Evaluate The Expression:$\[ -\frac{4}{9} \cdot \frac{1}{12} = \\]

by ADMIN 66 views

===========================================================

Introduction

When it comes to evaluating expressions involving fractions, it's essential to understand the rules and procedures for multiplying and dividing them. In this article, we will delve into the world of fractions and explore how to evaluate the expression −49⋅112-\frac{4}{9} \cdot \frac{1}{12}.

Understanding Fractions

Fractions are a way of representing part of a whole. They consist of two parts: the numerator and the denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts in the whole.

For example, the fraction 12\frac{1}{2} represents one half of a whole. The numerator is 1, and the denominator is 2.

Multiplying Fractions

When multiplying fractions, we multiply the numerators together and the denominators together. This is a fundamental rule in mathematics that helps us simplify complex expressions.

For example, let's consider the expression 12⋅34\frac{1}{2} \cdot \frac{3}{4}. To evaluate this expression, we multiply the numerators together (1 and 3) and the denominators together (2 and 4).

12⋅34=1⋅32⋅4=38\frac{1}{2} \cdot \frac{3}{4} = \frac{1 \cdot 3}{2 \cdot 4} = \frac{3}{8}

Evaluating the Expression

Now that we have a solid understanding of fractions and multiplying them, let's apply this knowledge to the expression −49⋅112-\frac{4}{9} \cdot \frac{1}{12}.

To evaluate this expression, we multiply the numerators together (-4 and 1) and the denominators together (9 and 12).

−49⋅112=−4⋅19⋅12=−4108-\frac{4}{9} \cdot \frac{1}{12} = -\frac{4 \cdot 1}{9 \cdot 12} = -\frac{4}{108}

Simplifying the Expression

When simplifying the expression −4108-\frac{4}{108}, we can see that both the numerator and the denominator have a common factor of 4.

−4108=−127-\frac{4}{108} = -\frac{1}{27}

Conclusion

In conclusion, evaluating the expression −49⋅112-\frac{4}{9} \cdot \frac{1}{12} requires a solid understanding of fractions and multiplying them. By following the rules and procedures outlined in this article, we can simplify complex expressions and arrive at the correct solution.

Frequently Asked Questions

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators together and the denominators together.

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to find the greatest common factor (GCF) of the numerator and the denominator and divide both numbers by the GCF.

Q: What is the difference between multiplying and dividing fractions?

A: When multiplying fractions, we multiply the numerators together and the denominators together. When dividing fractions, we invert the second fraction and multiply.

Final Thoughts

Evaluating expressions involving fractions can be a challenging task, but with practice and patience, it becomes second nature. By following the rules and procedures outlined in this article, we can simplify complex expressions and arrive at the correct solution.

Whether you're a student, a teacher, or simply someone who loves mathematics, this article has provided you with a comprehensive guide to evaluating the expression −49⋅112-\frac{4}{9} \cdot \frac{1}{12}. So, the next time you encounter a complex expression involving fractions, remember the rules and procedures outlined in this article and simplify it with ease.

Additional Resources

For more information on fractions and how to evaluate expressions involving them, check out the following resources:

  • Khan Academy: Fractions
  • Math Is Fun: Fractions
  • Purplemath: Fractions

By following these resources and practicing regularly, you'll become a master of evaluating expressions involving fractions in no time.

References

Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of resources on the topic.

====================================================================

Introduction

Evaluating expressions involving fractions can be a challenging task, but with practice and patience, it becomes second nature. In this article, we will address some of the most frequently asked questions about evaluating expressions involving fractions.

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators together and the denominators together. For example, to evaluate the expression 12⋅34\frac{1}{2} \cdot \frac{3}{4}, we multiply the numerators together (1 and 3) and the denominators together (2 and 4).

12⋅34=1⋅32⋅4=38\frac{1}{2} \cdot \frac{3}{4} = \frac{1 \cdot 3}{2 \cdot 4} = \frac{3}{8}

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to find the greatest common factor (GCF) of the numerator and the denominator and divide both numbers by the GCF. For example, to simplify the fraction 1218\frac{12}{18}, we find the GCF of 12 and 18, which is 6.

1218=12÷618÷6=23\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}

Q: What is the difference between multiplying and dividing fractions?

A: When multiplying fractions, we multiply the numerators together and the denominators together. When dividing fractions, we invert the second fraction and multiply. For example, to evaluate the expression 12÷34\frac{1}{2} \div \frac{3}{4}, we invert the second fraction and multiply.

12÷34=12⋅43=46=23\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \cdot \frac{4}{3} = \frac{4}{6} = \frac{2}{3}

Q: How do I evaluate an expression involving negative fractions?

A: When evaluating an expression involving negative fractions, we need to remember that a negative sign in the numerator or denominator affects the sign of the result. For example, to evaluate the expression −49⋅112-\frac{4}{9} \cdot \frac{1}{12}, we multiply the numerators together and the denominators together, and then simplify the result.

−49⋅112=−4⋅19⋅12=−4108=−127-\frac{4}{9} \cdot \frac{1}{12} = -\frac{4 \cdot 1}{9 \cdot 12} = -\frac{4}{108} = -\frac{1}{27}

Q: Can I simplify a fraction with a negative sign?

A: Yes, you can simplify a fraction with a negative sign. To simplify a fraction with a negative sign, we need to find the greatest common factor (GCF) of the numerator and the denominator, and then divide both numbers by the GCF. For example, to simplify the fraction −1218-\frac{12}{18}, we find the GCF of 12 and 18, which is 6.

−1218=−12÷618÷6=−23-\frac{12}{18} = -\frac{12 \div 6}{18 \div 6} = -\frac{2}{3}

Q: How do I evaluate an expression involving fractions with different denominators?

A: When evaluating an expression involving fractions with different denominators, we need to find the least common multiple (LCM) of the denominators and then convert both fractions to have the LCM as the denominator. For example, to evaluate the expression 12+13\frac{1}{2} + \frac{1}{3}, we find the LCM of 2 and 3, which is 6.

12+13=1⋅32⋅3+1⋅23⋅2=36+26=56\frac{1}{2} + \frac{1}{3} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}

Q: Can I use a calculator to evaluate expressions involving fractions?

A: Yes, you can use a calculator to evaluate expressions involving fractions. However, it's essential to understand the rules and procedures for evaluating expressions involving fractions, as calculators can sometimes produce incorrect results.

Conclusion

Evaluating expressions involving fractions can be a challenging task, but with practice and patience, it becomes second nature. By following the rules and procedures outlined in this article, you can simplify complex expressions and arrive at the correct solution.

Additional Resources

For more information on fractions and how to evaluate expressions involving them, check out the following resources:

  • Khan Academy: Fractions
  • Math Is Fun: Fractions
  • Purplemath: Fractions

By following these resources and practicing regularly, you'll become a master of evaluating expressions involving fractions in no time.

References