Subtract Using Additive Inverse - 7th Grade Math

1. Find the value of $-6-(-9)$ by rewriting as addition.

   $3$. $-6-(-9)=-6+9=3$ by adding the opposite.

2. Identify the sign change when subtracting a number $q$: what happens to $q$ in $p-q$?

   $q$ becomes $-q$. When subtracting, the sign changes to its opposite.

3. Find the value of $-5-8$ by rewriting as $-5+(-8)$.

   $-13$. $-5+(-8)=-13$ by adding two negatives.

4. State the formula for the distance between two rational numbers $a$ and $b$ on a number line.

   $|a-b|$. Distance is the absolute value of the difference.

5. Find and correct the error: $9-4=9+4$. What is the correct rewrite?

   $9-4=9+(-4)$. Must add the negative, not the positive.

6. Rewrite the expression $8-(-3)$ as addition.

   $8+3$. Subtracting a negative becomes adding a positive.

7. Which expression always equals the distance between $a$ and $b$: $a-b$, $|a-b|$, or $-(a-b)$?

   $|a-b|$. Absolute value ensures distance is always positive.

8. What is $-5-8$ when rewritten as addition?

   $-5+(-8)$. Subtracting positive $8$ means adding negative $8$.

9. Which is always true for distance: $|a-b|$ or $a-b$? Choose the correct expression.

   $|a-b|$. Distance must be non-negative, so use absolute value.

10. A temperature changes from $-3^{\circ}\text{C}$ to $5^{\circ}\text{C}$. What is the change in temperature?

    $8^{\circ}\text{C}$. $5-(-3)=5+3=8$ degrees change.

11. Find and correct the error: $8-(-2)=8+(-2)$. What is the correct result?

    $8-(-2)=8+2=10$. Error: $-(-2)$ should become $+2$, not $+(-2)$.

12. Find the distance between $3$ and $-4$ using an absolute value expression.

    $|3-(-4)|=7$. Calculate $3-(-4)=3+4=7$, distance is $7$ units.

13. Identify the correct rewrite of $p-(-q)$ using addition.

    $p+q$. Double negative becomes positive: $-(-q) = q$.

14. A temperature changes from $-3^\circ\text{C}$ to $4^\circ\text{C}$. What is the change in degrees?

    $|4-(-3)|=7^\circ\text{C}$. Temperature rose by $4-(-3)=7$ degrees.

15. A diver moves from $-12\text{ m}$ to $-5\text{ m}$. What distance did the diver move?

    $|-5-(-12)|=7\text{ m}$. Distance between depths is $|-5-(-12)|=|7|=7$ meters.

16. State the subtraction-as-additive-inverse rule using variables $p$ and $q$.

    $p-q=p+(-q)$. Subtraction equals adding the opposite (additive inverse).

17. Rewrite the expression $-5-9$ as addition.

    $-5+(-9)$. Subtracting positive $9$ means adding negative $9$.

18. The temperature changes from $-4^ irc$C to $9^ irc$C. What is the size of the change?

    $13^ irc\text{C}$. $|9-(-4)| = |9+4| = |13| = 13°C$ change.

19. Find the distance between $\frac{1}{2}$ and $\frac{5}{2}$ on a number line.

    $2$. $|\frac{5}{2}-\frac{1}{2}| = |\frac{4}{2}| = |2| = 2$ units.

20. Find the value of $4-(-6)$ using the additive inverse rule.

    $10$. $4-(-6) = 4+6 = 10$ by adding the opposite.

21. What is the additive inverse of a number $q$?

    $-q$. The additive inverse is the opposite sign of the number.

22. Find the value of $7-(-3)$ by rewriting as addition.

    $10$. $7-(-3)=7+3=10$ by adding the opposite.

23. What is the distance between $a$ and $b$ if $a-b=-12$?

    $12$. $|a-b|=|-12|=12$ since distance is always positive.

24. A diver is at $-12$ m and rises to $-3$ m. What is the distance risen?

    $9$. $|-3-(-12)| = |-3+12| = |9| = 9$ meters risen.

25. What is $7-(-3)$ when rewritten as addition?

    $7+3$. Subtracting a negative becomes adding a positive.

26. Which expression always equals the distance between $a$ and $b$: $a-b$ or $|a-b|$?

    $|a-b|$. Absolute value ensures distance is always positive.

27. Identify the distance between $p$ and $q$ written using subtraction as addition.

    $|p+(-q)|$. Distance formula using subtraction rewritten as addition.

28. Find the value of $-9-(-2)$ using the additive inverse rule.

    $-7$. $-9-(-2) = -9+2 = -7$ by adding the opposite.

29. What is the value of $q+(-q)$ for any rational number $q$?

    $0$. A number plus its additive inverse always equals zero.

30. Find the value of $-3-8$ using the additive inverse rule.

    $-11$. $-3-8 = -3+(-8) = -11$ by adding negatives.

31. Find the value of $\frac{2}{3}-\frac{5}{3}$ using $p+(-q)$.

    $-1$. $\frac{2}{3}+(-\frac{5}{3})=-\frac{3}{3}=-1$.

32. Find the distance between $-2$ and $5$ using an absolute value expression.

    $|-2-5|=7$. Calculate $-2-5=-7$, then $|-7|=7$ units.

33. What is $-9-(-9)$ when evaluated?

    $0$. Subtracting a number from itself always equals zero.

34. What is the additive inverse of $-7$?

    $7$. The additive inverse of a negative is positive.

35. Find the distance between $-2$ and $5$ on a number line.

    $7$. $|5-(-2)| = |5+2| = |7| = 7$ units apart.

36. A point moves from $x=-rac{3}{4}$ to $x=rac{1}{4}$. What is the distance moved?

    $1$. $|\frac{1}{4}-(-\frac{3}{4})| = |\frac{1}{4}+\frac{3}{4}| = |1| = 1$ unit.

37. Find the distance between $-7$ and $-1$ on a number line.

    $6$. $|-1-(-7)| = |-1+7| = |6| = 6$ units apart.

38. Find the distance between $-1.2$ and $0.5$.

    $|-1.2-0.5|=1.7$. Calculate $-1.2-0.5=-1.7$, then $|-1.7|=1.7$ units.

39. Which is always true for distance: $|a-b|=|b-a|$ or $|a-b|=a-b$?

    $|a-b|=|b-a|$. Distance is the same regardless of direction.

40. What is the distance between two rational numbers $a$ and $b$ on a number line?

    $|a-b|$. Distance is always positive, so use absolute value.

41. Find $|6-(-1)|$.

    $7$. $|6-(-1)| = |6+1| = |7| = 7$ by absolute value.

42. Find $|-4-3|$.

    $7$. $|-4-3| = |-7| = 7$ by absolute value.

43. Find the value of $-2.5-(-1.2)$ by rewriting as addition.

    $-1.3$. $-2.5-(-1.2)=-2.5+1.2=-1.3$.

44. What is the distance formula on a number line for rational numbers $a$ and $b$?

    $|a-b|$. Distance is the absolute value of the difference.

45. What is the distance between $\frac{1}{2}$ and $-\frac{5}{2}$ on the number line?

    $3$. $|\frac{1}{2}-(-\frac{5}{2})|=|\frac{1}{2}+\frac{5}{2}|=|3|=3$.

46. Find the distance between $\frac{1}{2}$ and $-\frac{3}{2}$.

    $\left|\frac{1}{2}-\left(-\frac{3}{2}\right)\right|=2$. $\frac{1}{2}-(-\frac{3}{2})=\frac{1}{2}+\frac{3}{2}=2$ units apart.

47. Identify the value of $|(-7)-(-2)|$ as a distance on the number line.

    $5$. $|-7-(-2)|=|-7+2|=|-5|=5$.

48. Evaluate $4-11$ using $4+(-11)$.

    $-7$. Rewrite as $4+(-11)$, then add to get $-7$.

49. Find the value of $\frac{3}{4}-\frac{1}{4}$ using additive inverse.

    $\frac{1}{2}$. $\frac{3}{4}+(-\frac{1}{4})=\frac{2}{4}=\frac{1}{2}$.

50. What is the distance between $-4$ and $3$ on the number line?

    $7$. $|3-(-4)|=|3+4|=|7|=7$.

51. Find the value of $12-5$ using $p-q=p+(-q)$.

    $7$. $12-5 = 12+(-5) = 7$ using the additive inverse rule.

52. What is the additive inverse of $q$?

    $-q$. The additive inverse is the opposite sign of a number.

53. State the subtraction-as-addition rule using additive inverse for $p-q$.

    $p-q=p+(-q)$. Subtraction equals adding the opposite (additive inverse).

54. Compute the distance between $2.1$ and $-0.4$ using $|a-b|$.

    $2.5$. $|2.1-(-0.4)|=|2.1+0.4|=|2.5|=2.5$.

55. Identify the equivalent expression for $p-q$ using addition: $p+q$ or $p+(-q)$.

    $p+(-q)$. Subtraction becomes addition of the negative.

56. Identify the correct rewrite of $p-q$ using addition and the additive inverse.

    $p+(-q)$. Replace subtraction with adding the opposite.

57. Evaluate $-6-(-2)$ using the additive inverse rule.

    $-4$. Rewrite as $-6+2=-4$ using the additive inverse rule.

58. State the rule that rewrites subtraction using the additive inverse.

    $p-q=p+(-q)$. Subtraction equals adding the opposite (additive inverse).

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