Perform The Indicated Operation And Show Your Solution:${ 500 - \left[ (15 \times 10) + \left(\frac{1}{2} \times 95\right) \right] }$
Introduction
In this article, we will be performing a mathematical operation involving subtraction, multiplication, and division. The given expression is: ${ 500 - \left[ (15 \times 10) + \left(\frac{1}{2} \times 95\right) \right] }$. Our goal is to simplify this expression and find the final result.
Step 1: Multiply 15 and 10
The first step is to multiply 15 and 10. This can be done using the multiplication property of whole numbers.
Step 2: Multiply 1/2 and 95
Next, we need to multiply 1/2 and 95. To do this, we can multiply the numerator (1) and the denominator (2) of the fraction by 95.
Step 3: Add the Results of Step 1 and Step 2
Now that we have the results of the two multiplications, we can add them together.
Step 4: Subtract the Result of Step 3 from 500
Finally, we need to subtract the result of Step 3 from 500.
Conclusion
In this article, we performed the indicated operation and simplified the given expression. We started by multiplying 15 and 10, then multiplied 1/2 and 95, added the results of the two multiplications, and finally subtracted the result from 500. The final result is 302.5.
Key Takeaways
- To solve the given expression, we need to follow the order of operations (PEMDAS).
- We need to multiply 15 and 10, then multiply 1/2 and 95.
- We need to add the results of the two multiplications, then subtract the result from 500.
Real-World Applications
This type of mathematical operation is commonly used in real-world applications such as finance, science, and engineering. For example, in finance, we may need to calculate the total cost of a project, which involves subtracting the cost of materials from the total budget. In science, we may need to calculate the average speed of an object, which involves subtracting the initial speed from the final speed.
Common Mistakes to Avoid
When performing mathematical operations, it's easy to make mistakes. Here are some common mistakes to avoid:
- Not following the order of operations (PEMDAS).
- Not multiplying the numerator and denominator of a fraction by the same number.
- Not adding or subtracting the correct numbers.
Final Thoughts
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when we have 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 exponential expressions next (e.g., 2^3).
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify an expression with multiple operations?
A: To simplify an expression with multiple operations, follow the order of operations (PEMDAS). Start by evaluating any expressions inside parentheses, then evaluate any exponential expressions, followed by multiplication and division operations, and finally addition and subtraction operations.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both operations that involve numbers, but they have different effects on the result. Multiplication involves adding a number a certain number of times, while division involves finding the result of a number being divided by another number.
Q: How do I handle fractions in mathematical operations?
A: When working with fractions in mathematical operations, remember to multiply the numerator and denominator by the same number. For example, if you need to multiply a fraction by a number, multiply the numerator and denominator by that number.
Q: What is the result of the indicated operation: 500 - [(15 × 10) + (1/2 × 95)]?
A: To solve this expression, follow the order of operations (PEMDAS). First, multiply 15 and 10:
15 × 10 = 150
Next, multiply 1/2 and 95:
1/2 × 95 = 47.5
Then, add the results of the two multiplications:
150 + 47.5 = 197.5
Finally, subtract the result from 500:
500 - 197.5 = 302.5
Q: Can I use a calculator to simplify an expression?
A: Yes, you can use a calculator to simplify an expression. However, it's essential to understand the order of operations and how to evaluate expressions manually, as calculators can sometimes make mistakes.
Q: How do I check my work when simplifying an expression?
A: To check your work when simplifying an expression, follow these steps:
- Write down the original expression.
- Simplify the expression using the order of operations (PEMDAS).
- Write down the simplified expression.
- Check that the simplified expression is correct by plugging it back into the original expression.
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid when simplifying expressions include:
- Not following the order of operations (PEMDAS).
- Not multiplying the numerator and denominator of a fraction by the same number.
- Not adding or subtracting the correct numbers.
Q: Can I use this method to simplify more complex expressions?
A: Yes, you can use this method to simplify more complex expressions. However, it's essential to understand the order of operations and how to evaluate expressions manually, as more complex expressions may require additional steps.
Conclusion
In this article, we answered some frequently asked questions about indicated operations and simplification. We covered topics such as the order of operations, simplifying expressions with multiple operations, handling fractions, and checking work. By following the steps outlined in this article, you can ensure that you arrive at the correct result when simplifying expressions.