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Absolute Value

Grade 6 · Mathematics · Worksheet 2

  1. Tane is monitoring the altitude of his paraglider during a flight. He starts at a launch point that is 145 meters above sea level. First, he climbs up another 213 meters to catch a thermal. Then, he descends 189 meters to avoid some clouds. Finally, he climbs up another 97 meters to reach a stable altitude. What is the total vertical distance Tane traveled during this part of his flight? Answer: ______________
  2. Noah is a pilot for a hot air balloon company. He takes tourists on scenic rides. During one ride, the balloon starts at ground level (0 meters). First, it ascends 1,200 meters to give passengers a great view of the mountains. Then, to avoid some low clouds, it descends 450 meters. Later, it ascends another 700 meters to catch a favorable wind. What is the total vertical distance the balloon traveled during the ride? Answer: ______________
  3. Isabella is a marine biologist studying the movements of a deep-sea research submersible. The submersible starts at sea level (0 meters). On its first dive, it descends to -1350 meters to observe a hydrothermal vent. Then it ascends 870 meters to study a layer of plankton. Finally, it descends another 420 meters to reach a deep ocean trench. What is the total distance the submersible traveled vertically during this mission? Answer: ______________
  4. |−250 + 175| − |−75| = ? Answer: ______________
  5. |−216 + 136| ÷ |−11 + 6| = ? Answer: ______________
  6. Emma is tracking the water level in a reservoir during a drought. The normal water level is marked as 0 meters. On Monday, the water level was at -2.3 meters. Due to heavy rain on Tuesday, it rose by 1.8 meters. Then on Wednesday, more evaporation occurred and it dropped by 0.9 meters. What was the total change in water level magnitude (absolute value of change) from Monday to Wednesday? Answer: ______________
  7. A submarine is exploring a deep ocean trench. The submarine starts at sea level (0 meters). It descends to 1250 meters below sea level, then ascends 480 meters, then descends another 320 meters. What is the submarine's final position relative to sea level? Answer: ______________
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Answer Key & Explanations

Absolute Value · Grade 6 · Worksheet 2

  1. Tane is monitoring the altitude of his paraglider during a flight. He starts at a launch point that is 145 meters above sea level. First, he climbs up another 213 meters to catch a thermal. Then, he descends 189 meters to avoid some clouds. Finally, he climbs up another 97 meters to reach a stable altitude. What is the total vertical distance Tane traveled during this part of his flight? Answer: 499 Solution: Identify each movement and its magnitude (absolute value). First climb: 213 meters up (magnitude = 213) First descent: 189 meters down (magnitude = 189) Second climb: 97 meters up (magnitude = 97) 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 climb: 213 meters up (magnitude = 213) First descent: 189 meters down (magnitude = 189) Second climb: 97 meters up (magnitude = 97) Step 2: Add the magnitudes of all movements to find the total vertical distance traveled. Total distance = 213 + 189 + 97 Step 3: Calculate the sum. 213 + 189 = 402 402 + 97 = 499 The total vertical distance Tane traveled is 499 meters.

  2. Noah is a pilot for a hot air balloon company. He takes tourists on scenic rides. During one ride, the balloon starts at ground level (0 meters). First, it ascends 1,200 meters to give passengers a great view of the mountains. Then, to avoid some low clouds, it descends 450 meters. Later, it ascends another 700 meters to catch a favorable wind. What is the total vertical distance the balloon traveled during the ride? Answer: 2350 Solution: The balloon first ascends 1,200 meters. Distance traveled = 1,200 meters. Step 2: The balloon then descends 450 meters.
    Full step-by-step solution

    Step 1: The balloon first ascends 1,200 meters. Distance traveled = 1,200 meters. Step 2: The balloon then descends 450 meters. Distance traveled = 450 meters. Step 3: The balloon finally ascends 700 meters. Distance traveled = 700 meters. Step 4: Add all the distances together: 1,200 + 450 + 700 = 2,350 meters. The total vertical distance traveled is 2,350 meters.

  3. Isabella is a marine biologist studying the movements of a deep-sea research submersible. The submersible starts at sea level (0 meters). On its first dive, it descends to -1350 meters to observe a hydrothermal vent. Then it ascends 870 meters to study a layer of plankton. Finally, it descends another 420 meters to reach a deep ocean trench. What is the total distance the submersible traveled vertically during this mission? Answer: 2640 Solution: Identify each movement and its magnitude (absolute value). First descent: 1350 meters down, magnitude = 1350. Ascend: 870 meters up, magnitude = 870.
    Full step-by-step solution

    Step 1: Identify each movement and its magnitude (absolute value). First descent: 1350 meters down, magnitude = 1350. Ascend: 870 meters up, magnitude = 870. Second descent: 420 meters down, magnitude = 420. Step 2: Add the magnitudes to find total distance: 1350 + 870 + 420. Step 3: Calculate step by step: 1350 + 870 = 2220. Then 2220 + 420 = 2640. The total vertical distance traveled is 2640 meters.

  4. |−250 + 175| − |−75| = ? Answer: 0 Solution: Calculate inside the first absolute value: −250 + 175 = −75 Apply absolute value to the first result: |−75| = 75 Apply absolute value to the second term: |−75| = 75 Subtract the results: 75 − 75 = 0 The answer is 0.
    Full step-by-step solution

    Step 1: Calculate inside the first absolute value: −250 + 175 = −75 Step 2: Apply absolute value to the first result: |−75| = 75 Step 3: Apply absolute value to the second term: |−75| = 75 Step 4: Subtract the results: 75 − 75 = 0 The answer is 0.

  5. |−216 + 136| ÷ |−11 + 6| = ? Answer: 16 Solution: Simplify inside the first absolute value: −216 + 136 = −80 Take the absolute value: |−80| = 80 Simplify inside the second absolute value: −11 + 6 = −5 Take the absolute value: |−5| = 5 Divide the results: 80 ÷ 5 = 16 The answer is 16.
    Full step-by-step solution

    Step 1: Simplify inside the first absolute value: −216 + 136 = −80 Step 2: Take the absolute value: |−80| = 80 Step 3: Simplify inside the second absolute value: −11 + 6 = −5 Step 4: Take the absolute value: |−5| = 5 Step 5: Divide the results: 80 ÷ 5 = 16 The answer is 16.

  6. Emma is tracking the water level in a reservoir during a drought. The normal water level is marked as 0 meters. On Monday, the water level was at -2.3 meters. Due to heavy rain on Tuesday, it rose by 1.8 meters. Then on Wednesday, more evaporation occurred and it dropped by 0.9 meters. What was the total change in water level magnitude (absolute value of change) from Monday to Wednesday? Answer: 0.9 Solution: Find the water level on Monday: -2.3 meters Calculate the water level on Wednesday after the changes: Tuesday: -2.3 + 1.8 = -0.5 meters Wednesday: -0.5 - 0.9 = -1.4 meters Find the total change from Monday to Wednesday: -1.4 - (-2.3) = -1.4 + 2.3 = 0.9 meters Since we need the magnitude…
    Full step-by-step solution

    Step 1: Find the water level on Monday: -2.3 meters Step 2: Calculate the water level on Wednesday after the changes: Tuesday: -2.3 + 1.8 = -0.5 meters Wednesday: -0.5 - 0.9 = -1.4 meters Step 3: Find the total change from Monday to Wednesday: -1.4 - (-2.3) = -1.4 + 2.3 = 0.9 meters Step 4: Since we need the magnitude (absolute value) of the change, and 0.9 is already positive, the answer is 0.9 The total change in water level magnitude from Monday to Wednesday is 0.9 meters.

  7. A submarine is exploring a deep ocean trench. The submarine starts at sea level (0 meters). It descends to 1250 meters below sea level, then ascends 480 meters, then descends another 320 meters. What is the submarine's final position relative to sea level? Answer: -1090 Solution: The submarine starts at 0 meters relative to sea level. Descending means going below sea level, so we subtract from the current position.
    Full step-by-step solution

    Let's go step-by-step. --- **Step 1: Start at sea level** The submarine starts at 0 meters relative to sea level. --- **Step 2: First descent** Descending means going below sea level, so we subtract from the current position. Descend 1250 m: 0 - 1250 = -1250 meters --- **Step 3: First ascent** Ascending means moving upward toward sea level, so we add to the current position. Ascend 480 m: -1250 + 480 = -770 meters --- **Step 4: Second descent** Descending again means subtracting from the current position. Descend 320 m: -770 - 320 = -1090 meters --- **Step 5: Interpret the result** -1090 meters means 1090 meters below sea level. --- **Final answer:** -1090