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Rational Multiplication/Division

Grade 7 · Ratios · Worksheet 1

  1. Liam is designing a rectangular garden for his school project. The garden's length is 3/4 of a kilometer and its width is 2/5 of a kilometer. He needs to calculate the total area to determine how much fertilizer to buy. What is the area of Liam's garden in square kilometers? Answer: ______________
  2. A rectangular prism is drawn on a coordinate plane with vertices at (0,0,0), (12,0,0), (12,8,0), (0,8,0), (0,0,5), (12,0,5), (12,8,5), and (0,8,5). A smaller rectangular prism is removed from the corner, with vertices at (0,0,0), (3,0,0), (3,2,0), (0,2,0), (0,0,2), (3,0,2), (3,2,2), and (0,2,2). What is the volume of the remaining solid? Answer: ______________
  3. Emma is planning a school fundraiser and needs to calculate the total amount of juice required. She expects 240 students to attend, and each student will be served 3/4 of a cup of juice. The juice comes in large containers that each hold 5 1/2 gallons. If there are 16 cups in a gallon, how many full containers of juice should Emma order? Answer: ______________
  4. A rectangular sign for a store is hung on a wall. Its vertices on a coordinate grid are at (0, 0), (0, 40), (60, 40), and (60, 0). A triangular section of the sign is painted with a special logo, with vertices at (0, 0), (0, 40), and (60, 0). The unpainted area of the sign (the part without the logo) is then cut into 8 equal rectangular pieces. What is the area of each rectangular piece? Answer: ______________
  5. A construction company is building a new community center with a rectangular floor plan. The length of the building is 3/4 of a kilometer and the width is 2/5 of a kilometer. The project manager needs to calculate the total area to determine how many solar panels can be installed on the roof. If each solar panel requires 1/10 of a square kilometer of space, how many complete solar panels can be installed on the roof? Answer: ______________
  6. Aroha is a conservation ranger in New Zealand. She is tracking the elevation changes of a hiking trail in the mountains. The trail has a total vertical descent of 3,675 meters over 15 equal sections. If the elevation change is negative (descending), what is the elevation change per section? Express your answer as a negative integer. Answer: ______________
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Answer Key & Explanations

Rational Multiplication/Division · Grade 7 · Worksheet 1

  1. Liam is designing a rectangular garden for his school project. The garden's length is 3/4 of a kilometer and its width is 2/5 of a kilometer. He needs to calculate the total area to determine how much fertilizer to buy. What is the area of Liam's garden in square kilometers? Answer: 3/10 Solution: To find the area of a rectangle, we multiply the length by the width. Write down the given dimensions. Length = 3/4 km Width = 2/5 km Write the formula for area.
    Full step-by-step solution

    To find the area of a rectangle, we multiply the length by the width. Step 1: Write down the given dimensions. Length = 3/4 km Width = 2/5 km Step 2: Write the formula for area. Area = Length × Width Step 3: Substitute the given values into the formula. Area = (3/4) × (2/5) Step 4: Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 3 × 2 = 6 Denominator: 4 × 5 = 20 So, Area = 6/20 Step 5: Simplify the fraction. Find the greatest common factor (GCF) of 6 and 20. The GCF is 2. Divide both the numerator and the denominator by 2. 6 ÷ 2 = 3 20 ÷ 2 = 10 So, 6/20 simplifies to 3/10. Step 6: State the final answer. The area of Liam's garden is 3/10 square kilometers.

  2. A rectangular prism is drawn on a coordinate plane with vertices at (0,0,0), (12,0,0), (12,8,0), (0,8,0), (0,0,5), (12,0,5), (12,8,5), and (0,8,5). A smaller rectangular prism is removed from the corner, with vertices at (0,0,0), (3,0,0), (3,2,0), (0,2,0), (0,0,2), (3,0,2), (3,2,2), and (0,2,2). What is the volume of the remaining solid? Answer: 468 Solution: Calculate the volume of the large rectangular prism Length = 12, Width = 8, Height = 5 Volume = 12 × 8 × 5 = 480 Calculate the volume of the smaller rectangular prism that was removed Length = 3, Width = 2, Height = 2 Volume = 3 × 2 × 2 = 12 Subtract the smaller volume from the larger volume 480…
    Full step-by-step solution

    Step 1: Calculate the volume of the large rectangular prism Length = 12, Width = 8, Height = 5 Volume = 12 × 8 × 5 = 480 Step 2: Calculate the volume of the smaller rectangular prism that was removed Length = 3, Width = 2, Height = 2 Volume = 3 × 2 × 2 = 12 Step 3: Subtract the smaller volume from the larger volume 480 - 12 = 468 The answer is 468.

  3. Emma is planning a school fundraiser and needs to calculate the total amount of juice required. She expects 240 students to attend, and each student will be served 3/4 of a cup of juice. The juice comes in large containers that each hold 5 1/2 gallons. If there are 16 cups in a gallon, how many full containers of juice should Emma order? Answer: 3 Solution: 240 students × 3/4 cup per student = 240 × 3/4 = 720/4 = 180 cups 180 cups ÷ 16 cups per gallon = 180/16 = 45/4 = 11.25 gallons 11.25 gallons ÷ 5.5 gallons per container = 11.25 ÷ 5.5 = 1125/550 = 225/110 = 45/22 ≈ 2.045 Since we need full containers, we round up to 3 containers.
    Full step-by-step solution

    Step 1: Calculate total cups needed 240 students × 3/4 cup per student = 240 × 3/4 = 720/4 = 180 cups Step 2: Convert cups to gallons 180 cups ÷ 16 cups per gallon = 180/16 = 45/4 = 11.25 gallons Step 3: Calculate number of containers needed 11.25 gallons ÷ 5.5 gallons per container = 11.25 ÷ 5.5 = 1125/550 = 225/110 = 45/22 ≈ 2.045 Step 4: Round up to full containers Since we need full containers, we round up to 3 containers. The answer is 3 full containers.

  4. A rectangular sign for a store is hung on a wall. Its vertices on a coordinate grid are at (0, 0), (0, 40), (60, 40), and (60, 0). A triangular section of the sign is painted with a special logo, with vertices at (0, 0), (0, 40), and (60, 0). The unpainted area of the sign (the part without the logo) is then cut into 8 equal rectangular pieces. What is the area of each rectangular piece? Answer: 150 Solution: Find the area of the entire rectangular sign. Length = 60, Width = 40. Area = 60 × 40 = 2400 square units.
    Full step-by-step solution

    Step 1: Find the area of the entire rectangular sign. Length = 60, Width = 40. Area = 60 × 40 = 2400 square units. Step 2: Find the area of the triangular painted logo. The triangle has base = 60 (along the bottom edge from (0,0) to (60,0)) and height = 40 (vertical from (0,0) to (0,40)). Area of triangle = (1/2) × base × height = (1/2) × 60 × 40 = (1/2) × 2400 = 1200 square units. Step 3: Find the unpainted area. Unpainted area = Total area - Painted area = 2400 - 1200 = 1200 square units. Step 4: Divide the unpainted area into 8 equal rectangular pieces. Area of each piece = 1200 ÷ 8 = 150 square units. The answer is 150.

  5. A construction company is building a new community center with a rectangular floor plan. The length of the building is 3/4 of a kilometer and the width is 2/5 of a kilometer. The project manager needs to calculate the total area to determine how many solar panels can be installed on the roof. If each solar panel requires 1/10 of a square kilometer of space, how many complete solar panels can be installed on the roof? Answer: 3 Solution: Area = length × width = (3/4) × (2/5) = 6/20 = 3/10 square kilometers Each panel requires 1/10 square kilometer Number of panels = Total area ÷ Area per panel = (3/10) ÷ (1/10) = (3/10) × (10/1) = 30/10 = 3 Since the question asks for complete panels, and we got exactly 3, the answer is 3…
    Full step-by-step solution

    Step 1: Calculate the area of the rectangular building Area = length × width = (3/4) × (2/5) = 6/20 = 3/10 square kilometers Step 2: Determine how many solar panels fit Each panel requires 1/10 square kilometer Number of panels = Total area ÷ Area per panel = (3/10) ÷ (1/10) = (3/10) × (10/1) = 30/10 = 3 Step 3: Since the question asks for complete panels, and we got exactly 3, the answer is 3 complete solar panels.

  6. Aroha is a conservation ranger in New Zealand. She is tracking the elevation changes of a hiking trail in the mountains. The trail has a total vertical descent of 3,675 meters over 15 equal sections. If the elevation change is negative (descending), what is the elevation change per section? Express your answer as a negative integer. Answer: -245 Solution: Identify the total vertical change and number of sections. Total descent = -3,675 meters (negative because descending) Number of sections = 15 To find the change per section, divide the total descent by the number of sections.
    Full step-by-step solution

    Step 1: Identify the total vertical change and number of sections. Total descent = -3,675 meters (negative because descending) Number of sections = 15 Step 2: To find the change per section, divide the total descent by the number of sections. -3,675 ÷ 15 = -245 Step 3: Check: 15 sections × (-245 meters per section) = -3,675 meters ✓ The answer is -245.