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Rational Addition/Subtraction

Grade 7 · Ratios · Worksheet 2

  1. Aroha is monitoring the depth of a research submarine during an underwater expedition. The submarine starts at a depth of -45.75 meters (below sea level). It first ascends by 18.5 meters, then descends by 32.25 meters, and finally ascends again by 9.75 meters. What is the final depth of the submarine relative to sea level? Answer: ______________
  2. Mason is keeping track of the stock price of a company over four days. On Monday, the stock price started at $72.50. On Tuesday, it dropped by $15.75. On Wednesday, it gained $9.40. On Thursday, it fell by $12.80. What is the final stock price after all these changes? Answer: ______________
  3. A rectangular garden is drawn on a coordinate plane with vertices at (-3, 2), (5, 2), (5, -4), and (-3, -4). A diagonal path is drawn from (-3, 2) to (5, -4). What is the length of this diagonal path? Round your answer to the nearest tenth. Answer: ______________
  4. A rectangular garden is drawn on a coordinate plane with vertices at (-3, 2), (5, 2), (5, -4), and (-3, -4). A circular fountain is placed at the center of the garden with a radius of 2 units. What is the total area of the garden that is NOT occupied by the fountain? (Use π = 3.14) Answer: ______________
  5. A scientist is tracking the temperature changes in a chemical reaction. The reaction starts at 15.75°C. In the first phase, the temperature increases by 8.25°C. In the second phase, it decreases by 12.5°C. In the final phase, it increases again by 6.75°C. What is the final temperature of the reaction? Answer: ______________
  6. Noah is keeping track of his savings account balance. He starts with $156.75. He then deposits his birthday money of $51.25. Later, he buys a new video game for $46.80. The next day, he pays his friend back $21.50 that he owed. Finally, he earns $31.60 by walking his neighbor's dog. What is Noah's final account balance? Answer: ______________
  7. Mere is keeping track of her electricity usage in kilowatt-hours (kWh) over four days. On Monday, her usage is -4.25 kWh relative to her baseline (meaning she used less than baseline). On Tuesday, she uses 2.5 kWh above baseline, so her change is +2.5. On Wednesday, she uses 6.75 kWh less than baseline, so her change is -6.75. On Thursday, she uses 4.5 kWh above baseline. What is Mere's total change in electricity usage relative to her baseline after these four days? Answer: ______________
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Answer Key & Explanations

Rational Addition/Subtraction · Grade 7 · Worksheet 2

  1. Aroha is monitoring the depth of a research submarine during an underwater expedition. The submarine starts at a depth of -45.75 meters (below sea level). It first ascends by 18.5 meters, then descends by 32.25 meters, and finally ascends again by 9.75 meters. What is the final depth of the submarine relative to sea level? Answer: -49.75 Solution: Start with the initial depth: -45.75 meters First ascent of 18.5 meters: -45.75 + 18.5 = -27.25 meters Then a descent of 32.25 meters: -27.25 - 32.25 = -59.5 meters Final ascent of 9.75 meters: -59.5 + 9.75 = -49.75 meters The final depth of the submarine is -49.75 meters below sea level.
    Full step-by-step solution

    Step 1: Start with the initial depth: -45.75 meters Step 2: First ascent of 18.5 meters: -45.75 + 18.5 = -27.25 meters Step 3: Then a descent of 32.25 meters: -27.25 - 32.25 = -59.5 meters Step 4: Final ascent of 9.75 meters: -59.5 + 9.75 = -49.75 meters The final depth of the submarine is -49.75 meters below sea level.

  2. Mason is keeping track of the stock price of a company over four days. On Monday, the stock price started at $72.50. On Tuesday, it dropped by $15.75. On Wednesday, it gained $9.40. On Thursday, it fell by $12.80. What is the final stock price after all these changes? Answer: 53.35 Solution: Start with Monday's price: $72.50 Subtract Tuesday's drop: 72.50 - 15.75 = 56.75 Add Wednesday's gain: 56.75 + 9.40 = 66.15 Subtract Thursday's fall: 66.15 - 12.80 = 53.35 The final stock price is $53.35.
    Full step-by-step solution

    Step 1: Start with Monday's price: $72.50 Step 2: Subtract Tuesday's drop: 72.50 - 15.75 = 56.75 Step 3: Add Wednesday's gain: 56.75 + 9.40 = 66.15 Step 4: Subtract Thursday's fall: 66.15 - 12.80 = 53.35 The final stock price is $53.35.

  3. A rectangular garden is drawn on a coordinate plane with vertices at (-3, 2), (5, 2), (5, -4), and (-3, -4). A diagonal path is drawn from (-3, 2) to (5, -4). What is the length of this diagonal path? Round your answer to the nearest tenth. Answer: 10.0 Solution: Identify the coordinates of the two endpoints of the diagonal path. The problem says the diagonal goes from (-3, 2) to (5, -4). Let (x1, y1) = (-3, 2) and (x2, y2) = (5, -4).
    Full step-by-step solution

    Step 1: Identify the coordinates of the two endpoints of the diagonal path. The problem says the diagonal goes from (-3, 2) to (5, -4). Let (x1, y1) = (-3, 2) and (x2, y2) = (5, -4). Step 2: Recall the distance formula for two points in a coordinate plane. Distance = sqrt( (x2 - x1)^2 + (y2 - y1)^2 ) Step 3: Calculate the horizontal difference (x2 - x1). x2 - x1 = 5 - (-3) = 5 + 3 = 8 Step 4: Calculate the vertical difference (y2 - y1). y2 - y1 = -4 - 2 = -6 Step 5: Square each difference. (8)^2 = 64 (-6)^2 = 36 Step 6: Add the squares. 64 + 36 = 100 Step 7: Take the square root. sqrt(100) = 10.0 Step 8: Round to the nearest tenth. 10.0 is already to the nearest tenth. Final answer: The length of the diagonal path is 10.0.

  4. A rectangular garden is drawn on a coordinate plane with vertices at (-3, 2), (5, 2), (5, -4), and (-3, -4). A circular fountain is placed at the center of the garden with a radius of 2 units. What is the total area of the garden that is NOT occupied by the fountain? (Use π = 3.14) Answer: 35.44 Solution: Find the area of the rectangular garden. The vertices are (-3, 2), (5, 2), (5, -4), and (-3, -4). Length along the x-axis: from -3 to 5, so length = 5 - (-3) = 5 + 3 = 8 units.
    Full step-by-step solution

    Step 1: Find the area of the rectangular garden. The vertices are (-3, 2), (5, 2), (5, -4), and (-3, -4). Length along the x-axis: from -3 to 5, so length = 5 - (-3) = 5 + 3 = 8 units. Width along the y-axis: from -4 to 2, so width = 2 - (-4) = 2 + 4 = 6 units. Area of rectangle = length × width = 8 × 6 = 48 square units. Step 2: Find the center of the garden (which is the center of the circle). The center is the midpoint of the rectangle's diagonals. Midpoint between (-3, 2) and (5, -4): x-coordinate = (-3 + 5)/2 = 2/2 = 1 y-coordinate = (2 + (-4))/2 = (2 - 4)/2 = -2/2 = -1 So the center is (1, -1). Step 3: Find the area of the circular fountain. Radius r = 2 units. Area of circle = π × r^2 = 3.14 × (2^2) = 3.14 × 4 = 12.56 square units. Step 4: Find the area NOT occupied by the fountain. This is the area of the rectangle minus the area of the circle. Area not occupied = 48 - 12.56 = 35.44 square units. Final Answer: 35.44

  5. A scientist is tracking the temperature changes in a chemical reaction. The reaction starts at 15.75°C. In the first phase, the temperature increases by 8.25°C. In the second phase, it decreases by 12.5°C. In the final phase, it increases again by 6.75°C. What is the final temperature of the reaction? Answer: 18.25 Solution: Start with the initial temperature: 15.75°C Add the first phase increase: 15.75 + 8.25 = 24.00°C Subtract the second phase decrease: 24.00 - 12.50 = 11.50°C Add the final phase increase: 11.50 + 6.75 = 18.25°C The final temperature is 18.25°C.
    Full step-by-step solution

    Step 1: Start with the initial temperature: 15.75°C Step 2: Add the first phase increase: 15.75 + 8.25 = 24.00°C Step 3: Subtract the second phase decrease: 24.00 - 12.50 = 11.50°C Step 4: Add the final phase increase: 11.50 + 6.75 = 18.25°C The final temperature is 18.25°C.

  6. Noah is keeping track of his savings account balance. He starts with $156.75. He then deposits his birthday money of $51.25. Later, he buys a new video game for $46.80. The next day, he pays his friend back $21.50 that he owed. Finally, he earns $31.60 by walking his neighbor's dog. What is Noah's final account balance? Answer: 171.30 Solution: Start with the initial balance: $156.75 Add the birthday money deposit: 156.75 + 51.25 = 208.00 Subtract the video game cost: 208.00 - 46.80 = 161.20 Subtract the money paid back to friend: 161.20 - 21.50 = 139.70 Add the dog-walking earnings: 139.70 + 31.60 = 171.30 The final balance is $171.30.
    Full step-by-step solution

    Step 1: Start with the initial balance: $156.75 Step 2: Add the birthday money deposit: 156.75 + 51.25 = 208.00 Step 3: Subtract the video game cost: 208.00 - 46.80 = 161.20 Step 4: Subtract the money paid back to friend: 161.20 - 21.50 = 139.70 Step 5: Add the dog-walking earnings: 139.70 + 31.60 = 171.30 The final balance is $171.30.

  7. Mere is keeping track of her electricity usage in kilowatt-hours (kWh) over four days. On Monday, her usage is -4.25 kWh relative to her baseline (meaning she used less than baseline). On Tuesday, she uses 2.5 kWh above baseline, so her change is +2.5. On Wednesday, she uses 6.75 kWh less than baseline, so her change is -6.75. On Thursday, she uses 4.5 kWh above baseline. What is Mere's total change in electricity usage relative to her baseline after these four days? Answer: -4.0 Solution: Start with Monday's change: -4.25 Add Tuesday's change: -4.25 + 2.5 = -1.75 Add Wednesday's change: -1.75 + (-6.75) = -8.5 Add Thursday's change: -8.5 + 4.5 = -4.0 The total change after four days is -4.0 kWh relative to baseline.
    Full step-by-step solution

    Step 1: Start with Monday's change: -4.25 Step 2: Add Tuesday's change: -4.25 + 2.5 = -1.75 Step 3: Add Wednesday's change: -1.75 + (-6.75) = -8.5 Step 4: Add Thursday's change: -8.5 + 4.5 = -4.0 The total change after four days is -4.0 kWh relative to baseline.