Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Equivalent Expressions

Grade 6 · Algebra · Worksheet 3

  1. Emma draws an area model to show the expression 7(3x + 15). She draws a large rectangle with a width of 7. The length is split into two parts: one part labeled 3x and the other part labeled 15. Which of the following expressions is equivalent to 7(3x + 15)? (A) 21x + 105 (B) 10x + 22 (C) 21x + 15 (D) 3x + 105 Answer: ______________
  2. (-3)² + 4 × (24 ÷ 6) = ? Answer: ______________
  3. Liam is planning a school fundraiser and needs to buy supplies. He has a budget of $1200. He spends 35% of his budget on decorations and 0.3 of his budget on food. What fraction of his total budget does Liam have left after these purchases? Answer: ______________
  4. Liam uses algebra tiles to model the expression 5(4y + 20). He draws a rectangle with a width of 5. The length is split into two parts: one part labeled 4y and the other part labeled 20. Which of the following expressions is equivalent to 5(4y + 20)? (A) 20y + 100 (B) 9y + 25 (C) 20y + 20 (D) 4y + 100 Answer: ______________
  5. Liam is designing a rectangular garden for his school project. The garden's length is 12.5 meters and its width is 8.4 meters. He needs to calculate the area to determine how much soil to buy. What is the area of Liam's garden in square meters?
    Answer: ______________
  6. Which expression is equivalent to 6(2x + 11) - 2(3x - 1)? Answer: ______________
  7. (-3)² + 4 × (18 ÷ 6) = ? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Equivalent Expressions · Grade 6 · Worksheet 3

  1. Emma draws an area model to show the expression 7(3x + 15). She draws a large rectangle with a width of 7. The length is split into two parts: one part labeled 3x and the other part labeled 15. Which of the following expressions is equivalent to 7(3x + 15)? (A) 21x + 105 (B) 10x + 22 (C) 21x + 15 (D) 3x + 105 Answer: 21x + 105 Solution: The expression 7(3x + 15) means the width is 7 and the total length is (3x + 15). Using the distributive property, multiply 7 by each term inside the parentheses. First, multiply 7 by 3x: 7 × 3x = 21x.
    Full step-by-step solution

    Step 1: The expression 7(3x + 15) means the width is 7 and the total length is (3x + 15). Step 2: Using the distributive property, multiply 7 by each term inside the parentheses. Step 3: First, multiply 7 by 3x: 7 × 3x = 21x. Step 4: Next, multiply 7 by 15: 7 × 15 = 105. Step 5: Add the two results: 21x + 105. Step 6: Check the options. Option (A) is 21x + 105, which matches. The answer is 21x + 105.

  2. (-3)² + 4 × (24 ÷ 6) = ? Answer: 25 Solution: Calculate the exponent first: (-3)² = 9 Calculate the division inside parentheses: 24 ÷ 6 = 4 Perform the multiplication: 4 × 4 = 16 Add the results: 9 + 16 = 25 The answer is 25.
    Full step-by-step solution

    Step 1: Calculate the exponent first: (-3)² = 9 Step 2: Calculate the division inside parentheses: 24 ÷ 6 = 4 Step 3: Perform the multiplication: 4 × 4 = 16 Step 4: Add the results: 9 + 16 = 25 The answer is 25.

  3. Liam is planning a school fundraiser and needs to buy supplies. He has a budget of $1200. He spends 35% of his budget on decorations and 0.3 of his budget on food. What fraction of his total budget does Liam have left after these purchases? Answer: 7/20 Solution: Liam's total budget = $1200. - Decorations: 35% of the budget Amount spent on decorations = 35/100 × 1200 = 0.35 × 1200 = $420. - Food: 0.3 of the budget 0.3 means 30% (since 0.3 = 30/100).
    Full step-by-step solution

    Let's go step by step. --- **Step 1: Understand the budget and the amounts spent** Liam's total budget = $1200. - Decorations: 35% of the budget Amount spent on decorations = 35/100 × 1200 = 0.35 × 1200 = $420. - Food: 0.3 of the budget 0.3 means 30% (since 0.3 = 30/100). Amount spent on food = 0.3 × 1200 = $360. --- **Step 2: Find total spent and amount left** Total spent = 420 + 360 = $780. Amount left = 1200 − 780 = $420. --- **Step 3: Fraction of budget left** Fraction left = (Amount left) / (Total budget) = 420 / 1200. Simplify: Divide numerator and denominator by 60: 420 ÷ 60 = 7, 1200 ÷ 60 = 20. So, 420/1200 = 7/20. --- **Step 4: Conclusion** Liam has 7/20 of his budget left after buying decorations and food. --- **Final answer:** 7/20

  4. Liam uses algebra tiles to model the expression 5(4y + 20). He draws a rectangle with a width of 5. The length is split into two parts: one part labeled 4y and the other part labeled 20. Which of the following expressions is equivalent to 5(4y + 20)? (A) 20y + 100 (B) 9y + 25 (C) 20y + 20 (D) 4y + 100 Answer: 20y + 100 Solution: The expression 5(4y + 20) means the width is 5 and the total length is (4y + 20). Using the distributive property, multiply the width by each term inside the parentheses. First, multiply 5 by 4y: 5 × 4y = 20y.
    Full step-by-step solution

    Step 1: The expression 5(4y + 20) means the width is 5 and the total length is (4y + 20). Step 2: Using the distributive property, multiply the width by each term inside the parentheses. Step 3: First, multiply 5 by 4y: 5 × 4y = 20y. Step 4: Next, multiply 5 by 20: 5 × 20 = 100. Step 5: Add the two results: 20y + 100. Step 6: Check the options. Option (A) is 20y + 100, which matches. The answer is 20y + 100.

  5. Liam is designing a rectangular garden for his school project. The garden's length is 12.5 meters and its width is 8.4 meters. He needs to calculate the area to determine how much soil to buy. What is the area of Liam's garden in square meters? Answer: 105 Solution: To find the area of a rectangle, we multiply its length by its width. Write down the given dimensions. Length = 12.5 meters Width = 8.4 meters Write the multiplication expression for the area.
    Full step-by-step solution

    To find the area of a rectangle, we multiply its length by its width. Step 1: Write down the given dimensions. Length = 12.5 meters Width = 8.4 meters Step 2: Write the multiplication expression for the area. Area = Length × Width Area = 12.5 × 8.4 Step 3: To make the multiplication easier, we can think of the decimals as fractions. 12.5 is the same as 125/10 8.4 is the same as 84/10 Step 4: Multiply these two fractions. Area = (125/10) × (84/10) Step 5: Multiply the numerators together and the denominators together. Numerator: 125 × 84 Denominator: 10 × 10 = 100 So, Area = (125 × 84) / 100 Step 6: Calculate 125 × 84. First, multiply 125 by 80: 125 × 80 = 10,000 Next, multiply 125 by 4: 125 × 4 = 500 Now, add the two results: 10,000 + 500 = 10,500 So, 125 × 84 = 10,500 Step 7: Now we have: Area = 10,500 / 100 Step 8: Dividing by 100 is the same as moving the decimal point two places to the left. 10,500 ÷ 100 = 105.0 Therefore, the area of Liam's garden is 105 square meters.

  6. Which expression is equivalent to 6(2x + 11) - 2(3x - 1)? Answer: 6x + 68 Solution: Combine the results: (12x + 66) + (-6x + 2). Combine like terms: 12x - 6x = 6x, and 66 + 2 = 68. The equivalent expression is 6x + 68.
    Full step-by-step solution

    Step 1: Apply the distributive property to the first term: 6(2x + 11) = 12x + 66. Step 2: Apply the distributive property to the second term: -2(3x - 1) = -6x + 2. Step 3: Combine the results: (12x + 66) + (-6x + 2). Step 4: Combine like terms: 12x - 6x = 6x, and 66 + 2 = 68. Step 5: The equivalent expression is 6x + 68. The answer is 6x + 68.

  7. (-3)² + 4 × (18 ÷ 6) = ? Answer: 21 Solution: Calculate the exponent first: (-3)² = 9 Calculate the division inside parentheses: 18 ÷ 6 = 3 Perform the multiplication: 4 × 3 = 12 Add the results: 9 + 12 = 21 The answer is 21.
    Full step-by-step solution

    Step 1: Calculate the exponent first: (-3)² = 9 Step 2: Calculate the division inside parentheses: 18 ÷ 6 = 3 Step 3: Perform the multiplication: 4 × 3 = 12 Step 4: Add the results: 9 + 12 = 21 The answer is 21.