Negative Numbers

lessonbunny.com

Answer Key & Explanations

Negative Numbers · Grade 6 · Worksheet 3

1. Ava 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 range. Then it descends 1,100 meters to enter a valley. Finally, it ascends 675 meters to reach its observation position. What is the balloon's final altitude relative to sea level? Answer: 1675 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 + 675 = 1,675 meters The final altitude is 1,675 meters above sea level.
   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 + 675 = 1,675 meters Step 5: The final altitude is 1,675 meters above sea level.

2. Emma's bank account balance is -$135. She deposits $79. What is her new balance? Answer: -$56 Solution: Start with the initial balance: -$135 (meaning Emma owes $135). She deposits $79, which means we add $79 to her balance: -$135 + $79. To add a positive number to a negative number, find the difference: 135 - 79 = 56.
   Full step-by-step solution

   Step 1: Start with the initial balance: -$135 (meaning Emma owes $135). Step 2: She deposits $79, which means we add $79 to her balance: -$135 + $79. Step 3: To add a positive number to a negative number, find the difference: 135 - 79 = 56. Step 4: Since the negative number (-135) has a larger absolute value than the positive number (79), the result is negative: -$56. The answer is -$56.

3. Matiu is exploring a vertical cave system. The entrance to the cave is at an elevation of 0 meters. He rappels down a vertical shaft that ends at a point represented on a coordinate grid as (0, -124). He then climbs up a slope to a second chamber that is at (0, -46). A vertical chimney (a narrow shaft) leads further down to a deep pool at (0, -238). On a separate coordinate map of the cave, the vertical line representing the main shaft connects the entrance (0, 0) to the bottom of the first drop (0, -124). How many meters higher is the second chamber than the deep pool? Answer: 192 Solution: Identify the elevations of the two locations. The second chamber is at (0, -46), so its elevation is -46 meters. The deep pool is at (0, -238), so its elevation is -238 meters.
   Full step-by-step solution

   Step 1: Identify the elevations of the two locations. The second chamber is at (0, -46), so its elevation is -46 meters. The deep pool is at (0, -238), so its elevation is -238 meters. Step 2: To find how many meters higher the second chamber is than the deep pool, subtract the elevation of the deep pool from the elevation of the second chamber. Difference = Elevation of second chamber - Elevation of deep pool Difference = (-46) - (-238) Step 3: Subtracting a negative number is the same as adding its positive value. Difference = -46 + 238 Step 4: Calculate the result. Difference = 238 - 46 Difference = 192 meters. The second chamber is 192 meters higher than the deep pool.

4. A rectangular city park is drawn on a coordinate plane with corners at (-15, 8), (25, 8), (25, -12), and (-15, -12). Each unit on the grid represents 1 meter. What is the area of this park in square meters? Answer: 800 Solution: Find the length of the rectangle by calculating the difference in x-coordinates Length = 25 - (-15) = 25 + 15 = 40 meters Find the width of the rectangle by calculating the difference in y-coordinates Width = 8 - (-12) = 8 + 12 = 20 meters Calculate the area using the formula: Area = length ×…
   Full step-by-step solution

   Step 1: Find the length of the rectangle by calculating the difference in x-coordinates Length = 25 - (-15) = 25 + 15 = 40 meters Step 2: Find the width of the rectangle by calculating the difference in y-coordinates Width = 8 - (-12) = 8 + 12 = 20 meters Step 3: Calculate the area using the formula: Area = length × width Area = 40 × 20 = 800 square meters The area of the park is 800 square meters.

5. Ava is tracking her company's quarterly profit changes. In Q1, they had a profit of $12,500. In Q2, they reported a loss of $8,750. In Q3, their profit increased by $6,200. In Q4, they had another loss of $4,150. What was the final profit or loss for the year? Answer: $5,800 Solution: Start with Q1 profit: +$12,500 Add Q2 loss: $12,500 - $8,750 = $3,750 Add Q3 profit increase: $3,750 + $6,200 = $9,950 Add Q4 loss: $9,950 - $4,150 = $5,800 Since the result is positive, this represents a final profit of $5,800 for the year.
   Full step-by-step solution

   Step 1: Start with Q1 profit: +$12,500 Step 2: Add Q2 loss: $12,500 - $8,750 = $3,750 Step 3: Add Q3 profit increase: $3,750 + $6,200 = $9,950 Step 4: Add Q4 loss: $9,950 - $4,150 = $5,800 Step 5: Since the result is positive, this represents a final profit of $5,800 for the year.

6. Mere's bank account balance is -$248. She deposits $175. What is her new balance? Answer: -$73 Solution: Start with the initial balance: -$248. She deposits $175, which means we add +175. Calculate: -248 + 175 = -73.
   Full step-by-step solution

   Step 1: Start with the initial balance: -$248. Step 2: She deposits $175, which means we add +175. Step 3: Calculate: -248 + 175 = -73. Step 4: The new balance is -$73. The answer is -$73.

7. Liam is tracking the temperature changes in his city. On Monday morning, it was -3°C. By noon, the temperature had risen by 8 degrees. Then overnight, it dropped by 11 degrees. What was the final temperature on Tuesday morning? Answer: -6 Solution: Monday morning temperature = -3°C. It rose by 8 degrees, so we add 8 to -3. -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 degrees, so we add 8 to -3. -3 + 8 = 5°C. So, by noon Monday, the temperature is 5°C. **Step 3: Overnight drop** Overnight, it dropped by 11 degrees. So we subtract 11 from 5°C. 5 - 11 = -6°C. **Step 4: Identify final time** The overnight drop leads to Tuesday morning. So Tuesday morning temperature = -6°C. **Final answer:** -6