Equivalent Expressions

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Answer Key & Explanations

Equivalent Expressions · Grade 6 · Worksheet 3

1. (-15) × (4 - 9) + 24 ÷ (-6) = ? Answer: 71 Solution: Solve inside the parentheses: 4 - 9 = -5 Replace the expression: (-15) × (-5) + 24 ÷ (-6) Perform multiplication: (-15) × (-5) = 75 Perform division: 24 ÷ (-6) = -4 Add the results: 75 + (-4) = 75 - 4 = 71 The answer is 71.
   Full step-by-step solution

   Step 1: Solve inside the parentheses: 4 - 9 = -5 Step 2: Replace the expression: (-15) × (-5) + 24 ÷ (-6) Step 3: Perform multiplication: (-15) × (-5) = 75 Step 4: Perform division: 24 ÷ (-6) = -4 Step 5: Add the results: 75 + (-4) = 75 - 4 = 71 The answer is 71.

2. Moana is collecting trading cards. Moana has 6 packs of cards, and each pack contains 13 cards. Which expression is equivalent to the total number of cards Moana has? Answer: 78 Solution: To find the total number of cards, multiply the number of packs by the number of cards per pack: 6 * 13 = 78.
3. Emma is planning a school carnival and needs to order prizes. She has a budget of $2,400. She spends 45% of her budget on games, 0.3 of her budget on food, and the remaining money on decorations. How much money does Emma spend on decorations? Answer: $600 Solution: Calculate the amount spent on games. 45% of $2400 = 0.45 * 2400 = $1080 Calculate the amount spent on food. 0.3 of $2400 = 0.3 * 2400 = $720 Find the total amount spent on games and food.
   Full step-by-step solution

   Step 1: Calculate the amount spent on games. 45% of $2400 = 0.45 * 2400 = $1080 Step 2: Calculate the amount spent on food. 0.3 of $2400 = 0.3 * 2400 = $720 Step 3: Find the total amount spent on games and food. $1080 + $720 = $1800 Step 4: Subtract the total spent from the original budget to find the amount left for decorations. $2400 - $1800 = $600 Emma spends $600 on decorations.

4. Emma is planning a school carnival and needs to order supplies. 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.

5. 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.

6. (-15) × (-4) + 24 ÷ (-6) = ? Answer: 56 Solution: First, perform the multiplication: (-15) × (-4) = 60 (since multiplying two negatives gives a positive) Next, perform the division: 24 ÷ (-6) = -4 (since dividing a positive by a negative gives a negative) Now add the results: 60 + (-4) = 56 60 - 4 = 56 The answer is 56.
   Full step-by-step solution

   Step 1: First, perform the multiplication: (-15) × (-4) = 60 (since multiplying two negatives gives a positive) Step 2: Next, perform the division: 24 ÷ (-6) = -4 (since dividing a positive by a negative gives a negative) Step 3: Now add the results: 60 + (-4) = 56 Step 4: 60 - 4 = 56 The answer is 56.

7. Which expression is equivalent to 14(4x + 9)? Answer: 56x + 126 Solution: Step 1: Apply the distributive property: 14(4x + 9) = 14 × 4x + 14 × 9 Step 2: Multiply: 14 × 4x = 56x Step 3: Multiply: 14 × 9 = 126 Step 4: Combine: 56x + 126 The answer is 56x + 126.
   Full step-by-step solution

   Step 1: Apply the distributive property: 14(4x + 9) = 14 × 4x + 14 × 9 Step 2: Multiply: 14 × 4x = 56x Step 3: Multiply: 14 × 9 = 126 Step 4: Combine: 56x + 126 The answer is 56x + 126.

8. (-3)² + 4 × (15 ÷ 3) = ? Answer: 29 Solution: Handle parentheses first. Inside parentheses: 15 ÷ 3 = 5 (-3)² + 4 × (5) Evaluate exponents. (-3)² means (-3) × (-3) = 9 9 + 4 × 5 Perform multiplication.
   Full step-by-step solution

   Let's solve step-by-step using the order of operations (PEMDAS/BODMAS). Step 1: Handle parentheses first. Inside parentheses: 15 ÷ 3 = 5 So the expression becomes: (-3)² + 4 × (5) Step 2: Evaluate exponents. (-3)² means (-3) × (-3) = 9 So the expression becomes: 9 + 4 × 5 Step 3: Perform multiplication. 4 × 5 = 20 So the expression becomes: 9 + 20 Step 4: Perform addition. 9 + 20 = 29 Final answer: 29

9. Noah is organizing a bake sale. Each tray holds 22 cupcakes. Noah has 5 full trays. Which expression shows the total number of cupcakes Noah has? Answer: 110 Solution: The total number of cupcakes is the number of trays times the number per tray. So 22 * 5 = 110.