Equivalent Expressions

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Equivalent Expressions · Grade 6 · Worksheet 1

1. A rectangular prism is described with dimensions: length = 12 cm, width = 8 cm, and height = 5 cm. What is the total surface area of this rectangular prism? Answer: 392 Solution: Calculate the area of the front and back faces (length × height) Area = 12 cm × 5 cm = 60 cm² Since there are 2 such faces: 2 × 60 cm² = 120 cm² Calculate the area of the left and right faces (width × height) Area = 8 cm × 5 cm = 40 cm² Since there are 2 such faces: 2 × 40 cm² = 80 cm² Calculate…
   Full step-by-step solution

   Step 1: Calculate the area of the front and back faces (length × height) Area = 12 cm × 5 cm = 60 cm² Since there are 2 such faces: 2 × 60 cm² = 120 cm² Step 2: Calculate the area of the left and right faces (width × height) Area = 8 cm × 5 cm = 40 cm² Since there are 2 such faces: 2 × 40 cm² = 80 cm² Step 3: Calculate the area of the top and bottom faces (length × width) Area = 12 cm × 8 cm = 96 cm² Since there are 2 such faces: 2 × 96 cm² = 192 cm² Step 4: Add all the areas together 120 cm² + 80 cm² + 192 cm² = 392 cm² The total surface area is 392 cm².

2. Sophia is making friendship bracelets. Each bracelet needs 5 inches of string. Sophia has 17 inches of string. Which expression below is equivalent to the total number of inches of string Sophia needs to make 5 bracelets? Answer: 25 Solution: Each bracelet needs 5 inches of string. Step 2: To find the total string for 5 bracelets, multiply: 5 × 5 = 25 inches. Step 3: So the expression 5c (or 5 × 5) represents the total.
   Full step-by-step solution

   Step 1: Each bracelet needs 5 inches of string. Step 2: To find the total string for 5 bracelets, multiply: 5 × 5 = 25 inches. Step 3: So the expression 5c (or 5 × 5) represents the total. The answer is 25.

3. Which expression is equivalent to 15(4x + 9)? Answer: 60x + 135 Solution: Step 1: Apply the distributive property: 15(4x + 9) = 15 × 4x + 15 × 9 Step 2: Multiply: 15 × 4x = 60x Step 3: Multiply: 15 × 9 = 135 Step 4: Combine: 60x + 135 The answer is 60x + 135.
   Full step-by-step solution

   Step 1: Apply the distributive property: 15(4x + 9) = 15 × 4x + 15 × 9 Step 2: Multiply: 15 × 4x = 60x Step 3: Multiply: 15 × 9 = 135 Step 4: Combine: 60x + 135 The answer is 60x + 135.

4. A rectangular prism is described with a length of 12 cm, width of 8 cm, and height of 5 cm. What is the total surface area of this prism? Answer: 392 Solution: Calculate the area of the front and back faces (length × height): 12 × 5 = 60 square cm each. Since there are 2 of these faces: 60 × 2 = 120 square cm.
   Full step-by-step solution

   Step 1: Calculate the area of the front and back faces (length × height): 12 × 5 = 60 square cm each. Since there are 2 of these faces: 60 × 2 = 120 square cm. Step 2: Calculate the area of the left and right faces (width × height): 8 × 5 = 40 square cm each. Since there are 2 of these faces: 40 × 2 = 80 square cm. Step 3: Calculate the area of the top and bottom faces (length × width): 12 × 8 = 96 square cm each. Since there are 2 of these faces: 96 × 2 = 192 square cm. Step 4: Add all the areas together: 120 + 80 + 192 = 392 square cm. The total surface area is 392 square cm.

5. Kaia is making friendship bracelets. Each bracelet needs 4 inches of string. Kaia has 18 inches of string. Which expression below is equivalent to the total number of inches of string Kaia needs to make 3 bracelets? Answer: 12 Solution: Each bracelet needs 4 inches of string. Step 2: To find the total string for 3 bracelets, multiply: 4 × 3 = 12 inches. Step 3: So the expression 4c (or 4 × 3) represents the total.
   Full step-by-step solution

   Step 1: Each bracelet needs 4 inches of string. Step 2: To find the total string for 3 bracelets, multiply: 4 × 3 = 12 inches. Step 3: So the expression 4c (or 4 × 3) represents the total. The answer is 12.

6. Noah is planning a school trip to the science museum. The museum charges $15 per student and $25 per adult. There are 36 students and 8 teachers going on the trip. The school bus costs $280 to rent for the day. What is the total cost of the field trip? Answer: $1020 Solution: Calculate the total cost for the students. 36 students × $15 per student = $540 Calculate the total cost for the adults (teachers). 8 adults × $25 per adult = $200 Add the student cost, adult cost, and bus cost together.
   Full step-by-step solution

   Step 1: Calculate the total cost for the students. 36 students × $15 per student = $540 Step 2: Calculate the total cost for the adults (teachers). 8 adults × $25 per adult = $200 Step 3: Add the student cost, adult cost, and bus cost together. $540 (students) + $200 (adults) + $280 (bus) = $1020 The total cost of the field trip is $1020.

7. Emma is planning a school carnival and needs to order prizes. She has a budget of $2,400. She spends 40% of her budget on games, 0.25 of her budget on food, and the remaining money on decorations. How much money does Emma spend on decorations? Answer: $840 Solution: Calculate the amount spent on games. 40% of $2,400 is 0.40 * 2400 = $960. Calculate the amount spent on food.
   Full step-by-step solution

   Step 1: Calculate the amount spent on games. 40% of $2,400 is 0.40 * 2400 = $960. Step 2: Calculate the amount spent on food. 0.25 of $2,400 is 0.25 * 2400 = $600. Step 3: Find the total amount spent on games and food. $960 + $600 = $1,560. Step 4: Subtract the total spent from the original budget to find the money left for decorations. $2,400 - $1,560 = $840. Emma spends $840 on decorations.