Simplify The Expression: 3 9 − 1 9 \frac{3}{9} - \frac{1}{9} 9 3 ​ − 9 1 ​

by ADMIN 75 views

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. When dealing with fractions, simplifying them can make a significant difference in the solution. In this article, we will focus on simplifying the expression 39−19\frac{3}{9} - \frac{1}{9} using step-by-step instructions.

Understanding the Expression

The given expression is 39−19\frac{3}{9} - \frac{1}{9}. To simplify this expression, we need to understand the concept of subtracting fractions. When subtracting fractions, we need to have the same denominator. In this case, both fractions have the same denominator, which is 9.

Step 1: Identify the Denominator

The denominator of a fraction is the number that is being divided into. In this case, the denominator is 9.

Step 2: Subtract the Numerators

Now that we have identified the denominator, we can subtract the numerators. The numerator of a fraction is the number that is being divided. In this case, the numerators are 3 and 1.

39−19=3−19\frac{3}{9} - \frac{1}{9} = \frac{3-1}{9}

Step 3: Simplify the Numerator

Now that we have subtracted the numerators, we can simplify the numerator. The numerator is 2.

3−19=29\frac{3-1}{9} = \frac{2}{9}

Step 4: Write the Final Answer

The final answer is 29\frac{2}{9}.

Conclusion

Simplifying the expression 39−19\frac{3}{9} - \frac{1}{9} is a straightforward process that involves identifying the denominator, subtracting the numerators, and simplifying the numerator. By following these steps, we can simplify the expression and arrive at the final answer.

Real-World Applications

Simplifying expressions is a crucial skill that has numerous real-world applications. In finance, simplifying expressions can help us calculate interest rates and investment returns. In science, simplifying expressions can help us understand complex phenomena and make predictions. In engineering, simplifying expressions can help us design and optimize systems.

Tips and Tricks

When simplifying expressions, it's essential to follow the order of operations (PEMDAS). This means that we need to perform operations in the following order:

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

By following this order, we can ensure that we simplify expressions correctly and avoid errors.

Common Mistakes

When simplifying expressions, there are several common mistakes that we can make. These include:

  • Not identifying the denominator
  • Not subtracting the numerators
  • Not simplifying the numerator
  • Not following the order of operations

By being aware of these common mistakes, we can avoid them and simplify expressions correctly.

Conclusion

Simplifying the expression 39−19\frac{3}{9} - \frac{1}{9} is a straightforward process that involves identifying the denominator, subtracting the numerators, and simplifying the numerator. By following these steps, we can simplify the expression and arrive at the final answer. Simplifying expressions is a crucial skill that has numerous real-world applications, and by following the order of operations and avoiding common mistakes, we can simplify expressions correctly and efficiently.

Final Answer

The final answer is 29\boxed{\frac{2}{9}}.

Additional Resources

For more information on simplifying expressions, check out the following resources:

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

References

  • "Algebra and Trigonometry" by Michael Sullivan
  • "Mathematics for Dummies" by Mark Ryan
  • "Calculus for Dummies" by Mark Ryan
    Simplify the Expression: A Q&A Guide =====================================

Introduction

In our previous article, we discussed how to simplify the expression 39−19\frac{3}{9} - \frac{1}{9}. In this article, we will provide a Q&A guide to help you understand the concept of simplifying expressions and answer any questions you may have.

Q: What is simplifying an expression?

A: Simplifying an expression is the process of reducing a complex expression to its simplest form. This involves combining like terms, canceling out common factors, and rearranging the expression to make it easier to understand and work with.

Q: Why is simplifying expressions important?

A: Simplifying expressions is important because it helps us to:

  • Understand complex concepts more easily
  • Solve problems more efficiently
  • Avoid errors and mistakes
  • Make calculations and computations more accurate

Q: How do I simplify an expression?

A: To simplify an expression, follow these steps:

  1. Identify the like terms and combine them.
  2. Cancel out any common factors.
  3. Rearrange the expression to make it easier to understand and work with.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x2x and 5x5x are like terms because they both have the variable xx and the same exponent.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, 2x+5x=7x2x + 5x = 7x.

Q: What are common factors?

A: Common factors are factors that are common to two or more terms. For example, 2x2x and 4x4x have a common factor of 2x2x.

Q: How do I cancel out common factors?

A: To cancel out common factors, divide the terms by the common factor. For example, 2x2x=1\frac{2x}{2x} = 1.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

  • Not identifying like terms
  • Not combining like terms
  • Not canceling out common factors
  • Not following the order of operations

Q: How do I know when to simplify an expression?

A: You should simplify an expression when:

  • The expression is complex and difficult to understand
  • The expression is too long and needs to be shortened
  • The expression needs to be rearranged to make it easier to work with

Q: Can I simplify expressions with fractions?

A: Yes, you can simplify expressions with fractions. To simplify a fraction, follow these steps:

  1. Identify the like terms and combine them.
  2. Cancel out any common factors.
  3. Rearrange the fraction to make it easier to understand and work with.

Q: Can I simplify expressions with decimals?

A: Yes, you can simplify expressions with decimals. To simplify a decimal, follow these steps:

  1. Identify the like terms and combine them.
  2. Cancel out any common factors.
  3. Rearrange the decimal to make it easier to understand and work with.

Conclusion

Simplifying expressions is an important concept in mathematics that helps us to understand complex concepts more easily, solve problems more efficiently, and avoid errors and mistakes. By following the steps outlined in this article, you can simplify expressions and make calculations and computations more accurate.

Final Answer

The final answer is 29\boxed{\frac{2}{9}}.

Additional Resources

For more information on simplifying expressions, check out the following resources:

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

References

  • "Algebra and Trigonometry" by Michael Sullivan
  • "Mathematics for Dummies" by Mark Ryan
  • "Calculus for Dummies" by Mark Ryan