Middle School Math Quiz: Add Rational Numbers On Number Line
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Add Rational Numbers On Number LineQuestion 1 of 20

Refer to the number line. Point AA represents −78-\frac{7}{8} and point BB represents 14\frac{1}{4}. If we calculate −78+(−38)-\frac{7}{8} + \left(-\frac{3}{8}\right) using the distance interpretation, where does the sum land relative to the marked points?

Question graphic
38\frac{3}{8} unit to the left of point AA
54\frac{5}{4} units to the right of point AA
54\frac{5}{4} units to the left of point BB
38\frac{3}{8} unit to the right of point BB
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Middle School Math Quiz

Middle School Math Quiz: Add Rational Numbers On Number Line

Practice Add Rational Numbers On Number Line in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Add Rational Numbers On Number Line, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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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.

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Question 1

Refer to the number line. Point AA represents −78-\frac{7}{8} and point BB represents 14\frac{1}{4}. If we calculate −78+(−38)-\frac{7}{8} + \left(-\frac{3}{8}\right) using the distance interpretation, where does the sum land relative to the marked points?

  1. 38\frac{3}{8} unit to the left of point AA (correct answer)
  2. 54\frac{5}{4} units to the right of point AA
  3. 54\frac{5}{4} units to the left of point BB
  4. 38\frac{3}{8} unit to the right of point BB
Explanation: Starting at −78-\frac{7}{8}, we move distance ∣−38∣=38|{-\frac{3}{8}}| = \frac{3}{8} in the negative direction: −78+(−38)=−108=−54-\frac{7}{8} + \left(-\frac{3}{8}\right) = -\frac{10}{8} = -\frac{5}{4}. Point AA is at −78-\frac{7}{8} and the sum is at −54-\frac{5}{4}. Since −54=−108-\frac{5}{4} = -\frac{10}{8} and −78-\frac{7}{8} to −108-\frac{10}{8} is 38\frac{3}{8} unit left. Choice B has wrong direction. Choice C gives distance from BB instead of relative position. Choice D confuses the direction and reference point.

Question 2

A submarine's depth changes are recorded as rational numbers, where negative values represent going deeper and positive values represent going toward the surface.

The submarine starts at depth −120-120 feet. It then changes by +45+45 feet, followed by a change of −30-30 feet. Using the number line interpretation of addition, what is the submarine's final depth?

  1. −105-105 feet (correct answer)
  2. −75-75 feet
  3. 105105 feet
  4. 7575 feet
Explanation: Starting at −120-120, the submarine moves distance ∣45∣=45|45| = 45 in the positive direction (toward surface): −120+45=−75-120 + 45 = -75. Then it moves distance ∣−30∣=30|{-30}| = 30 in the negative direction (deeper): −75+(−30)=−105-75 + (-30) = -105. The final depth is −105-105 feet. Choice B stops after the first move. Choice C gives the correct magnitude but incorrect sign. Choice D combines both errors from choices B and C.

Question 3

In a video game, a character's health points can go below zero (representing damage debt). Positive changes represent healing, and negative changes represent damage.

The character starts with −15-15 health points. The character receives healing of +22+22 points, takes damage of −8-8 points, and then receives healing of +4+4 points. What are the character's final health points?

  1. −3-3 health points
  2. +3+3 health points (correct answer)
  3. +7+7 health points
  4. −7-7 health points
Explanation: When you see a problem involving changes to a starting value, you're working with integer addition. Think of this as tracking movements on a number line, where positive numbers move right (up) and negative numbers move left (down). Start with the character's initial health: −15-15 points. Now apply each change in order. First, add the healing: −15+22=+7-15 + 22 = +7 points. Next, subtract the damage: +7+(−8)=+7−8=−1+7 + (-8) = +7 - 8 = -1 points. Finally, add the second healing: −1+4=+3-1 + 4 = +3 points. You can also solve this by combining all changes first: −15+22−8+4=−15+18=+3-15 + 22 - 8 + 4 = -15 + 18 = +3 points. Looking at the wrong answers: Choice A (−3-3) likely comes from miscalculating the final step, perhaps doing −1−4-1 - 4 instead of −1+4-1 + 4. Choice C (+7+7) represents stopping after the first healing and forgetting about the remaining damage and healing. Choice D (−7-7) could result from sign errors, possibly calculating −15−22+8+4-15 - 22 + 8 + 4 by treating the first healing as damage. The correct answer is B: +3+3 health points. Remember that adding a negative number is the same as subtracting, and subtracting a negative is the same as adding. When tracking multiple changes to an initial value, work step-by-step and pay careful attention to whether each change is positive or negative. Double-check your signs at each step.

Question 4

On a number line, start at 77 and add −4-4. Describe the movement and the final position (the value of 7+(−4)7+(-4)).

  1. Start at 0, move left 4 units, end at −4-4.
  2. Start at 7, move left 4 units, end at 33. (correct answer)
  3. Start at 7, move left −4-4 units, end at 1111.
  4. Start at 7, move right 4 units, end at 1111.
Explanation: This question tests interpreting p + q on a number line: start at p=7, move distance |q|=|-4|=4 units in the direction determined by the sign of q=-4 (right if positive, left if negative), ending at p+q=3. Number line addition: locate starting position p=7 (can be positive, negative, or zero), identify distance to move |q|=4 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=3. Example: 7+(-4) starts at 7 (p=7), moves left 4 units (q=-4, distance=4, direction=left), ends at 3 (7-4=3, or thinking: 7 is 4 more than 3, moving left 4 from 7 reaches 3); context: temperature -5°C rises 8° (adds +8): start -5, move right 8 units (positive rise), end at 3°C (-5+8=3). The correct interpretation is starting at position 7, moving a distance of 4 units to the left (since -4 is negative), and ending at the final position of 3. A common error is choosing the wrong direction, like moving right for a negative addition (as in choice B, ending at 11), or starting at the wrong position like 0 instead of 7 (choice C), or treating distance as signed like moving '-4 units' to the left interpreted as right (choice D). The process is: (1) locate p=7 on the number line (mark starting position), (2) determine |q|=4 distance, (3) determine direction (q negative→left), (4) move from p left 4 units, (5) mark final position at 3 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); mistakes: direction from sign confused (most common error: thinking negative addition moves right), distance as signed quantity (using -4 as distance when should use 4).

Question 5

A hiker is at an elevation of 2.52.5 meters relative to a reference point. The hiker then goes down 3.23.2 meters. On a number line, this is 2.5+(−3.2)2.5+(-3.2). What is the final elevation?

  1. −5.7-5.7 meters (start at 0, move left 5.7).
  2. −0.7-0.7 meters (start at 2.5, move left 3.2). (correct answer)
  3. 0.70.7 meters (start at 2.5, move left 1.8).
  4. 5.75.7 meters (start at 2.5, move right 3.2).
Explanation: This question tests interpreting p + q on a number line: start at p=2.5, move distance |q|=|-3.2|=3.2 units in the direction determined by the sign of q=-3.2 (right if positive, left if negative), ending at p+q=-0.7. Number line addition: locate starting position p=2.5 (can be positive, negative, or zero), identify distance to move |q|=3.2 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=-0.7. For example, -3 + (-6) starts at -3, adding -6 moves left 6 units (negative addition moves left), ending at -9 (farther left/more negative); or 2+5 starts at 2, moves right 5, ends at 7; or -5+8 starts at -5, moves right 8, crosses zero to end at +3. The correct interpretation is starting at position 2.5, moving a distance of 3.2 units to the left (since going down is -3.2, negative), and ending at the final position of -0.7 meters. A common error is choosing the wrong direction, like moving right for a negative change (as in choice A, ending at 5.7), or moving the wrong distance like 1.8 units (choice C), or starting at the wrong position like 0 (choice D). The process is: (1) locate p=2.5 on the number line (mark starting position), (2) determine |q|=3.2 distance, (3) determine direction (q negative→left), (4) move from p left 3.2 units, (5) mark final position at -0.7 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); contexts reinforce: elevation increase (+) moves right (higher), decrease (-) moves left (lower); mistakes: direction from sign confused.

Question 6

On a number line, what does adding −6-6 to −3-3 mean?

Compute −3+(−6)-3+(-6) by describing the move and identifying the final position.

  1. Start at −3-3, move right 6 units, end at 33
  2. Start at −3-3, move left 6 units, end at −9-9 (correct answer)
  3. Start at −6-6, move left 3 units, end at −9-9
  4. Start at 00, move left 6 units, end at −6-6
Explanation: This question tests interpreting p + q on a number line: start at p = -3, move distance |q| = 6 units in the direction determined by the sign of q = -6 (left if negative), ending at p + q = -9. In number line addition, locate the starting position p = -3 (negative, left of zero), identify the distance to move |-6| = 6 units, determine the direction from the sign of q (negative, so move left toward smaller numbers), and land at -3 + (-6) = -9. For example, -3 + (-6) starts at -3, moves left 6 units, ending at -9; or 2 + 5 starts at 2, moves right 5, ends at 7. The correct interpretation is starting at -3, moving left 6 units, and ending at -9, which matches choice B. A common error is wrong direction, like moving right for negative addition, leading to 3, or starting at the wrong position like 0 or -6. The process is: (1) locate p = -3 on the number line, (2) determine |q| = 6 distance, (3) determine direction (negative → left), (4) move left 6 from -3, (5) mark final position at -9. Sign rules: adding negative decreases the value, moving left to more negative; contexts like temperature dropping further reinforce this.

Question 7

On a number line, you start at −2.5-2.5 and add 1.751.75. You move a distance of ∣1.75∣|1.75| units in the direction of the sign of 1.751.75. What is −2.5+1.75-2.5+1.75?

  1. −4.25-4.25 (move left 1.751.75).
  2. −0.75-0.75 (move right 1.751.75). (correct answer)
  3. −0.75-0.75 (start at 00 and move left 0.750.75).
  4. 0.750.75 (move right 2.52.5).
Explanation: This question tests interpreting p + q on a number line: start at p=-2.5, move distance |q|=|1.75|=1.75 units in the direction determined by the sign of q=1.75 (right if positive, left if negative), ending at p+q=-0.75. Number line addition involves locating the starting position p=-2.5 (negative decimal), identifying the distance to move |q|=1.75, determining the direction from the sign of q (positive, so move right), and landing at -0.75. For example, 7 + (-4) starts at 7, moves left 4 units, ends at 3; in a context, if temperature is -5°C and rises 8° (adds +8), start at -5, move right 8 units, end at 3°C. Another example: -3 + (-6) starts at -3, moves left 6 units, ends at -9; or -5 + 8 starts at -5, moves right 8, ends at 3. The correct interpretation is moving right 1.75 from -2.5 to -0.75, which matches choice B. A common error is moving left to -4.25 or starting at 0. The process is: (1) locate p=-2.5, (2) determine |q|=1.75 distance, (3) determine direction (positive → right), (4) move right 1.75 from -2.5, (5) mark final position at -0.75; adding positive moves right even with decimals.

Question 8

Which choice correctly verifies the sum 6+(−9)6+(-9) using a number line interpretation?

  1. Start at 66, move right 9 units, end at 1515, so 6+(−9)=156+(-9)=15
  2. Start at 00, move left 9 units, end at −9-9, so 6+(−9)=−96+(-9)=-9
  3. Start at 66, move left 9 units, end at −3-3, so 6+(−9)=−36+(-9)=-3 (correct answer)
  4. Start at −9-9, move right 6 units, end at −3-3, so 6+(−9)=−36+(-9)=-3
Explanation: This question tests interpreting p + q on a number line: start at p = 6, move distance |q| = 9 units in the direction determined by the sign of q = -9 (left if negative), ending at p + q = -3. In number line addition, locate the starting position p = 6 (positive, right of zero), identify the distance to move |-9| = 9 units, determine the direction from the sign of q (negative, so move left toward smaller numbers), and land at 6 + (-9) = -3. For example, 7 + (-4) starts at 7, moves left 4, ends at 3; or -3 + (-6) starts at -3, moves left 6, ends at -9. The correct interpretation is starting at 6, moving left 9 units, and ending at -3, which matches choice C. A common error is starting at the wrong position like -9 or 0, or wrong direction like right to 15. The process is: (1) locate p = 6 on the number line, (2) determine |q| = 9 distance, (3) determine direction (negative → left), (4) move left 9 from 6, (5) mark final position at -3. Sign rules: adding negative decreases the value, moving left; mistakes often involve confusing the starting point.

Question 9

Consider -7+4 on a number line. You start at -7 and move the absolute value of 4 units in the correct direction. What is the final position?

  1. 11
  2. 3
  3. -11
  4. -3 (correct answer)
Explanation: Starting at -7 and moving in the positive direction (since 4 is positive) 4 units lands at -7 + 4 = -3, matching choice D. Ending at -11 would come from moving left (the wrong direction) instead of right. Ending at 11 or 3 would both require starting from a different position than -7. A real-world way to picture this: owing $7 and paying back $4 leaves you owing $3, or at position -3.

Question 10

Carlos owes $18.50 on his lunch account, which can be represented as -18.5. His parents add money to his account in two deposits: first $12.75, then $8.25. Using the number line model for addition, what does his account balance become after both deposits?

  1. $2.50 credit (correct answer)
  2. $2.50 debt
  3. $39.50 credit
  4. $6.00 credit
Explanation: Starting at -18.5, add the first deposit of 12.75 to get -18.5 + 12.75 = -5.75. Add the second deposit of 8.25 to get -5.75 + 8.25 = 2.5. A final balance of positive 2.5 means Carlos has a $2.50 credit. Choice B has the correct value but the wrong sign, showing debt instead of credit. Choice C comes from adding all the amounts together without accounting for the starting debt. Choice D shows only the net deposit amount, not the final account balance.

Question 11

A student claims: "−2+(−6)=4-2+(-6)=4 because you subtract a negative." Use number line reasoning to check the claim. Starting at −2-2, you add −6-6 by moving ∣−6∣|-6| units in the correct direction. Which choice is correct?

  1. The claim is correct: start at −2-2, move right 6, end at 44.
  2. The claim is incorrect: start at −2-2, move left 6, end at −8-8. (correct answer)
  3. The claim is incorrect: start at 0, move left 8, end at −8-8.
  4. The claim is correct: start at −6-6, move left 2, end at −8-8.
Explanation: This question tests interpreting p + q on a number line: start at p=-2, move distance |q|=|-6|=6 units in the direction determined by the sign of q=-6 (right if positive, left if negative), ending at p+q=-8, showing the claim of 4 is incorrect. Number line addition: locate starting position p=-2 (can be positive, negative, or zero), identify distance to move |q|=6 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=-8. Example: 7+(-4) starts at 7 (p=7), moves left 4 units (q=-4, distance=4, direction=left), ends at 3 (7-4=3, or thinking: 7 is 4 more than 3, moving left 4 from 7 reaches 3); context: temperature -5°C rises 8° (adds +8): start -5, move right 8 units (positive rise), end at 3°C (-5+8=3). The correct interpretation is that the claim is incorrect: starting at position -2, moving a distance of 6 units to the left (since -6 is negative), and ending at the final position of -8, not 4. A common error is choosing the wrong direction, like moving right for a negative addition (as in choice A, incorrectly claiming correct to 4), or starting at the wrong position like 0 or -6 (choices C and D), or confusing subtraction of negative as addition without proper movement. The process is: (1) locate p=-2 on the number line (mark starting position), (2) determine |q|=6 distance, (3) determine direction (q negative→left), (4) move from p left 6 units, (5) mark final position at -8 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); mistakes: direction from sign confused (most common error: thinking negative addition moves right, as in the student's claim), starting position wrong.

Question 12

On a number line, start at 00 and add −4-4. What movement does this represent, and what is the final position?

  1. Start at 0, move left 4 units, end at −4-4. (correct answer)
  2. Start at 0, move right 4 units, end at 44.
  3. Start at −4-4, move left 0 units, end at −4-4.
  4. Start at 0, move left −4-4 units, end at 44.
Explanation: This question tests interpreting p + q on a number line: start at p=0, move distance |q|=|-4|=4 units in the direction determined by the sign of q=-4 (right if positive, left if negative), ending at p+q=-4. Number line addition: locate starting position p=0 (can be positive, negative, or zero), identify distance to move |q|=4 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=-4. Example: 7+(-4) starts at 7 (p=7), moves left 4 units (q=-4, distance=4, direction=left), ends at 3 (7-4=3, or thinking: 7 is 4 more than 3, moving left 4 from 7 reaches 3); context: temperature -5°C rises 8° (adds +8): start -5, move right 8 units (positive rise), end at 3°C (-5+8=3). The correct interpretation is starting at position 0, moving a distance of 4 units to the left (since -4 is negative), and ending at the final position of -4. A common error is choosing the wrong direction, like moving right for a negative addition (as in choice A, ending at 4), or starting at the wrong position like -4 instead of 0 (choice C), or treating distance as signed like moving '-4 units' to the left interpreted as right (choice D). The process is: (1) locate p=0 on the number line (mark starting position), (2) determine |q|=4 distance, (3) determine direction (q negative→left), (4) move from p left 4 units, (5) mark final position at -4 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); mistakes: direction from sign confused (most common error: thinking negative addition moves right), distance as signed quantity (using -4 as distance when should use 4).

Question 13

A video game score is at 77 points. You lose 44 points, which can be modeled as adding −4-4. On a number line, start at 77 and add −4-4. What is the final score (what is 7+(−4)7+(-4))?

  1. Start at 77, move left 44 units, end at 33. (correct answer)
  2. Start at 00, move left 44 units, end at −4-4.
  3. Start at −4-4, move right 77 units, end at 33.
  4. Start at 77, move right 44 units, end at 1111.
Explanation: This question tests interpreting p + q on a number line: start at p=7, move distance |q|=|-4|=4 units in the direction determined by the sign of q=-4 (right if positive, left if negative), ending at p+q=3. Number line addition involves locating the starting position p=7 (positive score), identifying the distance to move |q|=4, determining the direction from the sign of q (negative, so move left toward smaller numbers), and landing at 3, like losing points in a game. For example, 7 + (-4) starts at 7, moves left 4 units, ends at 3; in a context, if temperature is -5°C and rises 8° (adds +8), start at -5, move right 8 units, end at 3°C. Another example: -3 + (-6) starts at -3, moves left 6 units, ends at -9; or -5 + 8 starts at -5, moves right 8, crosses zero to end at 3. The correct interpretation is starting at 7, moving left 4 units (since -4 is negative), ending at 3, which matches choice A. A common error is using the wrong direction, like moving right for negative addition to get 11, or starting at 0 instead of 7. The process is: (1) locate p=7, (2) determine |q|=4 distance, (3) determine direction (negative → left), (4) move left 4 from 7, (5) mark final position at 3; in contexts like scores, adding negative (losing points) decreases the value (moves left).

Question 14

A student says: "To find 7+(-4) on a number line, start at 7 and move left 4 units." Which ending number matches this movement?

  1. -3
  2. 3 (correct answer)
  3. 11
  4. -11
Explanation: Starting at 7 and moving left (the negative direction) 4 units lands at 7 minus 4 = 3, which matches choice B. Ending at -3 would mean moving right instead of left, the opposite of what the problem describes. Ending at 11 would result from moving right 4 units rather than left, and ending at -11 confuses the direction and distance entirely. A real-world way to picture this: withdrawing $4 from a $7 balance leaves $3.

Question 15

Using the coordinate system shown, point QQ is at position 56\frac{5}{6} on the number line. To find 56+(−113)\frac{5}{6} + \left(-1\frac{1}{3}\right), we move from QQ a distance of ∣−113∣\left|{-1\frac{1}{3}}\right| in the appropriate direction. What is the result of this addition?

  1. −12-\frac{1}{2} on the number line (correct answer)
  2. 12\frac{1}{2} on the number line
  3. −32-\frac{3}{2} on the number line
  4. 2162\frac{1}{6} on the number line
Explanation: Starting at 56\frac{5}{6}, we move distance ∣−113∣=43|{-1\frac{1}{3}}| = \frac{4}{3} in the negative direction. Converting: 56−43=56−86=−36=−12\frac{5}{6} - \frac{4}{3} = \frac{5}{6} - \frac{8}{6} = -\frac{3}{6} = -\frac{1}{2}. Choice B uses wrong direction (moved positive instead of negative). Choice C incorrectly adds the values: −56+(−43)-\frac{5}{6} + (-\frac{4}{3}). Choice D incorrectly adds absolute values: 56+43\frac{5}{6} + \frac{4}{3}.

Question 16

Start at 0 on a number line and add -4. Which statement correctly describes the movement and the final position?

  1. Move left -4 units; end at -4
  2. Move left 4 units; end at -4 (correct answer)
  3. Move right 4 units; end at 4
  4. Do not move; end at 0
Explanation: Starting at 0 and adding -4 means moving in the negative direction, since q = -4 is negative. The distance moved is the absolute value of -4, which is 4 units, and the direction is left because the number is negative. Moving left 4 units from 0 lands at -4, so 0 + (-4) = -4, matching Choice B. Choice A confuses the direction label with a negative distance, which does not make sense since distance moved is always positive. Choice C moves in the wrong direction, right instead of left, and Choice D incorrectly assumes no movement happens at all.

Question 17

On the number line shown, point PP is at −1-1 and point QQ is at 22. If you start at PP and add +3+3, which point do you land on?

  1. You land at −4-4
  2. You land at 22 (point QQ) (correct answer)
  3. You land at 00
  4. You land at 44
Explanation: This question tests interpreting p + q on a number line: start at p = -1 (point P), move distance |q| = 3 units in the direction determined by the sign of q = +3 (right if positive), ending at p + q = 2 (point Q). In number line addition, locate the starting position p = -1 (negative, left of zero), identify the distance to move |+3| = 3 units, determine the direction from the sign of q (positive, so move right toward larger numbers), and land at -1 + 3 = 2. For example, -5 + 8 starts at -5, moves right 8, crosses zero to end at +3; or 2 + 5 starts at 2, moves right 5, ends at 7. The correct interpretation is starting at -1, moving right 3 units, and ending at 2 (point Q), which matches choice B. A common error is wrong direction, like moving left to -4, or arithmetic like ending at 4 or 0. The process is: (1) locate p = -1 on the number line, (2) determine |q| = 3 distance, (3) determine direction (positive → right), (4) move right 3 from -1, (5) mark final position at 2. Sign rules: adding positive increases the value, moving right; number line points like P and Q help visualize the landing spot.

Question 18

A stock's value changes throughout the day. It starts at −$2.40-\$2.40 (meaning $2.40 below its opening price). The stock then has these changes: $+\1.85 , -$0.95 , and +$0.75 . Using number line addition, what is the stock's final position relative to its opening price?

  1. −$1.65-\$1.65 below opening price
  2. +$0.75+\$0.75 above opening price
  3. −$0.75-\$0.75 below opening price (correct answer)
  4. +$1.65+\$1.65 above opening price
Explanation: When you see a problem involving positive and negative changes to a starting value, you're working with integer addition on a number line. Think of moving right for positive changes and left for negative changes. Start at the initial position of −$2.40-\$2.40 (which means $2.40 below the opening price). Now apply each change step by step: First change: $+\1.85 . Moving right from -$2.40 : -$2.40 + $1.85 = -$0.55 Second change: -$0.95 . Moving left from -$0.55 : -$0.55 + (-$0.95) = -$0.55 - $0.95 = -$1.50 Third change: +$0.75 . Moving right from -$1.50 : -$1.50 + $0.75 = -$0.75 The final position is -$0.75 , meaning $0.75 below the opening price. Choice A (−$1.65-\$1.65) likely comes from adding the absolute values of all negative changes and subtracting positive ones incorrectly. Choice B (+$0.75+\$0.75) represents forgetting the negative sign in your final calculation. Choice D (+$1.65+\$1.65) suggests adding all the changes without considering their signs properly, then making the result positive. Strategy tip: When working with signed numbers, keep track of your running total after each step rather than trying to do everything at once. Draw a simple number line if it helps you visualize the movements, and always double-check whether your final answer should be positive or negative.

Question 19

The temperature is −5∘C-5^\circ\text{C} in the morning. By afternoon it rises 8∘C8^\circ\text{C}. Using number line addition, what is the afternoon temperature (what is −5+8-5+8)?

  1. 3∘C3^\circ\text{C} (start at −5-5, move right 8) (correct answer)
  2. 13∘C13^\circ\text{C} (move right 13 from 0)
  3. −13∘C-13^\circ\text{C} (move left 8 from −5-5)
  4. −3∘C-3^\circ\text{C} (start at −5-5, move right 2)
Explanation: Starting at -5 and moving right 8 units (since we're adding a positive 8), we land at 3 degrees C, matching choice A. Choice B incorrectly starts at 0 instead of -5, giving 13 instead of 3. Choice C moves in the wrong direction (left instead of right) for a positive addition, landing at -13. Choice D moves the wrong distance, only 2 units instead of 8, giving -3.

Question 20

A submarine is at an elevation of −3-3 meters (below sea level). It dives 66 more meters, which is adding −6-6. On a number line, start at −3-3 and add −6-6. Where is it now (what is −3+(−6)-3+(-6))?

  1. Start at −3-3, move right 66 units, end at 33.
  2. Start at −6-6, move left 33 units, end at −9-9.
  3. Start at 00, move left 99 units, end at −9-9.
  4. Start at −3-3, move left 66 units, end at −9-9. (correct answer)
Explanation: The problem specifically describes starting at negative 3 on the number line and moving in the direction of negative 6, which means moving left, since the value being added is negative, a distance of 6 units, ending at negative 9, matching choice D. Choice C also ends at negative 9, but it starts at 0 and moves left 9 units, which does not follow the specific process described in the problem of starting at negative 3. Choice B starts at the wrong point, negative 6, and moves left only 3 units, which also does not match the described process even though it happens to land on negative 9. Choice A moves in the wrong direction, right instead of left, which is incorrect because adding a negative number always moves you toward smaller values. Following the exact starting point and direction described in the problem, rather than just checking the final number, is what determines the correct choice here.