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Rational Addition/Subtraction

Grade 7 · Ratios · Worksheet 3

  1. 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 this garden? Answer: ______________
  2. Olivia is monitoring the elevation of a hot air balloon. The balloon starts at an elevation of 150 feet above sea level. It then descends 275 feet to pick up a passenger. Later, it ascends 190 feet to catch a wind current. Finally, it descends 65 feet to get a better view. What is the final elevation of the balloon relative to sea level? Answer: ______________
  3. (-3/5 + 7/10) - (2/3 - 5/6) = ? Answer: ______________
  4. Ava is monitoring the water depth in a tidal pool for her science project. At 6:00 AM, the water depth is -3.6 feet relative to a reference point (meaning it is below the reference). The tide comes in, and the depth increases by 5.1 feet. Later, the tide goes out, and the depth decreases by 7.6 feet. Finally, a small wave pushes water in, increasing the depth by 1.6 feet. What is the final water depth relative to the reference point? Answer: ______________
  5. (-7/12 + 5/8) - (-2/3 + 3/4) = ? Answer: ______________
  6. Kaia is tracking the altitude of a hot air balloon. The balloon starts at an altitude of -135 feet (below sea level). It then ascends 287 feet. After that, it descends 419 feet. Finally, it ascends 173 feet. What is the final altitude of the balloon? Answer: ______________
  7. Sophia is monitoring the water level in a fish tank for her science project. The water level starts at -8.25 inches below the fill line. She adds water, raising the level by 15.5 inches. Then, due to evaporation, the level drops by 7.75 inches. Finally, she adds more water, raising the level by 4.5 inches. What is the final water level relative to the fill line? Answer: ______________
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Answer Key & Explanations

Rational Addition/Subtraction · Grade 7 · Worksheet 3

  1. 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 this garden? Answer: 28 Solution: A = (-3, 2) B = (5, 2) C = (5, -4) D = (-3, -4) Points A and B have the same y-coordinate (y = 2), so AB is horizontal. Length AB = difference in x-coordinates = 5 - (-3) = 5 + 3 = 8.
    Full step-by-step solution

    Let's find the perimeter step by step. --- **Step 1: Identify the vertices of the rectangle** The points are: A = (-3, 2) B = (5, 2) C = (5, -4) D = (-3, -4) --- **Step 2: Determine the length and width** Points A and B have the same y-coordinate (y = 2), so AB is horizontal. Length AB = difference in x-coordinates = 5 - (-3) = 5 + 3 = 8. Points B and C have the same x-coordinate (x = 5), so BC is vertical. Length BC = difference in y-coordinates = 2 - (-4) = 2 + 4 = 6. --- **Step 3: Verify other sides** CD: C = (5, -4), D = (-3, -4) → same y = -4, horizontal length = 5 - (-3) = 8. DA: D = (-3, -4), A = (-3, 2) → same x = -3, vertical length = 2 - (-4) = 6. So the rectangle has length = 8 and width = 6. --- **Step 4: Calculate the perimeter** Perimeter formula for a rectangle: P = 2 × (length + width) P = 2 × (8 + 6) = 2 × 14 = 28. --- **Final answer:** 28

  2. Olivia is monitoring the elevation of a hot air balloon. The balloon starts at an elevation of 150 feet above sea level. It then descends 275 feet to pick up a passenger. Later, it ascends 190 feet to catch a wind current. Finally, it descends 65 feet to get a better view. What is the final elevation of the balloon relative to sea level? Answer: 0 Solution: Start with the initial elevation: 150 feet Descend 275 feet means subtract: 150 - 275 = -125 feet Ascend 190 feet means add: -125 + 190 = 65 feet Descend 65 feet means subtract: 65 - 65 = 0 feet The final elevation is 0 feet, which is exactly at sea level.
    Full step-by-step solution

    Step 1: Start with the initial elevation: 150 feet Step 2: Descend 275 feet means subtract: 150 - 275 = -125 feet Step 3: Ascend 190 feet means add: -125 + 190 = 65 feet Step 4: Descend 65 feet means subtract: 65 - 65 = 0 feet The final elevation is 0 feet, which is exactly at sea level.

  3. (-3/5 + 7/10) - (2/3 - 5/6) = ? Answer: 4/5 Solution: Simplify (-3/5 + 7/10) Find common denominator: 10 -3/5 = -6/10 -6/10 + 7/10 = 1/10 Simplify (2/3 - 5/6) Find common denominator: 6 2/3 = 4/6 4/6 - 5/6 = -1/6 Combine the results: 1/10 - (-1/6) = 1/10 + 1/6 Find common denominator for 1/10 + 1/6 Common denominator: 30 1/10 = 3/30 1/6 = 5/30 3/30…
    Full step-by-step solution

    Step 1: Simplify (-3/5 + 7/10) Find common denominator: 10 -3/5 = -6/10 -6/10 + 7/10 = 1/10 Step 2: Simplify (2/3 - 5/6) Find common denominator: 6 2/3 = 4/6 4/6 - 5/6 = -1/6 Step 3: Combine the results: 1/10 - (-1/6) = 1/10 + 1/6 Step 4: Find common denominator for 1/10 + 1/6 Common denominator: 30 1/10 = 3/30 1/6 = 5/30 3/30 + 5/30 = 8/30 Step 5: Simplify 8/30 = 4/15 The answer is 4/15.

  4. Ava is monitoring the water depth in a tidal pool for her science project. At 6:00 AM, the water depth is -3.6 feet relative to a reference point (meaning it is below the reference). The tide comes in, and the depth increases by 5.1 feet. Later, the tide goes out, and the depth decreases by 7.6 feet. Finally, a small wave pushes water in, increasing the depth by 1.6 feet. What is the final water depth relative to the reference point? Answer: -4.5 Solution: Start with the initial depth: -3.6 feet Add the increase from the tide: -3.6 + 5.1 = 1.5 feet Subtract the decrease from the tide going out: 1.5 - 7.6 = -6.1 feet Add the increase from the wave: -6.1 + 1.6 = -4.5 feet The final water depth is -4.5 feet relative to the reference point.
    Full step-by-step solution

    Step 1: Start with the initial depth: -3.6 feet Step 2: Add the increase from the tide: -3.6 + 5.1 = 1.5 feet Step 3: Subtract the decrease from the tide going out: 1.5 - 7.6 = -6.1 feet Step 4: Add the increase from the wave: -6.1 + 1.6 = -4.5 feet The final water depth is -4.5 feet relative to the reference point.

  5. (-7/12 + 5/8) - (-2/3 + 3/4) = ? Answer: -1/8 Solution: Calculate the first parentheses: -7/12 + 5/8 Find common denominator for 12 and 8: 24 -7/12 = -14/24 5/8 = 15/24 -14/24 + 15/24 = 1/24 Calculate the second parentheses: -2/3 + 3/4 Find common denominator for 3 and 4: 12 -2/3 = -8/12 3/4 = 9/12 -8/12 + 9/12 = 1/12 Subtract the results: (1/24) -…
    Full step-by-step solution

    Step 1: Calculate the first parentheses: -7/12 + 5/8 Find common denominator for 12 and 8: 24 -7/12 = -14/24 5/8 = 15/24 -14/24 + 15/24 = 1/24 Step 2: Calculate the second parentheses: -2/3 + 3/4 Find common denominator for 3 and 4: 12 -2/3 = -8/12 3/4 = 9/12 -8/12 + 9/12 = 1/12 Step 3: Subtract the results: (1/24) - (1/12) Find common denominator for 24 and 12: 24 1/24 = 1/24 1/12 = 2/24 1/24 - 2/24 = -1/24 Step 4: The answer is -1/24.

  6. Kaia is tracking the altitude of a hot air balloon. The balloon starts at an altitude of -135 feet (below sea level). It then ascends 287 feet. After that, it descends 419 feet. Finally, it ascends 173 feet. What is the final altitude of the balloon? Answer: -94 Solution: Start at -135 feet. Ascend 287 feet: -135 + 287 = 152 feet. Descend 419 feet: 152 - 419 = -267 feet.
    Full step-by-step solution

    Step 1: Start at -135 feet. Step 2: Ascend 287 feet: -135 + 287 = 152 feet. Step 3: Descend 419 feet: 152 - 419 = -267 feet. Step 4: Ascend 173 feet: -267 + 173 = -94 feet. The final altitude is -94 feet.

  7. Sophia is monitoring the water level in a fish tank for her science project. The water level starts at -8.25 inches below the fill line. She adds water, raising the level by 15.5 inches. Then, due to evaporation, the level drops by 7.75 inches. Finally, she adds more water, raising the level by 4.5 inches. What is the final water level relative to the fill line? Answer: 4 Solution: Start with the initial water level: -8.25 inches. Add the first water addition: -8.25 + 15.5 = 7.25 inches. Subtract the evaporation drop: 7.25 - 7.75 = -0.5 inches.
    Full step-by-step solution

    Step 1: Start with the initial water level: -8.25 inches. Step 2: Add the first water addition: -8.25 + 15.5 = 7.25 inches. Step 3: Subtract the evaporation drop: 7.25 - 7.75 = -0.5 inches. Step 4: Add the second water addition: -0.5 + 4.5 = 4 inches. The final water level is 4 inches above the fill line.