Renee Is Simplifying The Expression (7) \left(\frac{13}{29}\right)\left(\frac{1}{7}\right ]. She Recognizes That 7 And 1 7 \frac{1}{7} 7 1 Are Reciprocals, So She Would Like To Find Their Product Before She Multiplies By
Understanding the Concept of Reciprocals
In mathematics, reciprocals are numbers that, when multiplied together, result in a product of 1. For example, the reciprocal of 2 is 1/2, and the reciprocal of 1/2 is 2. In the given expression, Renee recognizes that 7 and 1/7 are reciprocals, which means that their product will be equal to 1.
The Importance of Simplifying Algebraic Expressions
Simplifying algebraic expressions is a crucial step in solving mathematical problems. It involves combining like terms, eliminating unnecessary variables, and reducing complex expressions to their simplest form. By simplifying expressions, mathematicians can make calculations easier, reduce errors, and arrive at accurate solutions.
Step 1: Identify the Reciprocals
In the given expression, Renee identifies that 7 and 1/7 are reciprocals. To simplify the expression, she will first find the product of these two numbers.
Step 2: Multiply the Reciprocals
To multiply the reciprocals, Renee will multiply 7 by 1/7. This can be done by multiplying the numerators (7 and 1) and the denominators (7 and 1).
# Multiply the reciprocals
numerator = 7 * 1
denominator = 7 * 7
result = numerator / denominator
print(result)
Step 3: Simplify the Result
After multiplying the reciprocals, Renee will simplify the result. Since the product of 7 and 1/7 is equal to 1, the result will be 1.
Step 4: Multiply by the Remaining Factor
Now that Renee has simplified the product of the reciprocals, she will multiply the result by the remaining factor, which is 13/29.
# Multiply the result by the remaining factor
numerator = 1 * 13
denominator = 1 * 29
result = numerator / denominator
print(result)
Step 5: Simplify the Final Result
After multiplying the result by the remaining factor, Renee will simplify the final result. This will involve combining like terms and reducing the expression to its simplest form.
Conclusion
In conclusion, simplifying algebraic expressions is an essential step in solving mathematical problems. By identifying reciprocals, multiplying them, and simplifying the result, mathematicians can make calculations easier, reduce errors, and arrive at accurate solutions. In this article, we have walked through the steps involved in simplifying the expression (7) (13/29) (1/7) using Python code. We hope that this article has provided a clear understanding of the concept of reciprocals and the importance of simplifying algebraic expressions.
Final Answer
The final answer to the problem is:
# Final answer
numerator = 13
denominator = 29
result = numerator / denominator
print(result)
The Final Result
The final result is 13/29.
Additional Tips and Resources
To simplify algebraic expressions, it is essential to identify like terms and combine them.
- Reciprocals are numbers that, when multiplied together, result in a product of 1.
- Simplifying expressions can make calculations easier, reduce errors, and arrive at accurate solutions.
- Python code can be used to simplify algebraic expressions and perform calculations.
References
Related Articles
- Simplifying Fractions
- Combining Like Terms
- Algebraic Identities
Frequently Asked Questions (FAQs) About Simplifying Algebraic Expressions ====================================================================
Q: What are algebraic expressions?
A: Algebraic expressions are mathematical expressions that contain variables, constants, and mathematical operations. They are used to represent relationships between variables and constants.
Q: Why is it important to simplify algebraic expressions?
A: Simplifying algebraic expressions is important because it makes calculations easier, reduces errors, and helps to arrive at accurate solutions. By simplifying expressions, mathematicians can make complex problems more manageable and easier to solve.
Q: What are reciprocals?
A: Reciprocals are numbers that, when multiplied together, result in a product of 1. For example, the reciprocal of 2 is 1/2, and the reciprocal of 1/2 is 2.
Q: How do I identify reciprocals in an algebraic expression?
A: To identify reciprocals in an algebraic expression, look for numbers that are multiplied together. If the product of these numbers is equal to 1, then they are reciprocals.
Q: How do I simplify an algebraic expression that contains reciprocals?
A: To simplify an algebraic expression that contains reciprocals, multiply the reciprocals together and simplify the result. Then, multiply the result by the remaining factors in the expression.
Q: What is the order of operations when simplifying algebraic expressions?
A: The order of operations when simplifying algebraic expressions 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 use Python to simplify algebraic expressions?
A: To use Python to simplify algebraic expressions, you can use the sympy library. This library provides a powerful tool for simplifying algebraic expressions and performing calculations.
Q: What are some common algebraic identities that I should know?
A: Some common algebraic identities that you should know include:
- The distributive property: a(b + c) = ab + ac
- The commutative property: a + b = b + a
- The associative property: (a + b) + c = a + (b + c)
- The identity property: a + 0 = a
- The inverse property: a + (-a) = 0
Q: How do I combine like terms in an algebraic expression?
A: To combine like terms in an algebraic expression, look for terms that have the same variable and coefficient. Then, add or subtract the coefficients of these terms to simplify the expression.
Q: What are some common mistakes to avoid when simplifying algebraic expressions?
A: Some common mistakes to avoid when simplifying algebraic expressions include:
- Not following the order of operations
- Not identifying and combining like terms
- Not simplifying expressions fully
- Not checking for errors in calculations
Q: How do I check my work when simplifying algebraic expressions?
A: To check your work when simplifying algebraic expressions, follow these steps:
- Re-read the original expression to make sure you understand it.
- Simplify the expression step-by-step, following the order of operations.
- Check your work by plugging the simplified expression back into the original equation.
- Verify that the simplified expression is equivalent to the original expression.
Conclusion
Simplifying algebraic expressions is an essential skill for mathematicians and scientists. By understanding the concepts of reciprocals, algebraic identities, and the order of operations, you can simplify complex expressions and arrive at accurate solutions. Remember to check your work carefully and avoid common mistakes when simplifying algebraic expressions.