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Rational Addition/Subtraction

Grade 7 · Ratios · Worksheet 2

  1. Tane is tracking the depth of a river during a storm. The river starts at a depth of 3.75 meters above normal. After heavy rain, the depth rises by 7.5 meters. Then, during a flash flood, it rises again by 4.25 meters. Finally, the water recedes, dropping by 15.5 meters. What is the final depth of the river relative to normal? Answer: ______________
  2. 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: ______________
  3. Olivia is checking the balance of her savings account. On Monday, she had $157.75. On Tuesday, she withdrew $93.50 to pay for a new bicycle. On Wednesday, she deposited her birthday money of $85.25. On Thursday, she transferred $111.00 to her checking account. What is Olivia's final savings account balance after all these transactions? Answer: ______________
  4. A scientist is tracking the temperature changes in a chemical reaction. The reaction starts at 22.5°C. During the first stage, the temperature increases by 7.25°C. In the second stage, it decreases by 13.8°C. Finally, in the third stage, it increases by 5.75°C. What is the final temperature of the reaction? Answer: ______________
  5. 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: ______________
  6. (-7/12 + 5/8) - (-3/4 + 11/24) = ? Answer: ______________
  7. (-3/4) + (7/8) - (-1/2) = ? Answer: ______________
  8. -3/4 + 2/3 - 1/6 = ? Answer: ______________
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Answer Key & Explanations

Rational Addition/Subtraction · Grade 7 · Worksheet 2

  1. Tane is tracking the depth of a river during a storm. The river starts at a depth of 3.75 meters above normal. After heavy rain, the depth rises by 7.5 meters. Then, during a flash flood, it rises again by 4.25 meters. Finally, the water recedes, dropping by 15.5 meters. What is the final depth of the river relative to normal? Answer: 0 Solution: Start with the initial depth: 3.75 meters above normal. Add the first rise: 3.75 + 7.5 = 11.25 meters. Add the second rise: 11.25 + 4.25 = 15.5 meters.
    Full step-by-step solution

    Step 1: Start with the initial depth: 3.75 meters above normal. Step 2: Add the first rise: 3.75 + 7.5 = 11.25 meters. Step 3: Add the second rise: 11.25 + 4.25 = 15.5 meters. Step 4: Subtract the drop: 15.5 - 15.5 = 0 meters. The final depth is 0 meters relative to normal, meaning the river is exactly at the normal level.

  2. 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.

  3. Olivia is checking the balance of her savings account. On Monday, she had $157.75. On Tuesday, she withdrew $93.50 to pay for a new bicycle. On Wednesday, she deposited her birthday money of $85.25. On Thursday, she transferred $111.00 to her checking account. What is Olivia's final savings account balance after all these transactions? Answer: $38.50 Solution: Start with Monday's balance: $157.75 Subtract Tuesday's withdrawal: $157.75 - $93.50 = $64.25 Add Wednesday's deposit: $64.25 + $85.25 = $149.50 Subtract Thursday's transfer: $149.50 - $111.00 = $38.50 Olivia's final savings account balance is $38.50.
    Full step-by-step solution

    Step 1: Start with Monday's balance: $157.75 Step 2: Subtract Tuesday's withdrawal: $157.75 - $93.50 = $64.25 Step 3: Add Wednesday's deposit: $64.25 + $85.25 = $149.50 Step 4: Subtract Thursday's transfer: $149.50 - $111.00 = $38.50 Olivia's final savings account balance is $38.50.

  4. A scientist is tracking the temperature changes in a chemical reaction. The reaction starts at 22.5°C. During the first stage, the temperature increases by 7.25°C. In the second stage, it decreases by 13.8°C. Finally, in the third stage, it increases by 5.75°C. What is the final temperature of the reaction? Answer: 21.7 Solution: Start with the initial temperature: 22.5°C Add the first increase: 22.5 + 7.25 = 29.75°C Subtract the decrease: 29.75 - 13.8 = 15.95°C Add the final increase: 15.95 + 5.75 = 21.7°C The answer is 21.7.
    Full step-by-step solution

    Step 1: Start with the initial temperature: 22.5°C Step 2: Add the first increase: 22.5 + 7.25 = 29.75°C Step 3: Subtract the decrease: 29.75 - 13.8 = 15.95°C Step 4: Add the final increase: 15.95 + 5.75 = 21.7°C The answer is 21.7.

  5. 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

  6. (-7/12 + 5/8) - (-3/4 + 11/24) = ? Answer: 1/2 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: -3/4 + 11/24 Find common denominator for 4 and 24: 24 -3/4 = -18/24 11/24 = 11/24 -18/24 + 11/24 = -7/24 Subtract the results:…
    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: -3/4 + 11/24 Find common denominator for 4 and 24: 24 -3/4 = -18/24 11/24 = 11/24 -18/24 + 11/24 = -7/24 Step 3: Subtract the results: (1/24) - (-7/24) Subtracting a negative is adding: 1/24 + 7/24 = 8/24 Step 4: Simplify the fraction: 8/24 = 1/3 The answer is 1/3.

  7. (-3/4) + (7/8) - (-1/2) = ? Answer: 5/8 Solution: Write the expression: (-3/4) + (7/8) - (-1/2) Subtracting a negative is the same as adding: (-3/4) + (7/8) + (1/2) Find a common denominator for 4, 8, and 2. The least common denominator is 8.
    Full step-by-step solution

    Step 1: Write the expression: (-3/4) + (7/8) - (-1/2) Step 2: Subtracting a negative is the same as adding: (-3/4) + (7/8) + (1/2) Step 3: Find a common denominator for 4, 8, and 2. The least common denominator is 8. Step 4: Convert each fraction: -3/4 = -6/8, 7/8 = 7/8, 1/2 = 4/8 Step 5: Add the fractions: (-6/8) + (7/8) + (4/8) = (-6 + 7 + 4)/8 = 5/8 Step 6: The answer is 5/8.

  8. -3/4 + 2/3 - 1/6 = ? Answer: -1/4 Solution: We have: -3/4 + 2/3 - 1/6 Find a common denominator for all fractions. The denominators are 4, 3, and 6. The least common multiple of 4, 3, and 6 is 12.
    Full step-by-step solution

    Let's solve step-by-step: We have: -3/4 + 2/3 - 1/6 Step 1: Find a common denominator for all fractions. The denominators are 4, 3, and 6. The least common multiple of 4, 3, and 6 is 12. Step 2: Convert each fraction to have denominator 12. -3/4 = ( -3 × 3 ) / (4 × 3) = -9/12 2/3 = ( 2 × 4 ) / (3 × 4) = 8/12 -1/6 = ( -1 × 2 ) / (6 × 2) = -2/12 Step 3: Rewrite the expression with the common denominator. -9/12 + 8/12 - 2/12 Step 4: Combine the numerators over the common denominator. Numerator: -9 + 8 - 2 First: -9 + 8 = -1 Then: -1 - 2 = -3 So we have: -3/12 Step 5: Simplify the fraction. -3/12 = -1/4 (dividing numerator and denominator by 3) Final answer: -1/4