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Rational Applications

Grade 7 · Ratios · Worksheet 1

  1. (-12)² ÷ 4 + 5 × (-3) = ? Answer: ______________
  2. Matiu is recording the daily temperature changes in his city for a science project. On Monday at 8:00 AM, the temperature was -8°C. By noon, the temperature had risen by 14°C. Then, from noon to 6:00 PM, the temperature dropped by 6°C. Overnight from 6:00 PM to Tuesday at 6:00 AM, the temperature fell by 10°C. What was the temperature on Tuesday at 6:00 AM? Answer: ______________
  3. Mason's bank account balance was -$127. He deposited $42 and then withdrew $57. What is his new balance? Answer: ______________
  4. Emma is exploring a cave system. Her elevation tracker shows that she starts at an entrance with an elevation of 15 meters above sea level. She descends 27 meters into the first chamber, then climbs 13 meters up a slope to a second chamber, and finally descends 19 meters to the lowest point of the cave. What is Emma's final elevation in meters? Answer: ______________
  5. Ava is tracking the temperature changes in her freezer for a science experiment. At 6:00 AM, the temperature inside the freezer was -16°C. She then opened the freezer door for 30 minutes, causing the temperature to rise by 11°C. After closing the door, the freezer's cooling system worked to lower the temperature by 6°C. Later in the day, she added a warm container of soup, which caused the temperature to increase by 21°C. What is the final temperature inside the freezer? Answer: ______________
  6. Mason is tracking the elevation of his submarine during a deep-sea exploration. He starts at a depth of 48 feet below sea level. He then ascends 15 feet to observe a coral reef. Later, he descends 32 feet to investigate a sunken ship. After that, he ascends 9 feet to get a better view of the ship's deck. What is Mason's final elevation relative to sea level? Answer: ______________
  7. (-3/4 + 2/3) × (-24) = ? Answer: ______________
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Answer Key & Explanations

Rational Applications · Grade 7 · Worksheet 1

  1. (-12)² ÷ 4 + 5 × (-3) = ? Answer: 21 Solution: Calculate the exponent first: (-12)² = 144 Perform division: 144 ÷ 4 = 36 Perform multiplication: 5 × (-3) = -15 Add the results: 36 + (-15) = 36 - 15 = 21 The final answer is 21.
    Full step-by-step solution

    Step 1: Calculate the exponent first: (-12)² = 144 Step 2: Perform division: 144 ÷ 4 = 36 Step 3: Perform multiplication: 5 × (-3) = -15 Step 4: Add the results: 36 + (-15) = 36 - 15 = 21 Step 5: The final answer is 21.

  2. Matiu is recording the daily temperature changes in his city for a science project. On Monday at 8:00 AM, the temperature was -8°C. By noon, the temperature had risen by 14°C. Then, from noon to 6:00 PM, the temperature dropped by 6°C. Overnight from 6:00 PM to Tuesday at 6:00 AM, the temperature fell by 10°C. What was the temperature on Tuesday at 6:00 AM? Answer: -10 Solution: Start with Monday 8:00 AM temperature: -8°C Add the rise from 8:00 AM to noon: -8 + 14 = 6°C Subtract the drop from noon to 6:00 PM: 6 - 6 = 0°C Subtract the overnight drop from 6:00 PM to Tuesday 6:00 AM: 0 - 10 = -10°C The temperature on Tuesday at 6:00 AM was -10°C.
    Full step-by-step solution

    Step 1: Start with Monday 8:00 AM temperature: -8°C Step 2: Add the rise from 8:00 AM to noon: -8 + 14 = 6°C Step 3: Subtract the drop from noon to 6:00 PM: 6 - 6 = 0°C Step 4: Subtract the overnight drop from 6:00 PM to Tuesday 6:00 AM: 0 - 10 = -10°C The temperature on Tuesday at 6:00 AM was -10°C.

  3. Mason's bank account balance was -$127. He deposited $42 and then withdrew $57. What is his new balance? Answer: -$142 Solution: Start with the initial balance: -$127. Deposit $42 means add $42: -127 + 42 = -85. Withdraw $57 means subtract $57: -85 - 57 = -142.
    Full step-by-step solution

    Step 1: Start with the initial balance: -$127. Step 2: Deposit $42 means add $42: -127 + 42 = -85. Step 3: Withdraw $57 means subtract $57: -85 - 57 = -142. The final balance is -$142.

  4. Emma is exploring a cave system. Her elevation tracker shows that she starts at an entrance with an elevation of 15 meters above sea level. She descends 27 meters into the first chamber, then climbs 13 meters up a slope to a second chamber, and finally descends 19 meters to the lowest point of the cave. What is Emma's final elevation in meters? Answer: -18 Solution: Start at 15 meters above sea level. Descend 27 meters: 15 - 27 = -12 meters. Climb 13 meters: -12 + 13 = 1 meter.
    Full step-by-step solution

    Step 1: Start at 15 meters above sea level. Step 2: Descend 27 meters: 15 - 27 = -12 meters. Step 3: Climb 13 meters: -12 + 13 = 1 meter. Step 4: Descend 19 meters: 1 - 19 = -18 meters. The final elevation is -18 meters (18 meters below sea level).

  5. Ava is tracking the temperature changes in her freezer for a science experiment. At 6:00 AM, the temperature inside the freezer was -16°C. She then opened the freezer door for 30 minutes, causing the temperature to rise by 11°C. After closing the door, the freezer's cooling system worked to lower the temperature by 6°C. Later in the day, she added a warm container of soup, which caused the temperature to increase by 21°C. What is the final temperature inside the freezer? Answer: 10 Solution: Start with the initial temperature: -16°C Temperature rises by 11°C: -16 + 11 = -5°C Temperature decreases by 6°C: -5 - 6 = -11°C Temperature increases by 21°C: -11 + 21 = 10°C The final temperature inside the freezer is 10°C.
    Full step-by-step solution

    Step 1: Start with the initial temperature: -16°C Step 2: Temperature rises by 11°C: -16 + 11 = -5°C Step 3: Temperature decreases by 6°C: -5 - 6 = -11°C Step 4: Temperature increases by 21°C: -11 + 21 = 10°C The final temperature inside the freezer is 10°C.

  6. Mason is tracking the elevation of his submarine during a deep-sea exploration. He starts at a depth of 48 feet below sea level. He then ascends 15 feet to observe a coral reef. Later, he descends 32 feet to investigate a sunken ship. After that, he ascends 9 feet to get a better view of the ship's deck. What is Mason's final elevation relative to sea level? Answer: -56 feet Solution: Start at -48 feet (48 feet below sea level). Ascend 15 feet: -48 + 15 = -33 feet. Descend 32 feet: -33 + (-32) = -65 feet.
    Full step-by-step solution

    Step 1: Start at -48 feet (48 feet below sea level). Step 2: Ascend 15 feet: -48 + 15 = -33 feet. Step 3: Descend 32 feet: -33 + (-32) = -65 feet. Step 4: Ascend 9 feet: -65 + 9 = -56 feet. Final answer: Mason's final elevation is -56 feet, or 56 feet below sea level.

  7. (-3/4 + 2/3) × (-24) = ? Answer: 2 Solution: Find a common denominator for -3/4 and 2/3. The least common denominator is 12. Convert -3/4 to -9/12 (multiply numerator and denominator by 3).
    Full step-by-step solution

    Step 1: Find a common denominator for -3/4 and 2/3. The least common denominator is 12. Step 2: Convert -3/4 to -9/12 (multiply numerator and denominator by 3). Step 3: Convert 2/3 to 8/12 (multiply numerator and denominator by 4). Step 4: Add the fractions: -9/12 + 8/12 = -1/12. Step 5: Multiply the result by -24: (-1/12) × (-24) = 24/12. Step 6: Simplify 24/12 = 2. The answer is 2.