Absolute Value

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Answer Key & Explanations

Absolute Value · Grade 6 · Worksheet 3

1. Liam is tracking the daily temperature changes in his city. On Monday morning, it was -3°C. By afternoon, the temperature rose by 8°C. Then overnight, it dropped by 5°C. What was the final temperature on Tuesday morning? Answer: 0 Solution: Start with Monday morning temperature. Monday morning: -3°C Temperature rose by 8°C by afternoon. -3 + 8 = 5°C So Monday afternoon temperature = 5°C Overnight, temperature dropped by 5°C.
   Full step-by-step solution

   Let's go step-by-step. Step 1: Start with Monday morning temperature. Monday morning: -3°C Step 2: Temperature rose by 8°C by afternoon. -3 + 8 = 5°C So Monday afternoon temperature = 5°C Step 3: Overnight, temperature dropped by 5°C. 5 - 5 = 0°C Step 4: This overnight change leads to Tuesday morning. So Tuesday morning temperature = 0°C Final answer: 0

2. Hana is a geologist studying the elevation changes along a hiking trail in a volcanic region. The trail starts at an elevation of 0 meters (sea level). The first section of the trail descends 340 meters into a crater. The next section ascends 175 meters to a ridge. The final section descends another 265 meters to a lava tube entrance. What is the total vertical distance Hana travels along the entire trail, 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 Second ascent: 175 meters up, magnitude = 175 Third descent: 265 meters down, magnitude = 265 Add the magnitudes of all movements to find the total vertical distance.
   Full step-by-step solution

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

3. Liam is monitoring the temperature in a science lab freezer. At 8:00 AM, the temperature was -15°C. By noon, it had warmed to -3°C. What was the absolute value of the temperature change from 8:00 AM to noon? Answer: 12 Solution: Identify the temperatures at the two times. At 8:00 AM, temperature = -15°C. At noon, temperature = -3°C.
   Full step-by-step solution

   Step 1: Identify the temperatures at the two times. At 8:00 AM, temperature = -15°C. At noon, temperature = -3°C. Step 2: Find the temperature change. Temperature change = final temperature − initial temperature = (-3) − (-15) Step 3: Simplify the subtraction. Subtracting -15 is the same as adding 15. So: (-3) + 15 = 12 Step 4: Interpret the result. The temperature change is 12°C. Step 5: Apply the absolute value. The problem asks for the absolute value of the temperature change. Absolute value means the positive magnitude, ignoring direction (warming or cooling). |12| = 12 Final Answer: 12

4. Matiu is helping his family monitor the water level in their well. The normal water level is marked as 0 meters. After a dry spell, the water level drops to -14 meters. Then, after a week of rain, it rises by 8 meters. Finally, due to increased usage, it drops another 6 meters. What is the total distance the water level moved from its starting point, considering only the magnitude of each movement? Answer: 28 Solution: Identify each movement and its magnitude (absolute value). First drop: 14 meters down → magnitude = 14 Second rise: 8 meters up → magnitude = 8 Third drop: 6 meters down → magnitude = 6 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 drop: 14 meters down → magnitude = 14 Second rise: 8 meters up → magnitude = 8 Third drop: 6 meters down → magnitude = 6 Step 2: Add the magnitudes of all movements to find the total distance traveled. Total distance = 14 + 8 + 6 Step 3: Calculate the sum. 14 + 8 = 22 22 + 6 = 28 The total distance the water level moved is 28 meters.

5. |−1500 + 900| ÷ |−12 + 8| = ? Answer: 150 Solution: Simplify inside the first absolute value: −1500 + 900 = −600 Find the absolute value: |−600| = 600 (distance from zero is 600) Simplify inside the second absolute value: −12 + 8 = −4 Find the absolute value: |−4| = 4 (distance from zero is 4) Divide the results: 600 ÷ 4 = 150 The answer is 150.
   Full step-by-step solution

   Step 1: Simplify inside the first absolute value: −1500 + 900 = −600 Step 2: Find the absolute value: |−600| = 600 (distance from zero is 600) Step 3: Simplify inside the second absolute value: −12 + 8 = −4 Step 4: Find the absolute value: |−4| = 4 (distance from zero is 4) Step 5: Divide the results: 600 ÷ 4 = 150 The answer is 150.

6. |−8| × |5| − |−12 ÷ 3| = ? Answer: 36 Solution: Evaluate |−8| = 8 Evaluate |5| = 5 Evaluate |−12 ÷ 3| = |−4| = 4 Substitute back into the expression: 8 × 5 − 4 Perform multiplication: 8 × 5 = 40 Perform subtraction: 40 − 4 = 36 The answer is 36.
   Full step-by-step solution

   Step 1: Evaluate |−8| = 8 Step 2: Evaluate |5| = 5 Step 3: Evaluate |−12 ÷ 3| = |−4| = 4 Step 4: Substitute back into the expression: 8 × 5 − 4 Step 5: Perform multiplication: 8 × 5 = 40 Step 6: Perform subtraction: 40 − 4 = 36 The answer is 36.

7. Liam is tracking the temperature changes in his city. On Monday morning, the temperature was -5°C. By noon, it had risen by 8 degrees. On Tuesday morning, it was 3°C, but then a cold front came through and dropped the temperature by 11 degrees. What was the final temperature on Tuesday after the cold front, and how does its distance from zero compare to Monday's morning temperature? Answer: -8°C, and Tuesday's final temperature is 3 degrees farther from zero than Monday's morning temperature. Solution: Find Monday's temperature at noon. Monday morning: -5°C Temperature rose by 8 degrees: -5 + 8 = 3°C at noon on Monday. Find Tuesday's temperature after the cold front.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find Monday's temperature at noon.** Monday morning: -5°C Temperature rose by 8 degrees: -5 + 8 = 3°C at noon on Monday. --- **Step 2: Find Tuesday's temperature after the cold front.** Tuesday morning: 3°C Temperature dropped by 11 degrees: 3 - 11 = -8°C after the cold front. So the final temperature on Tuesday is **-8°C**. --- **Step 3: Compare distances from zero.** Distance from zero means the absolute value of the temperature. Monday morning: |-5| = 5 Tuesday final: |-8| = 8 Difference in distances: 8 - 5 = 3 So Tuesday's final temperature is **3 degrees farther from zero** than Monday's morning temperature. --- **Final Answer:** -8°C, and Tuesday's final temperature is 3 degrees farther from zero than Monday's morning temperature.