Absolute Value

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Answer Key & Explanations

Absolute Value · Grade 6 · Worksheet 2

1. Charlotte is a mountain climber tracking her vertical position during an expedition. She starts at base camp, which is at 0 meters elevation. She climbs up 1420 meters to reach a ridge. Then she descends 780 meters into a valley to set up a shelter. Finally, she climbs back up 1050 meters to reach a summit. What is the total vertical distance Charlotte traveled during her climb, considering only the magnitude of each movement? Answer: 3250 Solution: Identify each movement and its magnitude (absolute value). First climb: 1420 meters up (magnitude = 1420) Descent: 780 meters down (magnitude = 780) Second climb: 1050 meters up (magnitude = 1050) Add the magnitudes of all movements to find the total distance traveled.
   Full step-by-step solution

   Step 1: Identify each movement and its magnitude (absolute value). First climb: 1420 meters up (magnitude = 1420) Descent: 780 meters down (magnitude = 780) Second climb: 1050 meters up (magnitude = 1050) Step 2: Add the magnitudes of all movements to find the total distance traveled. Total distance = 1420 + 780 + 1050 Step 3: Calculate the sum. 1420 + 780 = 2200 2200 + 1050 = 3250 The total vertical distance Charlotte traveled is 3250 meters.

2. Emma is a marine biologist studying the migration of sea turtles. She uses a submersible to track them underwater. She starts at sea level (0 meters). First, she descends 1375 meters to observe a deep-sea turtle. Then, she ascends 823 meters to follow a group of jellyfish. Finally, she descends another 549 meters to reach a coral reef. What is the total vertical distance Emma's submersible traveled during this journey? Answer: 2747 Solution: Identify each movement and its magnitude (absolute value). First descent: 1375 meters (magnitude = 1375). First ascent: 823 meters (magnitude = 823).
   Full step-by-step solution

   Step 1: Identify each movement and its magnitude (absolute value). First descent: 1375 meters (magnitude = 1375). First ascent: 823 meters (magnitude = 823). Second descent: 549 meters (magnitude = 549). Step 2: Add all the magnitudes to find the total distance. Total distance = 1375 + 823 + 549. Step 3: Calculate the sum. 1375 + 823 = 2198. Then 2198 + 549 = 2747. The total vertical distance traveled is 2747 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. Charlotte is a deep-sea explorer monitoring the vertical position of a research submersible. The submersible starts at sea level (0 meters). It first descends to -340 meters to collect samples. Then it ascends 175 meters to avoid a geological feature. Finally, it descends another 265 meters to reach a hydrothermal vent. What is the total vertical distance the submersible traveled, considering only the magnitude of each movement? Answer: 780 Solution: Identify each movement and its magnitude (absolute value). First descent: 340 meters down, magnitude = 340 First ascent: 175 meters up, magnitude = 175 Second descent: 265 meters down, magnitude = 265 Add the magnitudes to find the total distance traveled.
   Full step-by-step solution

   Step 1: Identify each movement and its magnitude (absolute value). First descent: 340 meters down, magnitude = 340 First ascent: 175 meters up, magnitude = 175 Second descent: 265 meters down, magnitude = 265 Step 2: Add the magnitudes to find the total distance traveled. Total distance = 340 + 175 + 265 Step 3: Calculate the sum. 340 + 175 = 515 515 + 265 = 780 The total vertical distance traveled by the submersible is 780 meters.

5. 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

6. |−1450 + 950| − |−320 + 180| = ? Answer: 360 Solution: Simplify inside the first absolute value: −1450 + 950 = −500 Find the absolute value: |−500| = 500 Simplify inside the second absolute value: −320 + 180 = −140 Find the absolute value: |−140| = 140 Subtract: 500 − 140 = 360 The answer is 360.
   Full step-by-step solution

   Step 1: Simplify inside the first absolute value: −1450 + 950 = −500 Step 2: Find the absolute value: |−500| = 500 Step 3: Simplify inside the second absolute value: −320 + 180 = −140 Step 4: Find the absolute value: |−140| = 140 Step 5: Subtract: 500 − 140 = 360 The answer is 360.