Assignment:Simplify The Expression $\[ 3 \frac{z^3}{6xy} \div \frac{9}{2xy} \\]

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying the expression ${ 3 \frac{z^3}{6xy} \div \frac{9}{2xy} }$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the concepts used.

Understanding the Expression

The given expression is a division of two fractions. To simplify it, we need to follow the order of operations (PEMDAS):

  1. Parentheses: None in this expression
  2. Exponents: None in this expression
  3. Multiplication and Division: From left to right
  4. Addition and Subtraction: From left to right

Step 1: Simplify the Division of Fractions

To simplify the division of fractions, we need to invert the second fraction and change the division sign to multiplication:

3z36xy÷92xy=3z36xy×2xy9{ 3 \frac{z^3}{6xy} \div \frac{9}{2xy} = 3 \frac{z^3}{6xy} \times \frac{2xy}{9} }

Step 2: Simplify the Multiplication of Fractions

Now, we can simplify the multiplication of fractions by multiplying the numerators and denominators separately:

3z36xy×2xy9=3z3×2xy6xy×9{ 3 \frac{z^3}{6xy} \times \frac{2xy}{9} = \frac{3z^3 \times 2xy}{6xy \times 9} }

Step 3: Cancel Out Common Factors

We can simplify the expression further by canceling out common factors in the numerator and denominator:

3z3×2xy6xy×9=6z3xy54xy{ \frac{3z^3 \times 2xy}{6xy \times 9} = \frac{6z^3xy}{54xy} }

Step 4: Simplify the Expression

Now, we can simplify the expression by canceling out common factors in the numerator and denominator:

6z3xy54xy=z39{ \frac{6z^3xy}{54xy} = \frac{z^3}{9} }

Conclusion

In this article, we simplified the expression ${ 3 \frac{z^3}{6xy} \div \frac{9}{2xy} }$ by following the order of operations and canceling out common factors. We hope this step-by-step guide has provided a clear understanding of the concepts used in simplifying algebraic expressions.

Frequently Asked Questions

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 order of operations is:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I simplify a division of fractions?

A: To simplify a division of fractions, we need to invert the second fraction and change the division sign to multiplication.

Q: How do I simplify a multiplication of fractions?

A: To simplify a multiplication of fractions, we need to multiply the numerators and denominators separately.

Q: How do I cancel out common factors?

A: To cancel out common factors, we need to identify the common factors in the numerator and denominator and cancel them out.

Additional Resources

For more information on simplifying algebraic expressions, we recommend the following resources:

  • Khan Academy: Algebraic Expressions
  • Mathway: Simplifying Algebraic Expressions
  • Wolfram Alpha: Simplifying Algebraic Expressions

Final Thoughts

Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the order of operations and canceling out common factors, we can simplify complex expressions and arrive at a final answer. We hope this article has provided a clear understanding of the concepts used in simplifying algebraic expressions.

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Introduction

In our previous article, we simplified the expression ${ 3 \frac{z^3}{6xy} \div \frac{9}{2xy} }$. We also provided a step-by-step guide on how to simplify algebraic expressions. In this article, we will answer some frequently asked questions on simplifying algebraic expressions.

Q&A

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 order of operations is:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I simplify a division of fractions?

A: To simplify a division of fractions, you need to invert the second fraction and change the division sign to multiplication.

Q: How do I simplify a multiplication of fractions?

A: To simplify a multiplication of fractions, you need to multiply the numerators and denominators separately.

Q: How do I cancel out common factors?

A: To cancel out common factors, you need to identify the common factors in the numerator and denominator and cancel them out.

Q: What is the difference between simplifying and solving an equation?

A: Simplifying an equation involves reducing the equation to its simplest form, while solving an equation involves finding the value of the variable that makes the equation true.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, you need to follow the order of operations and cancel out common factors.

Q: Can I simplify an expression with a negative exponent?

A: Yes, you can simplify an expression with a negative exponent by rewriting it as a fraction with a positive exponent.

Q: How do I simplify an expression with a fraction in the denominator?

A: To simplify an expression with a fraction in the denominator, you need to invert the fraction and change the division sign to multiplication.

Q: Can I simplify an expression with a variable in the denominator?

A: Yes, you can simplify an expression with a variable in the denominator by canceling out common factors.

Tips and Tricks

Tip 1: Follow the order of operations

When simplifying an expression, always follow the order of operations (PEMDAS).

Tip 2: Cancel out common factors

Canceling out common factors can help simplify an expression and make it easier to work with.

Tip 3: Use fractions to simplify expressions

Using fractions can help simplify expressions and make them easier to work with.

Tip 4: Check your work

Always check your work to make sure that the expression is simplified correctly.

Common Mistakes

Mistake 1: Not following the order of operations

Not following the order of operations can lead to incorrect simplifications.

Mistake 2: Not canceling out common factors

Not canceling out common factors can make an expression more complicated than it needs to be.

Mistake 3: Not using fractions to simplify expressions

Not using fractions to simplify expressions can make it harder to work with the expression.

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the order of operations and canceling out common factors, we can simplify complex expressions and arrive at a final answer. We hope this Q&A guide has provided a clear understanding of the concepts used in simplifying algebraic expressions.

Additional Resources

For more information on simplifying algebraic expressions, we recommend the following resources:

  • Khan Academy: Algebraic Expressions
  • Mathway: Simplifying Algebraic Expressions
  • Wolfram Alpha: Simplifying Algebraic Expressions

Final Thoughts

Simplifying algebraic expressions is a crucial skill that can help us solve complex problems and arrive at a final answer. By following the order of operations and canceling out common factors, we can simplify complex expressions and make them easier to work with. We hope this Q&A guide has provided a clear understanding of the concepts used in simplifying algebraic expressions.