Evaluating the Expression: 4(1/2x5x7)
Evaluating mathematical expressions can be a challenging task, especially when dealing with complex expressions involving multiple operations and parentheses. In this article, we will break down the expression 4(1/2x5x7) and evaluate it step by step.
Understanding the Order of Operations
Before we begin evaluating the expression, it's essential to understand the order of operations. The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponents (such as squaring or cubing) next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Evaluating the Expression
Now that we understand the order of operations, let's evaluate the expression 4(1/2x5x7).
Step 1: Evaluate Expressions Inside Parentheses
Inside the parentheses, we have the expression 1/2x5x7. To evaluate this expression, we need to follow the order of operations.
Step 2: Evaluate Division
First, we evaluate the division operation: 1/2 = 0.5.
Step 3: Evaluate Multiplication
Next, we evaluate the multiplication operations from left to right:
0.5 * 5 = 2.5 2.5 * 7 = 17.5
Step 4: Evaluate the Expression Outside the Parentheses
Now that we have evaluated the expression inside the parentheses, we can multiply the result by 4:
4 * 17.5 = 70
Final Answer
Therefore, the final answer to the expression 4(1/2x5x7) is 70.
