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Expression Properties

Grade 6 · Algebra · Worksheet 3

  1. Use the distributive property to rewrite: 15(2x + 5y) = ? Answer: ______________
  2. (-3)² + 4 × (-2) - 18 ÷ 3 = ? Answer: ______________
  3. Use the distributive property to rewrite: 9(2x + 7) = ? Answer: ______________
  4. Use the distributive property to rewrite: 6(11x + 16) = ? Answer: ______________
  5. Use the distributive property to rewrite: 6(2x + 5y - 3z) = ? Answer: ______________
  6. A rectangular garden has a length of 12.5 meters and a width of 8.4 meters. The owner wants to build a fence around the entire garden. Write an expression for the perimeter of the garden and then calculate the total length of fencing needed in meters.
    Answer: ______________
  7. Maria is planning a school fundraiser and needs to calculate the profit from selling tickets. She sells 120 tickets at $8.50 each. The printing costs for the tickets were $45, and she spent $125 on decorations. What was Maria's total profit from the ticket sales? Answer: ______________
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Answer Key & Explanations

Expression Properties · Grade 6 · Worksheet 3

  1. Use the distributive property to rewrite: 15(2x + 5y) = ? Answer: 30x + 75y Solution: Step 1: Apply the distributive property: 15(2x + 5y) = 15 × 2x + 15 × 5y Step 2: Multiply: 15 × 2x = 30x Step 3: Multiply: 15 × 5y = 75y Step 4: Combine: 30x + 75y The answer is 30x + 75y.
    Full step-by-step solution

    Step 1: Apply the distributive property: 15(2x + 5y) = 15 × 2x + 15 × 5y Step 2: Multiply: 15 × 2x = 30x Step 3: Multiply: 15 × 5y = 75y Step 4: Combine: 30x + 75y The answer is 30x + 75y.

  2. (-3)² + 4 × (-2) - 18 ÷ 3 = ? Answer: -5 Solution: Calculate the exponent: (-3)² = 9 Calculate the multiplication: 4 × (-2) = -8 Calculate the division: 18 ÷ 3 = 6 Substitute back into the expression: 9 + (-8) - 6 Add 9 and -8: 9 + (-8) = 1 Subtract 6: 1 - 6 = -5 The answer is -5.
    Full step-by-step solution

    Step 1: Calculate the exponent: (-3)² = 9 Step 2: Calculate the multiplication: 4 × (-2) = -8 Step 3: Calculate the division: 18 ÷ 3 = 6 Step 4: Substitute back into the expression: 9 + (-8) - 6 Step 5: Add 9 and -8: 9 + (-8) = 1 Step 6: Subtract 6: 1 - 6 = -5 The answer is -5.

  3. Use the distributive property to rewrite: 9(2x + 7) = ? Answer: 18x + 63 Solution: Identify the expression: 9(2x + 7) Apply the distributive property: a(b + c) = ab + ac Multiply 9 by 2x: 9 × 2x = 18x Multiply 9 by 7: 9 × 7 = 63 Combine the results: 18x + 63 The answer is 18x + 63.
    Full step-by-step solution

    Step 1: Identify the expression: 9(2x + 7) Step 2: Apply the distributive property: a(b + c) = ab + ac Step 3: Multiply 9 by 2x: 9 × 2x = 18x Step 4: Multiply 9 by 7: 9 × 7 = 63 Step 5: Combine the results: 18x + 63 The answer is 18x + 63.

  4. 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.

  5. Use the distributive property to rewrite: 6(2x + 5y - 3z) = ? Answer: 12x + 30y - 18z Solution: 6 × 2x = 12x 6 × 5y = 30y 6 × (-3z) = -18z Combine the results: 12x + 30y - 18z The answer is 12x + 30y - 18z.
    Full step-by-step solution

    Step 1: Apply the distributive property: multiply 6 by each term inside the parentheses. Step 2: 6 × 2x = 12x Step 3: 6 × 5y = 30y Step 4: 6 × (-3z) = -18z Step 5: Combine the results: 12x + 30y - 18z The answer is 12x + 30y - 18z.

  6. A rectangular garden has a length of 12.5 meters and a width of 8.4 meters. The owner wants to build a fence around the entire garden. Write an expression for the perimeter of the garden and then calculate the total length of fencing needed in meters. Answer: 41.8 Solution: We have a rectangular garden. The perimeter is the total distance around the garden, which is the length of fencing needed. Perimeter = 2 × (length + width) Length = 12.5 m Width = 8.4 m Expression: Perimeter = 2 × (12.5 + 8.4) 12.5 + 8.4 = 20.9 Multiply by 2 2 × 20.9 = 41.8 The total length of…
    Full step-by-step solution

    Step 1: Understand the problem We have a rectangular garden. The perimeter is the total distance around the garden, which is the length of fencing needed. Step 2: Recall the perimeter formula for a rectangle Perimeter = 2 × (length + width) Step 3: Write the expression Length = 12.5 m Width = 8.4 m Expression: Perimeter = 2 × (12.5 + 8.4) Step 4: Calculate inside the parentheses 12.5 + 8.4 = 20.9 Step 5: Multiply by 2 2 × 20.9 = 41.8 Step 6: State the final answer The total length of fencing needed is 41.8 meters.

  7. Maria is planning a school fundraiser and needs to calculate the profit from selling tickets. She sells 120 tickets at $8.50 each. The printing costs for the tickets were $45, and she spent $125 on decorations. What was Maria's total profit from the ticket sales? Answer: 850 Solution: 120 tickets × $8.50 per ticket = $1020 Printing costs: $45 Decoration costs: $125 Total expenses = $45 + $125 = $170 Profit = Total revenue - Total expenses Profit = $1020 - $170 = $850 Maria's total profit from the ticket sales was $850.
    Full step-by-step solution

    Step 1: Calculate total revenue from ticket sales 120 tickets × $8.50 per ticket = $1020 Step 2: Calculate total expenses Printing costs: $45 Decoration costs: $125 Total expenses = $45 + $125 = $170 Step 3: Calculate profit Profit = Total revenue - Total expenses Profit = $1020 - $170 = $850 Maria's total profit from the ticket sales was $850.