7th Grade Math Quiz
Practice Add Rational Numbers On Number Line in 7th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
Question 1 / 20
0 of 20 answered
In a chemistry lab, temperature changes are recorded relative to room temperature. Positive values represent increases above room temperature, and negative values represent decreases below room temperature.
A solution starts at −4.8°C relative to room temperature. The temperature changes by +2.3°C, then by −6.7°C, and finally by +3.1°C. What is the final temperature relative to room temperature?
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 7th Grade Math.
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.
In a chemistry lab, temperature changes are recorded relative to room temperature. Positive values represent increases above room temperature, and negative values represent decreases below room temperature.
A solution starts at −4.8°C relative to room temperature. The temperature changes by +2.3°C, then by −6.7°C, and finally by +3.1°C. What is the final temperature relative to room temperature?
Explanation: When you encounter problems involving temperature changes or any sequence of positive and negative values, you're working with integer addition. Think of this as moving along a number line, where positive changes move you right and negative changes move you left. Start with the initial temperature of −4.8°C and apply each change in order. First, add +2.3°C: −4.8+2.3=−2.5°C. Next, add −6.7°C (which means subtracting): −2.5+(−6.7)=−2.5−6.7=−9.2°C. Finally, add +3.1°C: −9.2+3.1=−6.1°C. Looking at the wrong answers: Choice A (1.7°C) likely comes from ignoring negative signs and just working with absolute values. Choice B (−1.7°C) might result from calculation errors, perhaps forgetting to apply one of the changes correctly. Choice C (6.1°C) gives you the right numerical value but the wrong sign, suggesting you may have treated some negative changes as positive ones. The correct answer is D: −6.1°C. Remember to track your signs carefully in multi-step problems like this. A helpful strategy is to write out each step completely rather than trying to do it all in your head. When adding negative numbers, it's often clearer to rewrite them as subtraction: −2.5+(−6.7) becomes −2.5−6.7, which many students find easier to calculate accurately.
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 feet. It then changes by +45 feet, followed by a change of −30 feet. Using the number line interpretation of addition, what is the submarine's final depth?
Explanation: Starting at −120, the submarine moves distance ∣45∣=45 in the positive direction (toward surface): −120+45=−75. Then it moves distance ∣−30∣=30 in the negative direction (deeper): −75+(−30)=−105. The final depth is −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.
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 health points. The character receives healing of +22 points, takes damage of −8 points, and then receives healing of +4 points. What are the character's final 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 points. Now apply each change in order. First, add the healing: −15+22=+7 points. Next, subtract the damage: +7+(−8)=+7−8=−1 points. Finally, add the second healing: −1+4=+3 points. You can also solve this by combining all changes first: −15+22−8+4=−15+18=+3 points. Looking at the wrong answers: Choice A (−3) likely comes from miscalculating the final step, perhaps doing −1−4 instead of −1+4. Choice C (+7) represents stopping after the first healing and forgetting about the remaining damage and healing. Choice D (−7) could result from sign errors, possibly calculating −15−22+8+4 by treating the first healing as damage. The correct answer is B: +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.
On a number line, start at 3 and add 5. You move a distance of ∣5∣ units in the direction of the sign of 5. Where do you end up (what is 3+5)?
Explanation: This question tests interpreting p + q on a number line: start at p=3, move distance |q|=|5|=5 units in the direction determined by the sign of q=5 (right if positive, left if negative), ending at p+q=8. Number line addition: locate starting position p=3 (can be positive, negative, or zero), identify distance to move |q|=5 (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. 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 3, moving a distance of 5 units to the right (since 5 is positive), and ending at the final position of 8. A common error is choosing the wrong direction, like moving left for a positive addition (as in choice A, ending at -2), or starting at the wrong position like 0 instead of 3 (choice B), or moving the wrong distance like 3 units instead of 5 (choice D). The process is: (1) locate p=3 on the number line (mark starting position), (2) determine |q|=5 distance, (3) determine direction (q positive→right), (4) move from p right 5 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); contexts reinforce: deposit (+) moves balance right (increases), withdrawal (-) moves left (decreases), temperature rise (+) moves right (warmer), fall (-) moves left (cooler).
On a number line, start at 7 and add −4. Describe the movement and the final position (the value of 7+(−4)).
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).
Which statement correctly describes adding −43 to 21 on a number line, and gives the correct final value?
Explanation: This question tests interpreting p + q on a number line: start at p=1/2, move distance |q|=|-3/4|=3/4 units in the direction determined by the sign of q=-3/4 (right if positive, left if negative), ending at p+q=-1/4. Number line addition: locate starting position p=1/2 (can be positive, negative, or zero), identify distance to move |q|=3/4 (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=-1/4. 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 1/2, moving a distance of 3/4 units to the left (since -3/4 is negative), and ending at the final position of -1/4. A common error is choosing the wrong direction, like moving right for a negative addition (as in choice A, ending at 5/4), or starting at the wrong position like -3/4 instead of 1/2 (choice B), or treating distance as signed like moving '-3/4 units' to the left interpreted as right (choice D). The process is: (1) locate p=1/2 on the number line (mark starting position), (2) determine |q|=3/4 distance, (3) determine direction (q negative→left), (4) move from p left 3/4 units, (5) mark final position at -1/4 (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 -3/4 as distance when should use 3/4).
On a number line, start at 3 and add 5. You move a distance of ∣5∣ units in the direction of the sign of 5. Where do you end up (what is 3+5)?
Explanation: This question tests interpreting p + q on a number line: start at p=3, move distance |q|=|5|=5 units in the direction determined by the sign of q=5 (right if positive, left if negative), ending at p+q=8. Number line addition involves locating the starting position p=3 (positive, to the right of zero), identifying the distance to move |q|=5 (magnitude regardless of sign), determining the direction from the sign of q (positive, so move right toward larger numbers), and landing at 8. For example, like 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 2 + 5 starts at 2, moves right 5, ends at 7; or -5 + 8 starts at -5, moves right 8, ends at 3. The correct interpretation is starting at 3, moving right 5 units (since 5 is positive), ending at 8, which matches choice C. A common error is moving in the wrong direction, like left for positive addition, or starting at the wrong position such as 0 or switching p and q. The process is: (1) locate p=3 on the number line, (2) determine |q|=5 distance, (3) determine direction (positive → right), (4) move right 5 from 3, (5) mark final position at 8; remember, adding positive increases the value (moves right), while adding negative decreases it (moves left).
A hiker is at an elevation of 2.5 meters relative to a reference point. The hiker then goes down 3.2 meters. On a number line, this is 2.5+(−3.2). What is the final elevation?
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.
A video game character is at position −5 on a number line. The character moves +8 units. Using number line addition, what is the final position (what is −5+8)?
Explanation: This question tests interpreting p + q on a number line: start at p=-5, move distance |q|=|8|=8 units in the direction determined by the sign of q=8 (right if positive, left if negative), ending at p+q=3. Number line addition: locate starting position p=-5 (can be positive, negative, or zero), identify distance to move |q|=8 (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. 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 -5, moving a distance of 8 units to the right (since +8 is positive), and ending at the final position of 3. A common error is choosing the wrong direction, like moving left for a positive addition (as in choice A, ending at -13), or starting at the wrong position like 8 instead of -5 (choice C), or moving the wrong distance like 5 units instead of 8 (choice D). The process is: (1) locate p=-5 on the number line (mark starting position), (2) determine |q|=8 distance, (3) determine direction (q positive→right), (4) move from p right 8 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); contexts reinforce: deposit (+) moves balance right (increases), withdrawal (-) moves left (decreases), temperature rise (+) moves right (warmer), fall (-) moves left (cooler).
On a number line, start at −3 and add −6. You move a distance of ∣−6∣ units in the direction of the sign of −6. What is the final position (the value of −3+(−6))?
Explanation: This question tests interpreting p + q on a number line: start at p=-3, 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=-9. Number line addition: locate starting position p=-3 (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=-9. 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 -3, moving a distance of 6 units to the left (since -6 is negative), and ending at the final position of -9. A common error is choosing the wrong direction, like moving right for a negative addition (as in choice A, ending at 3), or starting at the wrong position like -6 instead of -3 (choice B), or not moving at all (choice D). The process is: (1) locate p=-3 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 -9 (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 -6 as distance when should use 6).
On a number line, what does adding −6 to −3 mean?
Compute −3+(−6) by describing the move and identifying the final position.
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.
On a number line, you start at −2.5 and add 1.75. You move a distance of ∣1.75∣ units in the direction of the sign of 1.75. What is −2.5+1.75?
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.
Which choice correctly verifies the sum 6+(−9) using a number line interpretation?
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.
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?
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 7andpayingback4 leaves you owing $3, or at position -3.
A science lab records a temperature of −2∘C. Later, the temperature drops by 3.5∘C. This can be written as −2+(−3.5). What is the new temperature?
Explanation: This question tests interpreting p + q on a number line: start at p = -2, move distance |q| = 3.5 units in the direction determined by the sign of q = -3.5 (left if negative), ending at p + q = -5.5. In number line addition, locate the starting position p = -2 (negative, left of zero), identify the distance to move |-3.5| = 3.5 units, determine the direction from the sign of q (negative, so move left toward smaller numbers), and land at -2 + (-3.5) = -5.5. For example, -3 + (-6) starts at -3, moves left 6, ends at -9; or 7 + (-4) starts at 7, moves left 4, ends at 3. The correct interpretation is starting at -2, moving left 3.5 units, and ending at -5.5, which matches choice A. A common error is wrong direction, like moving right to 1.5, or context misapplied like temperature drop adding positive. The process is: (1) locate p = -2 on the number line, (2) determine |q| = 3.5 distance, (3) determine direction (negative → left), (4) move left 3.5 from -2, (5) mark final position at -5.5. Sign rules: adding negative decreases the value, moving left; temperature drop contexts reinforce this movement to cooler (more negative).
A student claims: “−2+(−6)=4 because you subtract a negative.” Use number line reasoning to check the claim. Starting at −2, you add −6 by moving ∣−6∣ units in the correct direction. Which choice is correct?
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.
On a number line, start at 0 and add −4. What movement does this represent, and what is the final position?
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).
A student's lunch account balance is -\1.75(theyowemoney).Theydeposit$2.50.Onanumberlinethisis-1.75+2.50$. What is the new balance?
Explanation: Starting at negative 1.75 and moving right 2.50 units, since the deposit is a positive amount, lands on a new balance of positive 0.75, matching choice B. Choice A incorrectly starts at 0 instead of the actual starting balance of negative 1.75, ignoring the amount already owed. Choice C moves in the wrong direction, left instead of right, which does not match a positive deposit increasing the balance. Choice D uses the wrong distance, moving only 1.00 unit instead of the full 2.50 deposit amount. Since a deposit always increases the balance, the correct move on the number line is always to the right by the exact amount deposited.
A video game score is at 7 points. You lose 4 points, which can be modeled as adding −4. On a number line, start at 7 and add −4. What is the final score (what is 7+(−4))?
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).
On a number line, begin at −5 and add 8. Describe the movement (distance and direction) and the final position (what is −5+8)?
Explanation: This question tests interpreting p + q on a number line: start at p=-5, move distance |q|=|8|=8 units in the direction determined by the sign of q=8 (right if positive, left if negative), ending at p+q=3. Number line addition involves locating the starting position p=-5 (negative, left of zero), identifying the distance to move |q|=8, determining the direction from the sign of q (positive, so move right toward larger numbers), and landing at 3. 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 2 + 5 starts at 2, moves right 5, ends at 7; or -5 + 8 starts at -5, moves right 8, ends at 3. The correct interpretation is moving right 8 units from -5, ending at 3, which matches choice B. A common error is moving left for positive addition, ending at -13, or switching the starting point and distance. The process is: (1) locate p=-5, (2) determine |q|=8 distance, (3) determine direction (positive → right), (4) move right 8 from -5, (5) mark final position at 3; adding positive increases the value (moves right), as in temperature rising.