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Absolute Value

Grade 6 · Mathematics · Worksheet 1

  1. Maria is tracking the altitude of a submarine during a research mission. The submarine starts at sea level (0 meters). It first descends to -250 meters to study deep-sea life. Then it ascends 180 meters to avoid a strong current. Finally, it descends another 120 meters to reach its target location. What is the total distance the submarine traveled from its starting point, considering only the magnitude of the movements? Answer: ______________
  2. |−2400 + 1600| − |−350 + 150| = ? Answer: ______________
  3. Aroha is a deep-sea explorer piloting a submersible. She starts at sea level (0 meters). First, she descends 1,250 meters to investigate a hydrothermal vent. Then, she ascends 480 meters to observe a school of fish. Finally, she descends another 340 meters to reach an ancient shipwreck. What is the total vertical distance Aroha's submersible traveled during this mission? Answer: ______________
  4. Emma is exploring a cave system. She starts at an elevation of 0 meters at the entrance. She descends 45 meters to reach an underground river, then climbs up 20 meters to a dry ledge, and finally descends another 35 meters to the deepest chamber. What is the total vertical distance Emma traveled during her descent and ascent, considering only the magnitude of each movement? Answer: ______________
  5. Aroha is recording the movement of a hot air balloon during a race. The balloon starts at ground level (0 meters). It first ascends 1350 meters to catch a strong wind. Then it descends 870 meters to avoid a restricted airspace. Finally, it ascends another 420 meters to reach the finish altitude. What is the total vertical distance the balloon traveled during the race? Answer: ______________
  6. A rectangular swimming pool is drawn on a coordinate plane with corners at (-5, 2), (7, 2), (7, -4), and (-5, -4). A lifeguard station is located at point (1, -1). What is the sum of the absolute values of the differences between the station's x-coordinate and the pool's left and right edges? Answer: ______________
  7. Liam is tracking the temperature changes in his city. On Monday morning, the temperature was -5°C. By afternoon, it had risen by 8 degrees. On Tuesday morning, it was 3°C colder than Monday afternoon. What was the temperature on Tuesday morning? Answer: ______________
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Answer Key & Explanations

Absolute Value · Grade 6 · Worksheet 1

  1. Maria is tracking the altitude of a submarine during a research mission. The submarine starts at sea level (0 meters). It first descends to -250 meters to study deep-sea life. Then it ascends 180 meters to avoid a strong current. Finally, it descends another 120 meters to reach its target location. What is the total distance the submarine traveled from its starting point, considering only the magnitude of the movements? Answer: 550 Solution: Identify the individual movements and their magnitudes (absolute values). First descent: 250 meters down (magnitude = 250) First ascent: 180 meters up (magnitude = 180) Second descent: 120 meters down (magnitude = 120) Add the magnitudes of all movements to find the total distance traveled.
    Full step-by-step solution

    Step 1: Identify the individual movements and their magnitudes (absolute values). First descent: 250 meters down (magnitude = 250) First ascent: 180 meters up (magnitude = 180) Second descent: 120 meters down (magnitude = 120) Step 2: Add the magnitudes of all movements to find the total distance traveled. Total distance = 250 + 180 + 120 Step 3: Calculate the sum. 250 + 180 = 430 430 + 120 = 550 The total distance the submarine traveled is 550 meters.

  2. |−2400 + 1600| − |−350 + 150| = ? Answer: 600 Solution: Simplify inside the first absolute value: −2400 + 1600 = −800 Find the absolute value: |−800| = 800 Simplify inside the second absolute value: −350 + 150 = −200 Find the absolute value: |−200| = 200 Subtract: 800 − 200 = 600 The answer is 600.
    Full step-by-step solution

    Step 1: Simplify inside the first absolute value: −2400 + 1600 = −800 Step 2: Find the absolute value: |−800| = 800 Step 3: Simplify inside the second absolute value: −350 + 150 = −200 Step 4: Find the absolute value: |−200| = 200 Step 5: Subtract: 800 − 200 = 600 The answer is 600.

  3. Aroha is a deep-sea explorer piloting a submersible. She starts at sea level (0 meters). First, she descends 1,250 meters to investigate a hydrothermal vent. Then, she ascends 480 meters to observe a school of fish. Finally, she descends another 340 meters to reach an ancient shipwreck. What is the total vertical distance Aroha's submersible traveled during this mission? Answer: 2070 Solution: Identify each movement and its magnitude (absolute value). First descent: 1,250 meters down (magnitude = 1,250) First ascent: 480 meters up (magnitude = 480) Second descent: 340 meters down (magnitude = 340) Add the magnitudes of all movements to find the total distance.
    Full step-by-step solution

    Step 1: Identify each movement and its magnitude (absolute value). First descent: 1,250 meters down (magnitude = 1,250) First ascent: 480 meters up (magnitude = 480) Second descent: 340 meters down (magnitude = 340) Step 2: Add the magnitudes of all movements to find the total distance. Total distance = 1,250 + 480 + 340 Step 3: Calculate the sum. 1,250 + 480 = 1,730 1,730 + 340 = 2,070 The total vertical distance Aroha's submersible traveled is 2,070 meters.

  4. Emma is exploring a cave system. She starts at an elevation of 0 meters at the entrance. She descends 45 meters to reach an underground river, then climbs up 20 meters to a dry ledge, and finally descends another 35 meters to the deepest chamber. What is the total vertical distance Emma traveled during her descent and ascent, considering only the magnitude of each movement? Answer: 100 Solution: Identify each movement and its magnitude (absolute value). First descent: 45 meters down → magnitude = 45 First ascent: 20 meters up → magnitude = 20 Second descent: 35 meters down → magnitude = 35 Add the magnitudes of all movements to find the total vertical distance traveled.
    Full step-by-step solution

    Step 1: Identify each movement and its magnitude (absolute value). First descent: 45 meters down → magnitude = 45 First ascent: 20 meters up → magnitude = 20 Second descent: 35 meters down → magnitude = 35 Step 2: Add the magnitudes of all movements to find the total vertical distance traveled. Total distance = 45 + 20 + 35 Step 3: Calculate the sum. 45 + 20 = 65 65 + 35 = 100 The total vertical distance Emma traveled is 100 meters.

  5. Aroha is recording the movement of a hot air balloon during a race. The balloon starts at ground level (0 meters). It first ascends 1350 meters to catch a strong wind. Then it descends 870 meters to avoid a restricted airspace. Finally, it ascends another 420 meters to reach the finish altitude. What is the total vertical distance the balloon traveled during the race? Answer: 2640 Solution: The balloon ascends 1350 meters. Distance = 1350 meters. The balloon descends 870 meters.
    Full step-by-step solution

    Step 1: The balloon ascends 1350 meters. Distance = 1350 meters. Step 2: The balloon descends 870 meters. Distance = 870 meters. Step 3: The balloon ascends 420 meters. Distance = 420 meters. Step 4: Add all the distances: 1350 + 870 + 420 = 2640 meters. The total vertical distance traveled is 2640 meters.

  6. A rectangular swimming pool is drawn on a coordinate plane with corners at (-5, 2), (7, 2), (7, -4), and (-5, -4). A lifeguard station is located at point (1, -1). What is the sum of the absolute values of the differences between the station's x-coordinate and the pool's left and right edges? Answer: 12 Solution: Identify the x-coordinates of the pool's left and right edges. The left edge is at x = -5 and the right edge is at x = 7. Find the absolute difference between the station's x-coordinate (1) and the left edge (-5).
    Full step-by-step solution

    Step 1: Identify the x-coordinates of the pool's left and right edges. The left edge is at x = -5 and the right edge is at x = 7. Step 2: Find the absolute difference between the station's x-coordinate (1) and the left edge (-5). |1 - (-5)| = |1 + 5| = |6| = 6. Step 3: Find the absolute difference between the station's x-coordinate (1) and the right edge (7). |1 - 7| = |-6| = 6. Step 4: Add the two absolute differences together. 6 + 6 = 12. The answer is 12.

  7. Liam is tracking the temperature changes in his city. On Monday morning, the temperature was -5°C. By afternoon, it had risen by 8 degrees. On Tuesday morning, it was 3°C colder than Monday afternoon. What was the temperature on Tuesday morning? Answer: 0 Solution: Monday morning: -5°C It rose by 8 degrees, so: -5 + 8 = 3°C Monday afternoon temperature = 3°C Tuesday morning was 3°C colder than Monday afternoon.
    Full step-by-step solution

    Let's go step-by-step. **Step 1: Monday morning temperature** Monday morning: -5°C **Step 2: Monday afternoon temperature** It rose by 8 degrees, so: -5 + 8 = 3°C Monday afternoon temperature = 3°C **Step 3: Tuesday morning temperature** Tuesday morning was 3°C colder than Monday afternoon. Monday afternoon = 3°C 3°C colder means subtract 3: 3 - 3 = 0°C **Step 4: Conclusion** The temperature on Tuesday morning was 0°C. **Final answer:** 0