Negative Numbers

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Answer Key & Explanations

Negative Numbers · Grade 6 · Worksheet 2

1. Ava is tracking the altitude of a hot air balloon during a flight. The balloon starts at 250 meters above sea level. It ascends 180 meters to catch a favorable wind current, then descends 95 meters to avoid some clouds. Finally, it ascends another 120 meters to reach its cruising altitude. What is the balloon's final altitude relative to sea level? Answer: 455 Solution: Start with the initial altitude: 250 meters Add the first ascent: 250 + 180 = 430 meters Subtract the descent: 430 - 95 = 335 meters Add the final ascent: 335 + 120 = 455 meters The balloon's final altitude is 455 meters above sea level.
   Full step-by-step solution

   Step 1: Start with the initial altitude: 250 meters Step 2: Add the first ascent: 250 + 180 = 430 meters Step 3: Subtract the descent: 430 - 95 = 335 meters Step 4: Add the final ascent: 335 + 120 = 455 meters The balloon's final altitude is 455 meters above sea level.

2. Olivia has a bank account balance of -$45. She deposits $25. What is her new balance? Answer: -$20 Solution: Start with the initial balance: -$45 (this means she owes $45). She deposits $25, which means we add +25 to the balance: -45 + 25. To add a positive number to a negative number, find the difference: 45 - 25 = 20.
   Full step-by-step solution

   Step 1: Start with the initial balance: -$45 (this means she owes $45). Step 2: She deposits $25, which means we add +25 to the balance: -45 + 25. Step 3: To add a positive number to a negative number, find the difference: 45 - 25 = 20. Since the negative number is larger in absolute value, the result is negative. Step 4: So -45 + 25 = -20. The new balance is -$20.

3. -25 + 42 = ? Answer: 17 Solution: Start with -25. The difference between 42 and 25 is 17. Since 42 is greater than 25, the result will be positive.
   Full step-by-step solution

   Step 1: Start with -25. Step 2: Adding a positive number (42) means moving to the right on the number line. Step 3: The difference between 42 and 25 is 17. Step 4: Since 42 is greater than 25, the result will be positive. Step 5: -25 + 42 = 17. The answer is 17.

4. Liam is tracking the temperature changes in his city. At 6 AM, the temperature was -5°C. By noon, it had risen by 12°C. Then, a cold front moved in and the temperature dropped by 17°C by 6 PM. What was the final temperature at 6 PM? Answer: -10°C Solution: Start with the initial temperature at 6 AM At 6 AM, the temperature was -5°C. By noon, it rose by 12°C. So we add 12 to -5: -5 + 12 = 7°C At noon, the temperature is 7°C.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Start with the initial temperature at 6 AM** At 6 AM, the temperature was -5°C. --- **Step 2: Temperature rise by noon** By noon, it rose by 12°C. So we add 12 to -5: -5 + 12 = 7°C At noon, the temperature is 7°C. --- **Step 3: Temperature drop by 6 PM** A cold front moved in and the temperature dropped by 17°C by 6 PM. So we subtract 17 from 7°C: 7 - 17 = -10°C --- **Step 4: Final temperature** At 6 PM, the temperature is -10°C. --- **Final answer:** -10°C

5. -8 × 6 + 144 ÷ (-12) = ? Answer: -60 Solution: Perform the multiplication: -8 × 6 = -48 Perform the division: 144 ÷ (-12) = -12 Add the results: -48 + (-12) = -60 The answer is -60.
   Full step-by-step solution

   Step 1: Perform the multiplication: -8 × 6 = -48 Step 2: Perform the division: 144 ÷ (-12) = -12 Step 3: Add the results: -48 + (-12) = -60 The answer is -60.

6. Maria is tracking her company's quarterly profits. In Q1, they had a profit of $12,500. In Q2, they had a loss of $8,750. In Q3, they had a profit of $15,200. What was the company's total profit or loss for the first three quarters? Answer: $18,950 Solution: Represent the Q1 profit as a positive number: +12500 Represent the Q2 loss as a negative number: -8750 Represent the Q3 profit as a positive number: +15200 Add all three values together: 12500 + (-8750) + 15200 First, add 12500 and -8750: 12500 - 8750 = 3750 Then add 15200 to 3750: 3750 + 15200…
   Full step-by-step solution

   Step 1: Represent the Q1 profit as a positive number: +12500 Step 2: Represent the Q2 loss as a negative number: -8750 Step 3: Represent the Q3 profit as a positive number: +15200 Step 4: Add all three values together: 12500 + (-8750) + 15200 Step 5: First, add 12500 and -8750: 12500 - 8750 = 3750 Step 6: Then add 15200 to 3750: 3750 + 15200 = 18950 Step 7: Since the result is positive, it represents a profit of $18,950.

7. Isabella'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 the account: -85 + 120. To add a negative and a positive, find the difference: 120 - 85 = 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 the account: -85 + 120. Step 3: To add a negative and a positive, find the difference: 120 - 85 = 35. Step 4: Since the positive number (120) is larger, the result is positive: $35. The answer is $35.

8. Noah's bank account balance is -$156. He deposits $231. What is his new balance? Answer: $75 Solution: Start with the initial balance: -$156. Add the deposit: -$156 + $231. Since the numbers have different signs, find the difference: 231 - 156 = 75.
   Full step-by-step solution

   Step 1: Start with the initial balance: -$156. Step 2: Add the deposit: -$156 + $231. Step 3: Since the numbers have different signs, find the difference: 231 - 156 = 75. Step 4: The larger number (231) is positive, so the result is positive: $75. The answer is $75.

9. 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. What was the final profit or loss at the end of Q3? Answer: $9,950 Solution: Start with the Q1 profit: $12,500 Subtract the Q2 loss: $12,500 - $8,750 = $3,750 Add the Q3 profit increase: $3,750 + $6,200 = $9,950 Since the result is positive, it represents a profit.
   Full step-by-step solution

   Step 1: Start with the Q1 profit: $12,500 Step 2: Subtract the Q2 loss: $12,500 - $8,750 = $3,750 Step 3: Add the Q3 profit increase: $3,750 + $6,200 = $9,950 Step 4: Since the result is positive, it represents a profit. The final profit at the end of Q3 is $9,950.