Expression Properties

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Answer Key & Explanations

Expression Properties · Grade 6 · Worksheet 2

1. Emma is organizing a school craft fair. She has 13 identical tables that she needs to arrange in rows. She decides to set up 7 tables in the first row and the rest in the second row. To find the total number of chairs needed, she multiplies the number of tables by 9 chairs per table. Write an equivalent expression using the distributive property to represent the total number of chairs. Answer: 9(7) + 9(6) Solution: Emma has 13 tables total. She puts 7 tables in the first row, so the second row has 13 - 7 = 6 tables. Each table needs 9 chairs.
   Full step-by-step solution

   Step 1: Emma has 13 tables total. She puts 7 tables in the first row, so the second row has 13 - 7 = 6 tables. Step 2: Each table needs 9 chairs. The total number of chairs is 9 * 13. Step 3: Using the distributive property, 9 * 13 can be written as 9 * (7 + 6). Step 4: Distribute: 9 * (7 + 6) = 9(7) + 9(6). Step 5: So the equivalent expression is 9(7) + 9(6). The answer is 9(7) + 9(6).

2. Liam is designing a rectangular garden for his school's community project. The garden's length is 15.2 meters and its width is 8.6 meters. He needs to install a decorative fence around the entire perimeter and cover the garden area with special soil. How many meters of fencing does Liam need to purchase? Answer: 47.6 Solution: Identify the formula for perimeter of a rectangle: P = 2 × (length + width) Substitute the given values: P = 2 × (15.2 + 8.6) Add the length and width: 15.2 + 8.6 = 23.8 Multiply by 2: 2 × 23.8 = 47.6 Liam needs 47.6 meters of fencing.
   Full step-by-step solution

   Step 1: Identify the formula for perimeter of a rectangle: P = 2 × (length + width) Step 2: Substitute the given values: P = 2 × (15.2 + 8.6) Step 3: Add the length and width: 15.2 + 8.6 = 23.8 Step 4: Multiply by 2: 2 × 23.8 = 47.6 Step 5: Liam needs 47.6 meters of fencing.

3. Use the distributive property to rewrite: 6(11x + 16) = ? Answer: 66x + 96 Solution: Here, a = 6, b = 11x, c = 16. Multiply 6 by 11x: 6 × 11x = 66x. Multiply 6 by 16: 6 × 16 = 96.
   Full step-by-step solution

   Step 1: Apply the distributive property: a(b + c) = ab + ac. Here, a = 6, b = 11x, c = 16. Step 2: Multiply 6 by 11x: 6 × 11x = 66x. Step 3: Multiply 6 by 16: 6 × 16 = 96. Step 4: Combine the results: 66x + 96. The answer is 66x + 96.

4. Emma is planning a school fundraiser and needs to mix two types of juice to create a special blend. She has 4 liters of mango juice that costs $2.50 per liter and 6 liters of pineapple juice that costs $1.75 per liter. What is the cost per liter of the mixed juice blend? Answer: 2.05 Solution: Calculate the total cost of mango juice: 4 liters × $2.50/liter = $10.00 Calculate the total cost of pineapple juice: 6 liters × $1.75/liter = $10.50 Find the total cost of all juice: $10.00 + $10.50 = $20.50 Find the total amount of juice: 4 liters + 6 liters = 10 liters Calculate the cost per…
   Full step-by-step solution

   Step 1: Calculate the total cost of mango juice: 4 liters × $2.50/liter = $10.00 Step 2: Calculate the total cost of pineapple juice: 6 liters × $1.75/liter = $10.50 Step 3: Find the total cost of all juice: $10.00 + $10.50 = $20.50 Step 4: Find the total amount of juice: 4 liters + 6 liters = 10 liters Step 5: Calculate the cost per liter of the mixture: $20.50 ÷ 10 liters = $2.05 per liter The answer is 2.05.

5. A school is planning a field trip and needs to calculate transportation costs. There are 180 students going on the trip, and each school bus can carry 36 students. The bus company charges $85 per bus for the trip. Additionally, the school must pay a $50 administration fee for the entire trip. How much will the school pay in total for transportation? Answer: 475 Solution: Calculate how many buses are needed by dividing total students by bus capacity: 180 ÷ 36 = 5 buses Calculate the bus cost by multiplying number of buses by cost per bus: 5 × $85 = $425 Add the administration fee to the bus cost: $425 + $50 = $475 The total transportation cost is $475
   Full step-by-step solution

   Step 1: Calculate how many buses are needed by dividing total students by bus capacity: 180 ÷ 36 = 5 buses Step 2: Calculate the bus cost by multiplying number of buses by cost per bus: 5 × $85 = $425 Step 3: Add the administration fee to the bus cost: $425 + $50 = $475 Step 4: The total transportation cost is $475

6. Use the distributive property to rewrite: 8(2x + 5y - 3) = ? Answer: 16x + 40y - 24 Solution: Multiply 8 by 2x: 8 × 2x = 16x. Multiply 8 by 5y: 8 × 5y = 40y. Multiply 8 by -3: 8 × (-3) = -24.
   Full step-by-step solution

   Step 1: Apply the distributive property: a(b + c - d) = ab + ac - ad. Step 2: Multiply 8 by 2x: 8 × 2x = 16x. Step 3: Multiply 8 by 5y: 8 × 5y = 40y. Step 4: Multiply 8 by -3: 8 × (-3) = -24. Step 5: Combine the terms: 16x + 40y - 24. The answer is 16x + 40y - 24.