- What is the value of the expression 12 + 3 × 2 - 10 ÷ 5?
Answer: 16
Following the order of operations, first perform multiplication and division from left to right. 3 × 2 = 6 and 10 ÷ 5 = 2. The expression becomes 12 + 6 - 2. Now, perform addition and subtraction from left to right. 12 + 6 = 18. Then, 18 - 2 = 16.
- Which expression has the same value as 50 - (10 + 4 × 5)?
Answer: 10 + 40 ÷ (8 - 4)
First, find the value of the given expression: 50 - (10 + 4 × 5) = 50 - (10 + 20) = 50 - 30 = 20. Now, evaluate the answer choices to find which one also equals 20. A) (50 - 10) + 4 × 5 = 40 + 20 = 60. B) 50 - 10 + 4 × 5 = 50 - 10 + 20 = 60. C) 10 + 40 ÷ (8 - 4) = 10 + 40 ÷ 4 = 10 + 10 = 20. D) (50 - 10 + 4) × 5 = (40 + 4) × 5 = 44 × 5 = 220. Choice C is the correct answer.
- What is the missing number that makes the equation true? 4 × ( ? + 3) = 20
Answer: 2
To solve for the missing number, you can work backward. The equation shows that 4 times some quantity equals 20. That quantity must be 5, because 20 ÷ 4 = 5. The quantity in the parentheses is (? + 3), so ? + 3 = 5. The missing number must be 2, because 2 + 3 = 5.
- What is the value of the expression 48 ÷ 4 + 2 × (5 - 1)?
Answer: 20
To solve this problem, follow the order of operations (PEMDAS/BODMAS). First, solve the operation in the parentheses: (5 - 1) = 4. The expression becomes 48 ÷ 4 + 2 × 4. Next, perform multiplication and division from left to right. 48 ÷ 4 = 12, and 2 × 4 = 8. The expression is now 12 + 8. Finally, perform addition: 12 + 8 = 20.
- What is the difference between the values of Expression A and Expression B?
Answer: 12
First, evaluate Expression A: 3 × (4 + 6) = 3 × 10 = 30. Next, evaluate Expression B: 3 × 4 + 6 = 12 + 6 = 18. Finally, find the difference between their values: 30 − 18 = 12.
- A prize of $100 is shared equally among 4 friends. One of the friends, Maria, then buys a book for $12 using her share of the money. How much money does Maria have left?
Answer: $13
First, find Maria's share of the prize money by dividing the total prize by the number of friends: $100 ÷ 4 = $25. Next, subtract the cost of the book from her share: $25 - $12 = $13. Maria has $13 left.
- What is the value of 5 × 4 + 3 × 2 + 1?
Answer: 27
According to the order of operations, multiplication is performed before addition. First, calculate 5 × 4 = 20. Next, calculate 3 × 2 = 6. The expression becomes 20 + 6 + 1. Finally, add the numbers from left to right: 20 + 6 = 26, and 26 + 1 = 27.
- A bus starts with 45 passengers. At the first stop, 5 passengers get off. At the second stop, 3 groups of 4 passengers get on. How many passengers are on the bus now?
Answer: 52
This problem can be represented by the expression 45 - 5 + 3 × 4. First, calculate the number of passengers getting on: 3 × 4 = 12. The expression becomes 45 - 5 + 12. Now, do the addition and subtraction from left to right. First, 45 - 5 = 40. Then, 40 + 12 = 52. There are 52 passengers on the bus.
- What is the value of 36 ÷ 6 ÷ 3?
Answer: 2
When an expression has only division, the operations are performed from left to right. First, calculate 36 ÷ 6 = 6. Then, use that result for the next operation: 6 ÷ 3 = 2.
- Liam buys 4 packs of trading cards for $3 each and a binder for $7. He pays with a $20 bill. How much change does he receive?
Answer: $1.00
First, calculate the total cost of the items. The cost of the cards is 4 × $3 = $12. Add the cost of the binder: $12 + $7 = $19. This is the total cost. The change is the amount paid minus the total cost: $20 - $19 = $1.00.
- In which step did Samara make her first mistake?
Answer: Step 2
The correct way to solve 50 − 10 + 4 × 2 is: First, multiplication: 4 × 2 = 8. The expression becomes 50 − 10 + 8. Next, addition and subtraction are done from left to right. So, 50 − 10 = 40. Then, 40 + 8 = 48. Samara correctly did the multiplication in Step 1. However, in Step 2, she added 10 + 8 before subtracting 10 from 50. This violates the left-to-right rule for addition and subtraction. Her first mistake was in Step 2.
- Maya thinks of a number. She subtracts 3 from it, then multiplies the result by 4. Finally, she adds 6. If the final answer is 30, what number did Maya think of?
Answer: 9
To find the original number, work backward from the final answer and reverse the operations. The final answer is 30. The last step was adding 6, so subtract 6: 30 - 6 = 24. The step before that was multiplying by 4, so divide by 4: 24 ÷ 4 = 6. The first step was subtracting 3, so add 3: 6 + 3 = 9. The original number was 9.
- Mr. Chen has a board that is 15 feet long. He cuts off 3 pieces that are each 2 feet long. Then he cuts the remaining piece in half. How long is each of the final two pieces?
Answer: 4.5 feet
First, calculate the total length of the 3 pieces cut off: 3 × 2 = 6 feet. Next, find the length of the remaining board: 15 - 6 = 9 feet. Finally, cut the remaining piece in half: 9 ÷ 2 = 4.5 feet. Each of the final two pieces is 4.5 feet long.
- What is the value of 5 + 3 × (10 - 4)?
Answer: 23
According to the order of operations, first calculate the expression inside the parentheses: 10 - 4 = 6. The expression becomes 5 + 3 × 6. Next, perform the multiplication: 3 × 6 = 18. The expression becomes 5 + 18. Finally, perform the addition: 5 + 18 = 23.
- Which expression has the greatest value?
Answer: (10 + 6) × (4 - 2)
Evaluate each expression using the order of operations. A) 10 + 12 - 4 = 22 - 4 = 18. B) 16 × 2 - 4 = 32 - 4 = 28. C) 10 + 6 × 2 = 10 + 12 = 22. D) 16 × 2 = 32. Comparing the results (18, 28, 22, 32), the expression in choice D has the greatest value.
- To make the equation 6 × 5 - 2 + 3 = 21 true, parentheses should be placed around which part of the expression?
Answer: 5 - 2
Test each option. A) 6 × (5 - 2) + 3 = 6 × 3 + 3 = 18 + 3 = 21. This is true. B) 6 × 5 - (2 + 3) = 30 - 5 = 25. False. C) (6 × 5) - 2 + 3 = 30 - 2 + 3 = 31. False. D) 6 × (5 - 2 + 3) = 6 × (3 + 3) = 6 × 6 = 36. False. Therefore, placing parentheses around 5 - 2 makes the equation true.
- A cook has 32 potatoes. He uses 8 of them for a stew. He then divides the remaining potatoes equally into 4 bags. How many potatoes are in each bag?
Answer: 6
First, find the number of potatoes remaining after the cook uses some for stew: 32 - 8 = 24. Then, divide the remaining potatoes into 4 equal bags: 24 ÷ 4 = 6. There are 6 potatoes in each bag. The expression representing this is (32 - 8) ÷ 4.
- Which of the following statements is true?
Answer: 18 - 3 × 2 + 4 = 16
Evaluate each statement using the order of operations. A) 15 - 5 × 2 = 15 - 10 = 5, not 20. B) 12 + 8 ÷ 4 = 12 + 2 = 14, not 5. C) 20 ÷ 5 + 5 = 4 + 5 = 9, not 2. D) 18 - 3 × 2 + 4 = 18 - 6 + 4 = 12 + 4 = 16. This statement is true.
- Who is correct?
Answer: Ben
To evaluate 4 + 8 × 2, follow the order of operations. Multiplication comes before addition. So, first calculate 8 × 2 = 16. Then, add 4: 4 + 16 = 20. Ben's answer of 20 is correct. Anna likely added first: (4 + 8) × 2 = 24.
- An expression is simplified using the correct order of operations.
Expression: 60 ÷ (5 + 1) × 2
Which operation should be performed first?
Answer: Add 5 and 1, because it is in parentheses.
The order of operations (PEMDAS/BODMAS) states that operations inside parentheses must be performed first. In the expression 60 ÷ (5 + 1) × 2, the operation 5 + 1 is inside parentheses, so it must be calculated before any other step.
