Simplify: 24 × 2 + (56 ÷ 7) × 4 ÷ 2 – 58
The Correct Answer and Explanation is:
Correct Answer:
24 × 2 + (56 ÷ 7) × 4 ÷ 2 – 58 = 0
Step-by-Step Explanation:
To simplify this expression, follow the order of operations. This is often remembered using PEMDAS:
- P: Parentheses
- E: Exponents
- MD: Multiplication and Division (from left to right)
- AS: Addition and Subtraction (from left to right)
Let’s apply these rules step by step to:
24 × 2 + (56 ÷ 7) × 4 ÷ 2 – 58
Step 1: Parentheses
We first simplify the part inside the parentheses:
- 56 ÷ 7 = 8
Now substitute that into the expression:
24 × 2 + 8 × 4 ÷ 2 – 58
Step 2: Multiplication and Division (from left to right)
- 24 × 2 = 48
- 8 × 4 = 32
- 32 ÷ 2 = 16
Now the expression becomes:
48 + 16 – 58
Step 3: Addition and Subtraction (from left to right)
- 48 + 16 = 64
- 64 – 58 = 6
So, the simplified result is:
6
Wait — earlier, I had written 0 as the answer, which is incorrect. Let’s correct the final answer:
✅ Final Answer: 6
Explanation
This expression tests understanding of the proper order in which operations should be done in mathematics. Many students make the mistake of moving from left to right without respecting the rules of operation, especially when parentheses and multiple steps are involved.
In this problem, we begin by simplifying the expression inside the parentheses. Since parentheses take the highest priority in the order of operations, we evaluate 56 ÷ 7, which gives us 8. After substituting this result back, we continue solving with multiplication and division from left to right.
Multiplication and division are treated equally in terms of priority, so we perform them in the order they appear from left to right. First, we calculate 24 × 2, which gives 48. Then we move to 8 × 4, which equals 32, and then divide 32 ÷ 2, giving 16.
After all the multiplication and division is done, we are left with a simple expression: 48 + 16 – 58. Addition and subtraction also follow the left-to-right rule. Adding 48 + 16 gives 64, and subtracting 58 from that gives us 6.
Understanding the order of operations is essential for solving problems correctly in algebra and arithmetic. It ensures consistency and avoids confusion when multiple types of operations appear in a single expression.
