1515 yards on one play and loses 1515 yards on the next play. What is the net change in yardage?
    Answer: 00 yards 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 $50 and withdrawing $50 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.
  6. In a card game, positive cards add points and negative cards subtract points. Jamie draws cards with values +8+8, −12-12, +15+15, −6-6, and +7+7. To end the round with exactly 00 points, Jamie needs to draw one more card. What value must this card have, and why does this demonstrate additive inverses?
    Answer: −12-12, because it's the additive inverse of the current total, making the final sum zero The current total is 8-12+15-6+7=12. To reach zero, Jamie needs a card worth -12, since 12+(-12)=0, the additive inverse of the total. This matches choice C. Choice A incorrectly assumes the inverse must share the same sign as the original number; an additive inverse always has the opposite sign. Choice B only considers one card already drawn (-6) rather than the running total of all five cards. Choice D uses only the largest single card (+15) instead of the total of all cards drawn so far.
  7. A robot moves forward 2.5 meters and then moves backward 2.5 meters. Which equation both models this situation and correctly shows the net change in position?
    Answer: 2.5+(−2.5)=02.5 + (-2.5) = 0 Moving forward 2.5 meters is a positive change, and moving backward 2.5 meters is a negative change, so the situation is modeled by 2.5 + (-2.5). Adding these opposite values gives a net change of 0, which matches this being the correct equation both for the situation and for the arithmetic. Choice B is wrong because multiplying does not represent combining forward and backward movements. Choice C is wrong because it adds two positive movements, which would mean the robot moved 5 meters forward only. Choice D is wrong because it adds two negative movements, which would mean the robot moved 5 meters backward only.
  8. Which number must be added to 34\dfrac{3}{4} to make 00?
    Answer: −34-\dfrac{3}{4} 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 $50 and withdrawal of $50 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.
  9. During a science experiment, the temperature rises by 8∘C8^\circ\text{C} and later falls by 8∘C8^\circ\text{C}. What is the total change in temperature?
    Answer: 0∘C0^\circ\text{C} 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 $50 and withdrawal of $50 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.
  10. Are −9-9 and 99 additive inverses? (In other words, do they add to 00?)
    Answer: Yes, because −9+9=0-9 + 9 = 0. 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 $50 and withdrawal of $50 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.
  11. In football, a team gains 1515 yards on one play and loses 1515 yards on the next play. What is the net change in yards?
    Answer: 00 yards 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 $50 and withdrawal of $50 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, gaining +15 yards and losing -15 yards: 15 + (-15) = 0 net. The net change in yards is 0 yards, as the gain and loss are additive inverses that cancel. A common error might be adding to 30 yards or halving to 15 yards 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 15 + (-15) = 0, yes; if 15 + 15 = 30 ≠ 0, not). In sports contexts like football, identify opposites (gain ↔ loss), and they combine to zero net effect; remember the commutative property (15 + (-15) = (-15) + 15 = 0).
  12. A weather station records wind speed changes each hour: up 55 mph, down 88 mph, up 1212 mph, down 33 mph, up 66 mph, then down 1212 mph. After these changes, the wind speed is the same as it was at the start. Which statement best explains how this shows additive inverses?
    Answer: The increases (+5,+12,+6+5, +12, +6) total +23+23 mph, which equals the decreases (−8,−3,−12-8, -3, -12) total of −23-23 mph The increases are +5, +12, and +6 mph, totaling +23 mph. The decreases are -8, -3, and -12 mph, totaling -23 mph. Since +23 and -23 are opposite in sign and equal in magnitude, they are additive inverses, and their sum is zero, confirming the wind speed returns to its starting value. This matches choice B. Choice A is incorrect because individual increases don't pair with equal individual decreases (+5 does not pair with -5, for example); the additive inverse relationship exists between the totals, not individual pairs. Choice C misunderstands additive inverses: the initial and final wind speeds are equal to each other, not additive inverses of each other. Choice D incorrectly assumes that having an equal number of increases and decreases is what makes them additive inverses; what matters is that the total magnitudes are equal and opposite, not how many individual changes occurred.
  13. A hiker climbs 200200 m up a trail and then goes 200200 m back down to the starting elevation. What is the total change in elevation?
    Answer: 00 m 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 $50 and withdrawal of $50 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 total change in elevation is 0 m, as the up and down are additive inverses. A common error is adding distances to get 400 m or halving to 200 m, but net change considers direction and cancels to zero. To find an additive inverse, flip the sign (200 → -200). In contexts like hiking, opposite directions cancel; properties: commutative, so order doesn't matter.
  14. Which statement correctly defines an additive inverse?
    Answer: The additive inverse of aa is the number that makes a+(inverse)=0a + (\text{inverse}) = 0. 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 $50 and withdrawing $50 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.
  15. A hiker climbs 200200 meters up a trail and then goes 200200 meters back down to the starting elevation. Which expression shows the net change in elevation?
    Answer: 200+(−200)=0200 + (-200) = 0 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 $50 and withdrawing $50 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.
  16. What is the additive inverse of 77?
    Answer: −7-7 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 $50 and withdrawal of $50 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. The additive inverse of 7 is -7, flipping the positive sign to negative. A common error is claiming it's 7 (same number) or the reciprocal 1/7, but that's for multiplication. To find an additive inverse, flip the sign (7 → -7). You can verify by checking if 7 + (-7) = 0, yes; properties: inverse is unique and commutative.
  17. Which number must be added to 12\frac{1}{2} to make 00?
    Answer: −12-\frac{1}{2} 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 $50 and withdrawing $50 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.
  18. A hiker's elevation changes during a hike as follows: +120+120 ft, −45-45 ft, +90+90 ft, −165-165 ft. At the end of the hike, the hiker is back at the same elevation as the start. Which statement correctly explains this using additive inverses?
    Answer: The elevation returned to start because the sum of all four elevation changes equals zero, so the complete set of changes acts as its own additive inverse. Adding all four changes: 120+(-45)+90+(-165)=0. Since the total is zero, the full set of changes are additive inverses of zero, matching choice D. Choice A is false because both 120 and 90 are positive; two positive numbers are never additive inverses of each other. Choice B is false for the same reason: -45 and -165 are both negative. Choice C pairs the largest gain and largest loss, but 120+(-165)=-45, not zero, so these two values are not additive inverses of each other.
  19. A student deposits $35 into a school store account and later withdraws $35. What is the net change in the account balance?
    Answer: $0 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 $50 and withdrawal of $50 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 deposit of $35 is modeled as +35, and a withdrawal of $35 as -35, combined: 35 + (-35) = 0 net (back to starting balance). In this case, the net change in the account balance is $0, as the deposit and withdrawal are additive inverses that cancel each other out. A common error might be thinking the net is $70 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 $100 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).
  20. Are 55 and −5-5 additive inverses? (Additive inverses add to 00.)
    Answer: Yes, because 5+(−5)=05 + (-5) = 0. 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 $50 and withdrawal of $50 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, 5 and -5 sum to 5 + (-5) = 0, so they are inverses. Yes, 5 and -5 are additive inverses because 5 + (-5) = 0. A common error is confusing with multiplication (5 × (-5) = -25, not relevant) or miscalculating the sum as 10. To find an additive inverse, flip the sign (5 → -5). Verifying: check if 5 + (-5) = 0, yes; mistakes include thinking only 0 has an inverse, but all numbers do.

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