Negative Numbers

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Answer Key & Explanations

Negative Numbers · Grade 6 · Worksheet 3

1. Liam is tracking the altitude of a hot air balloon during a science expedition. The balloon starts at 1,250 meters above sea level. It first ascends 850 meters to pass over a mountain ridge. Then it descends 1,100 meters to collect atmospheric data. Finally, it ascends 725 meters to reach its final observation point. What is the balloon's final altitude relative to sea level? Answer: 1725 Solution: Start with the initial altitude: 1,250 meters Add the first ascent: 1,250 + 850 = 2,100 meters Subtract the descent: 2,100 - 1,100 = 1,000 meters Add the final ascent: 1,000 + 725 = 1,725 meters The final altitude relative to sea level is 1,725 meters.
   Full step-by-step solution

   Step 1: Start with the initial altitude: 1,250 meters Step 2: Add the first ascent: 1,250 + 850 = 2,100 meters Step 3: Subtract the descent: 2,100 - 1,100 = 1,000 meters Step 4: Add the final ascent: 1,000 + 725 = 1,725 meters Step 5: The final altitude relative to sea level is 1,725 meters.

2. Liam is tracking the temperature changes in his city. On Monday morning, it was -3°C. By noon, the temperature had risen by 8°C. Then overnight, it dropped by 11°C. What was the final temperature on Tuesday morning? Answer: -6 Solution: Monday morning temperature = -3°C. It rose by 8°C. So: -3 + 8 = 5°C.
   Full step-by-step solution

   Let's go step by step. **Step 1: Start with Monday morning temperature** Monday morning temperature = -3°C. **Step 2: Temperature rise by noon** It rose by 8°C. So: -3 + 8 = 5°C. At noon, the temperature is 5°C. **Step 3: Overnight drop** Overnight, it dropped by 11°C. So: 5 - 11 = -6°C. **Step 4: Interpret the final temperature** This overnight change leads to Tuesday morning's temperature. Thus, Tuesday morning temperature = -6°C. **Final Answer:** -6

3. -25 + (-13) - 7 = ? Answer: -45 Solution: Start with -25 + (-13) Adding a negative is the same as subtracting: -25 - 13 = -38 Now subtract 7 from -38: -38 - 7 = -45 The final answer is -45.
   Full step-by-step solution

   Step 1: Start with -25 + (-13) Step 2: Adding a negative is the same as subtracting: -25 - 13 = -38 Step 3: Now subtract 7 from -38: -38 - 7 = -45 Step 4: The final answer is -45.

4. Ava is tracking the altitude of a hot air balloon during a flight. The balloon starts at 1,250 meters above sea level. It first ascends 850 meters to catch a favorable wind current. Then it descends 1,100 meters to fly through a valley. Finally, it ascends 475 meters to reach its landing zone. What is the balloon's final altitude relative to sea level? Answer: 1475 Solution: The balloon starts at 1,250 meters. It ascends 850 meters. This is a positive change: 1,250 + 850 = 2,100 meters.
   Full step-by-step solution

   Step 1: The balloon starts at 1,250 meters. Step 2: It ascends 850 meters. This is a positive change: 1,250 + 850 = 2,100 meters. Step 3: It descends 1,100 meters. This is a negative change: 2,100 - 1,100 = 1,000 meters. Step 4: It ascends 475 meters. This is a positive change: 1,000 + 475 = 1,475 meters. The final altitude is 1,475 meters above sea level.

5. Liam is monitoring the temperature in a science experiment. The liquid starts at 15°C. During the first phase, the temperature drops by 22 degrees. In the second phase, it rises by 18 degrees. What is the final temperature of the liquid? Answer: 11 Solution: Start with the initial temperature. The liquid starts at 15°C. During the first phase, the temperature drops by 22 degrees.
   Full step-by-step solution

   Let's go step-by-step. **Step 1: Start with the initial temperature.** The liquid starts at 15°C. **Step 2: Apply the first change (temperature drop).** During the first phase, the temperature drops by 22 degrees. That means: 15 − 22 = −7°C So after the first phase, the temperature is −7°C. **Step 3: Apply the second change (temperature rise).** In the second phase, it rises by 18 degrees. That means: −7 + 18 = 11°C **Step 4: State the final temperature.** The final temperature is 11°C. **Final Answer:** 11

6. A rectangular garden is drawn on a coordinate plane with corners at (-3, 2), (5, 2), (5, -4), and (-3, -4). What is the perimeter of the garden? Answer: 28 Solution: A = (-3, 2) B = (5, 2) C = (5, -4) D = (-3, -4) Plotting these in order: A → B → C → D → A. A = (-3, 2), B = (5, 2) Since the y-coordinates are the same (y = 2), this is a horizontal segment.
   Full step-by-step solution

   Let's find the perimeter step by step. --- **Step 1: Identify the vertices and sides** The vertices are: A = (-3, 2) B = (5, 2) C = (5, -4) D = (-3, -4) Plotting these in order: A → B → C → D → A. --- **Step 2: Find the length of side AB** A = (-3, 2), B = (5, 2) Since the y-coordinates are the same (y = 2), this is a horizontal segment. Length = |5 - (-3)| = |5 + 3| = 8. So AB = 8. --- **Step 3: Find the length of side BC** B = (5, 2), C = (5, -4) Since the x-coordinates are the same (x = 5), this is a vertical segment. Length = | -4 - 2 | = | -6 | = 6. So BC = 6. --- **Step 4: Find the length of side CD** C = (5, -4), D = (-3, -4) Same y-coordinate (y = -4), horizontal segment. Length = | -3 - 5 | = | -8 | = 8. So CD = 8. --- **Step 5: Find the length of side DA** D = (-3, -4), A = (-3, 2) Same x-coordinate (x = -3), vertical segment. Length = | 2 - (-4) | = | 2 + 4 | = 6. So DA = 6. --- **Step 6: Find the perimeter** Perimeter = AB + BC + CD + DA = 8 + 6 + 8 + 6 = 28. --- **Final answer:** 28

7. Maya is tracking the elevation changes during her mountain hike. She starts at the trailhead at 1,250 meters above sea level. She climbs 850 meters to reach the summit, then descends 1,150 meters into a valley. Finally, she climbs another 420 meters to reach a mountain hut. What is Maya's final elevation relative to sea level? Answer: 1370 Solution: Start at the trailhead: 1,250 meters Climb 850 meters: 1,250 + 850 = 2,100 meters Descend 1,150 meters: 2,100 - 1,150 = 950 meters Climb 420 meters: 950 + 420 = 1,370 meters Maya's final elevation is 1,370 meters above sea level.
   Full step-by-step solution

   Step 1: Start at the trailhead: 1,250 meters Step 2: Climb 850 meters: 1,250 + 850 = 2,100 meters Step 3: Descend 1,150 meters: 2,100 - 1,150 = 950 meters Step 4: Climb 420 meters: 950 + 420 = 1,370 meters Maya's final elevation is 1,370 meters above sea level.

8. Sophia's bank account balance is -$85. She deposits $120. What is her new balance? Answer: $35 Solution: Start with the initial balance: -$85 (meaning she owes $85). She deposits $120, which means we add $120 to her balance: -85 + 120. Calculate: -85 + 120 = 35.
   Full step-by-step solution

   Step 1: Start with the initial balance: -$85 (meaning she owes $85). Step 2: She deposits $120, which means we add $120 to her balance: -85 + 120. Step 3: Calculate: -85 + 120 = 35. Step 4: The new balance is $35. The answer is $35.