Add Rational Numbers on Number Line - 7th Grade Math

1. What is the distance moved from $p$ to $p+q$ on the number line (in terms of $q$)?

   $|q|$ units. Distance is always the absolute value of the change.

2. Which direction do you move from $p$ when adding a positive number $q$?

   To the right

3. What is the sum $p+q$ if $p=-4$ and you move $6$ units right on the number line?

   $2$. Moving right means adding: $-4+6=2$.

4. What does $|q|$ mean in the expression $p+q$ interpreted on a number line?

   The distance moved from $p$ (always nonnegative). Absolute value gives the magnitude of movement regardless of direction.

5. A diver is at $-12$ m and rises $5$ m. What is the new position as a sum $p+q$?

   $-12+5=-7$. Rising means adding a positive value to the depth.

6. What does $p+q$ represent on a number line in terms of starting point $p$ and distance $|q|$?

   The point $|q|$ units from $p$, right if $q>0$ and left if $q<0$. The sign of $q$ determines direction: positive means right, negative means left.

7. Interpretation: A diver is at $-6$ m and rises $4$ m. What is the new position?

   $-2$ m. Rising means adding positive: $-6+4=-2$ meters.

8. Which direction do you move on the number line when $q>0$ in $p+q$?

   Move right. Positive values move right on the number line.

9. Identify the sum: starting at $p=-3$ and adding $q=5$, what is $p+q$?

   $2$. Start at $-3$, move right $5$ units: $-3+5=2$.

10. Identify the result of $p+q$ if $p=-2$ and $q=-5$.

    $-7$. Start at $-2$, move left $5$ more units: $-2+(-5)=-7$.

11. Identify the sum: starting at $p=4$ and adding $q=-7$, what is $p+q$?

    $-3$. Start at $4$, move left $7$ units: $4-7=-3$.

12. What does $|q|$ mean in the interpretation of $p+q$ on a number line?

    The distance moved from $p$

13. Interpretation: The temperature is $-3^\circ\text{C}$ and increases by $7^\circ\text{C}$. What is the new temperature?

    $4^\circ\text{C}$. Temperature increase means add: $-3+7=4$ degrees.

14. What is $4+(-7)$?

    $-3$. Start at $4$, move left $7$ units to reach $-3$.

15. Identify the distance moved from $p=7$ when computing $p+q$ for $q=-2$.

    $2$ units

16. What is $-5+9$?

    $4$. Start at $-5$, move right $9$ units: $-5+9=4$.

17. What is the additive inverse of a number $q$ (the number that makes $q+?=0$)?

    $-q$. The additive inverse is the opposite sign that sums to zero.

18. What is $7+(-12)$?

    $-5$. Start at $7$, move left $12$ units: $7-12=-5$.

19. Interpretation: Your bank balance is $\25$ and you spend $\40$. What is the new balance?

    $- \15$. Spending is negative: $25+(-40)=-15$ dollars.

20. Which direction do you move on the number line to represent $p+q$ when $q$ is negative?

    Move left from $p$ by $|q|$ units. Negative values always indicate leftward movement on the number line.

21. Which direction do you move from $p$ when adding a negative number $q$?

    To the left

22. Identify the missing addend: $-4+q=1$. What is $q$?

    $q=5$. Solve by finding what added to $-4$ gives $1$: $-4+5=1$.

23. Identify the result of $p+q$ if $p=7$ and $q=-9$.

    $-2$. Start at $7$, move left $9$ units: $7-9=-2$.

24. What is $2.5+(-3.1)$?

    $-0.6$. Start at $2.5$, move left $3.1$ units: $2.5-3.1=-0.6$.

25. What is the value of $p$ if $p+q=r$, $q=-6$, and $r=1$?

    $7$. Solve $p+(-6)=1$: $p=1-(-6)=1+6=7$.

26. What is the distance moved from $p$ when adding $q$ in $p+q$?

    A distance of $|q|$ units. The absolute value $|q|$ gives the distance regardless of direction.

27. What is $\frac{3}{4}+\left(-\frac{1}{2}\right)$?

    $\frac{1}{4}$. Convert to common denominator: $\frac{3}{4}-\frac{2}{4}=\frac{1}{4}$.

28. What is the sum $p+q$ if $p=1.2$ and you move $3.5$ units left on the number line?

    $-2.3$. Moving left means subtracting: $1.2-3.5=-2.3$.

29. Which direction do you move on the number line to represent $p+q$ when $q$ is positive?

    Move right from $p$ by $|q|$ units. Positive values always indicate rightward movement on the number line.

30. What is $-\frac{2}{3}+\frac{1}{6}$?

    $-\frac{1}{2}$. Common denominator: $-\frac{4}{6}+\frac{1}{6}=-\frac{3}{6}=-\frac{1}{2}$

31. What is $p+0$ for any rational number $p$?

    $p$. Adding zero doesn't change the position on the number line.

32. What is $-2+(-6)$?

    $-8$. Start at $-2$, move left $6$ more units: $-2-6=-8$.

33. A bank balance is $15$ dollars and you spend $23$ dollars. What is the new balance?

    $15+(-23)=-8$. Spending is subtraction: $15-23=-8$.

34. What is the value of $p+0$ for any rational number $p$?

    $p$. Adding zero doesn't change the value (additive identity property).

35. What is $-1.2+0.5$?

    $-0.7$. Start at $-1.2$, move right $0.5$: $-1.2+0.5=-0.7$.

36. What does $p+q$ represent on a number line, starting at $p$?

    The point $|q|$ units from $p$ in the direction of $q$

37. What is $\frac{5}{8}+\left(-\frac{3}{8}\right)$?

    $\frac{1}{4}$. Same denominator: $\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}$.

38. What is $-3+5$?

    $2$. Start at $-3$, move right $5$ units to reach $2$.

39. What is $-6+(-2)$?

    $-8$. Both negative: start at $-6$, move left $2$ more units.

40. What is the absolute value $|q|$ for a rational number $q$?

    The distance from $0$ to $q$ on the number line. Absolute value measures distance without considering direction.

41. What does $p+q$ represent on a number line in terms of distance from $p$?

    The point $|q|$ units from $p$, in the direction of $q$. Adding $q$ means moving $|q|$ units from $p$ in the positive or negative direction.

42. Identify the distance moved from $p=-4$ when computing $p+q$ for $q=3$.

    $3$ units

43. Which direction do you move on the number line when $q<0$ in $p+q$?

    Move left. Negative values move left on the number line.

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