Evaluate The Expression:$\[ \left(-3 \frac{2}{3}\right)^2 \\]
Introduction
When it comes to evaluating expressions involving fractions and negative numbers, it's essential to follow the correct order of operations and understand the rules for handling these types of numbers. In this article, we will evaluate the expression and explore the steps involved in simplifying it.
Understanding the Expression
The given expression is . To evaluate this expression, we need to first understand what it means to raise a negative number to a power. When a negative number is raised to an even power, the result is always positive. On the other hand, when a negative number is raised to an odd power, the result is always negative.
Converting the Mixed Number to an Improper Fraction
Before we can evaluate the expression, we need to convert the mixed number to an improper fraction. To do this, we multiply the whole number part by the denominator and then add the numerator.
Evaluating the Expression
Now that we have converted the mixed number to an improper fraction, we can evaluate the expression. We will use the rule that states .
Simplifying the Result
The result of the expression is . This is already in its simplest form, so we don't need to simplify it further.
Conclusion
In this article, we evaluated the expression and explored the steps involved in simplifying it. We converted the mixed number to an improper fraction and then used the rule for raising a power to evaluate the expression. The result was , which is already in its simplest form.
Frequently Asked Questions
- What is the result of raising a negative number to an even power?
- The result is always positive.
- What is the result of raising a negative number to an odd power?
- The result is always negative.
- How do you convert a mixed number to an improper fraction?
- Multiply the whole number part by the denominator and then add the numerator.
Final Thoughts
Evaluating expressions involving fractions and negative numbers requires a clear understanding of the rules for handling these types of numbers. By following the correct order of operations and using the rules for raising a power, we can simplify complex expressions and arrive at the correct result.
Additional Resources
Related Articles
- Evaluating Expressions with Fractions
- Simplifying Expressions with Negative Numbers
- Converting Between Mixed Numbers and Improper Fractions
Introduction
Evaluating expressions involving fractions and negative numbers can be a challenging task, especially for students who are new to algebra. In this article, we will answer some of the most frequently asked questions about evaluating expressions with fractions and negative numbers.
Q&A
Q: What is the order of operations when evaluating expressions with fractions and negative numbers?
A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions 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.
Q: How do I handle negative numbers when evaluating expressions?
A: When evaluating expressions with negative numbers, remember that a negative number raised to an even power is always positive, and a negative number raised to an odd power is always negative.
Q: What is the difference between a fraction and a decimal?
A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. For example, the fraction 1/2 represents one half of a whole. A decimal, on the other hand, is a way of expressing a fraction as a number with a decimal point. For example, the decimal 0.5 represents the same value as the fraction 1/2.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator. For example, the mixed number 3 1/2 can be converted to an improper fraction as follows:
3 1/2 = (3 * 2) + 1 = 7/2
Q: What is the rule for multiplying fractions?
A: When multiplying fractions, multiply the numerators together and multiply the denominators together. For example, the product of 1/2 and 3/4 is:
(1 * 3) / (2 * 4) = 3/8
Q: What is the rule for dividing fractions?
A: When dividing fractions, invert the second fraction and multiply. For example, the quotient of 1/2 and 3/4 is:
(1 * 4) / (2 * 3) = 4/6 = 2/3
Q: How do I simplify a fraction?
A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, the fraction 6/8 can be simplified as follows:
GCD(6, 8) = 2 6/2 = 3 8/2 = 4 So, 6/8 = 3/4
Conclusion
Evaluating expressions involving fractions and negative numbers requires a clear understanding of the rules for handling these types of numbers. By following the correct order of operations and using the rules for multiplying and dividing fractions, we can simplify complex expressions and arrive at the correct result.
Frequently Asked Questions
- What is the order of operations when evaluating expressions with fractions and negative numbers?
- How do I handle negative numbers when evaluating expressions?
- What is the difference between a fraction and a decimal?
- How do I convert a mixed number to an improper fraction?
- What is the rule for multiplying fractions?
- What is the rule for dividing fractions?
- How do I simplify a fraction?
Final Thoughts
Evaluating expressions involving fractions and negative numbers requires practice and patience. By following the correct order of operations and using the rules for handling these types of numbers, we can simplify complex expressions and arrive at the correct result.
Additional Resources
- Order of Operations
- Rules for Multiplying and Dividing Fractions
- Converting Mixed Numbers to Improper Fractions
- Simplifying Fractions