Understand Additive Inverses - 7th Grade Math

1. Find and correct the false statement: "$-7$ is the additive inverse of $-7$." What is the correct inverse?

   Correct inverse: $7$. The inverse of $-7$ is $7$, not itself.

2. What is the value of $-2 + 7 + 2$?

   $7$. The opposites $-2$ and $2$ cancel, leaving $7$.

3. What is the sum of a number and its opposite, written $a + (-a)$?

   $0$. Opposite numbers cancel each other out.

4. What is the net change after a gain of $10$ points and a loss of $10$ points?

   $0$ points. Equal gains and losses cancel out.

5. Choose the word that completes the sentence: $a$ and $-a$ are called ____.

   additive inverses. This is the mathematical term for opposite numbers that sum to zero.

6. What is $2.5 + (-2.5)$?

   $0$. Decimal opposites sum to zero.

7. What is the opposite of a deposit of $$ dollars: a deposit of $50$ or a withdrawal of $50$?

   A withdrawal of $50$ dollars (represented by $-50$). Deposits and withdrawals are opposites.

8. Which number is the additive inverse of $-12$?

   $12$. The opposite of negative is positive.

9. Which expression represents opposite quantities combining to make $0$: $7+7$ or $7+(-7)$?

   $7+(-7)$. Opposites have different signs and sum to zero.

10. Which integer represents the opposite of an elevation of $-120$ meters?

    $120$. Negative elevation means below sea level; its opposite is positive.

11. What is $-4 + 4$?

    $0$. Opposites cancel each other out.

12. What is the sum of a number and its opposite, $a + (-a)$?

    $0$. Additive inverses always sum to zero.

13. Identify the missing number $x$ so that $-\frac{3}{4} + x = 0$.

    $\frac{3}{4}$. Positive fraction cancels the negative.

14. What is the additive inverse of $7$?

    $-7$. The opposite of a positive number is its negative.

15. What is the value of $ + (-6) = 0$? Identify the missing number.

    $6$. Need the opposite of $-6$ to sum to zero.

16. Find and correct the error: "The additive inverse of $-9$ is $-9$."

    Correct: The additive inverse of $-9$ is $9$. The inverse of negative is positive.

17. Which integer represents the opposite of a debt of $20?

    $20$. A debt is negative, so its opposite is positive.

18. What is the value of $\frac{3}{4} + \left(-\frac{3}{4}\right)$?

    $0$. Opposite fractions sum to zero.

19. Which pair are additive inverses: $(4,-4)$ or $(4,4)$?

    $(4,-4)$. Numbers with opposite signs are inverses.

20. What is $-\frac{5}{6} + \frac{5}{6}$?

    $0$. Negative and positive fractions cancel.

21. What is the net elevation change for going up $200$ ft and then down $200$ ft?

    $0$ ft. Equal up and down movements cancel.

22. Identify the missing number that makes the sum $0$: $-8 + = 0$.

    $8$. Add the opposite of $-8$ to get zero.

23. What is the additive inverse of $\frac{5}{6}$?

    $-\frac{5}{6}$. Change the sign to find the inverse.

24. Which value makes the sum $-9 + \Box = 0$ true?

    $9$. Find the additive inverse of $-9$ to make the sum zero.

25. What is $9 + (-9)$?

    $0$. A number plus its opposite equals zero.

26. What is the opposite of moving $3$ units to the right on a number line?

    Moving $3$ units to the left. Left and right movements are opposites on a number line.

27. What is the additive inverse of $9$?

    $-9$. The opposite of positive is negative.

28. Identify the temperature change that cancels a drop of $-6^{\circ}\text{C}$ to make $0^{\circ}\text{C}$ change.

    An increase of $6^{\circ}\text{C}$. Opposite temperature changes sum to zero.

29. Which statement is always true for any number $a$: $a + a = 0$ or $a + (-a) = 0$?

    $a + (-a) = 0$. Additive inverses have opposite signs and sum to zero.

30. What is the definition of an additive inverse of a number $a$?

    The number $-a$, because $a + (-a) = 0$. Additive inverses sum to zero by definition.

31. Identify the pair of opposite quantities in the expression $-4 + 4$.

    $-4$ and $4$. Opposite quantities have the same absolute value but different signs.

32. What is the value of $14 + (-6) + (-14)$?

    $-6$. Group the opposites: $14 + (-14) = 0$, leaving $-6$.

33. What is the value of $23 + (-23)$?

    $0$. Additive inverses always sum to zero.

34. Identify the missing number $x$ so that $x + (-0.2) = 0$.

    $0.2$. Need positive to cancel negative $0.2$.

35. What is the net change if you deposit $10$ and then withdraw $10$?

    $0$. Deposit and withdrawal cancel out.

36. Which statement is always true for additive inverses of $a$: $a+b=0$ or $a+b=1$?

    $a + b = 0$. Inverses sum to $0$, not $1$.

37. What is the value of $-8 + 8 + 5$?

    $5$. The opposites cancel, leaving only the $5$.

38. What is the opposite of a temperature change of $-6^\circ\text{C}$?

    A temperature change of $6^\circ\text{C}$. Temperature increases and decreases are opposites.

39. What is the opposite of moving $6$ units right on a number line?

    Moving $6$ units left (a change of $-6$). Opposite directions cancel each other.

40. What is the opposite of a gain of $50 when modeling with integers?

    A loss of $50 (modeled by $-50$). Gains and losses are opposites in financial contexts.

41. Which number is the additive inverse of $7$?

    $-7$. The opposite of positive $7$ is negative $7$.

42. Identify the missing number $x$ so that $-8 + x = 0$.

    $8$. Need positive $8$ to cancel negative $8$.

43. What is the value of $-3 + 3$?

    $0$. Opposites cancel when added together.

44. Identify the missing number $x$ so that $x + 13 = 0$.

    $-13$. Need the opposite of $13$ to make zero.

45. What is the value of $-31 + 31$?

    $0$. Opposites cancel each other out when added.

46. What is the distance from $5$ to $0$ and from $-5$ to $0$ on a number line?

    Both distances are $5$. Opposites are equidistant from zero.

47. What is $\frac{1}{3} + -\frac{1}{3}$?

    $0$. Opposite fractions sum to zero.

48. Identify the missing number that makes the sum $0$: $5 + = 0$.

    $-5$. Add the opposite of $5$ to get zero.

49. Which option is a pair of additive inverses: $(-6, 6)$ or $(-6, -6)$?

    $(-6, 6)$. Opposites have different signs.

50. What is the additive inverse of $-12$?

    $12$. The opposite of negative is positive.

51. Find and correct the statement: "The additive inverse of $9$ is $9$."

    Correct: The additive inverse of $9$ is $-9$. The additive inverse has the opposite sign.

52. What is the net elevation change if you go up $30$ m and then down $30$ m?

    $0$ m. Up and down movements cancel.

53. Which value makes the sum $\Box + 15 = 0$ true?

    $-15$. Find the additive inverse of $15$ to make the sum zero.

54. What is the additive inverse of $0$?

    $0$. Zero is its own additive inverse.

55. What is the additive inverse of $0$?

    $0$. Zero is its own additive inverse since $0 + 0 = 0$.

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