Understanding Negative Fractions

Oct 13, 2025 by windailys.com 14 views

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Introduction

In mathematics, multiplying fractions is a fundamental operation that involves multiplying the numerators and denominators of two or more fractions. When dealing with negative fractions, it's essential to understand the rules of multiplying negative numbers. In this article, we will evaluate the expression: $${-\frac{3}{8} \times \left(-\frac{12}{5}\right)}$$ and explore the concept of multiplying negative fractions.

Understanding Negative Fractions

A negative fraction is a fraction with a negative numerator or denominator. For example, $\-\frac{3}{8}$ is a negative fraction with a negative numerator and a positive denominator. When multiplying negative fractions, we need to consider the rules of multiplying negative numbers.

Rules of Multiplying Negative Numbers

When multiplying two or more negative numbers, the result is always positive. On the other hand, when multiplying a negative number and a positive number, the result is always negative. This is because the negative sign is a placeholder that indicates the direction of the number on the number line.

Evaluating the Expression

Now that we have a basic understanding of negative fractions and the rules of multiplying negative numbers, let's evaluate the expression: $${-\frac{3}{8} \times \left(-\frac{12}{5}\right)}$$. To evaluate this expression, we need to multiply the numerators and denominators of the two fractions.

Multiplying Numerators and Denominators

When multiplying fractions, we multiply the numerators and denominators separately. In this case, we have:

{-\frac{3}{8} \times \left(-\frac{12}{5}\right) = \frac{(-3) \times (-12)}{8 \times 5}}

Simplifying the Expression

Now that we have multiplied the numerators and denominators, we can simplify the expression by evaluating the numerator and denominator separately.

$\frac{(-3) \times (-12)}{8 \times 5} = \frac{36}{40}$

Reducing the Fraction

To reduce the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 36 and 40 is 4.

$\frac{36}{40} = \frac{36 \div 4}{40 \div 4} = \frac{9}{10}$

Conclusion

In conclusion, the expression $${-\frac{3}{8} \times \left(-\frac{12}{5}\right)}$$ evaluates to $\frac{9}{10}$ . When multiplying negative fractions, it's essential to understand the rules of multiplying negative numbers and to simplify the expression by evaluating the numerator and denominator separately.

Frequently Asked Questions

Q: What is the rule for multiplying negative fractions?

A: When multiplying negative fractions, the result is always positive.

Q: How do I simplify a fraction after multiplying the numerators and denominators?

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

Q: What is the greatest common divisor (GCD) of 36 and 40?

A: The GCD of 36 and 40 is 4.

Final Thoughts

In this article, we evaluated the expression $${-\frac{3}{8} \times \left(-\frac{12}{5}\right)}$$ and explored the concept of multiplying negative fractions. We learned that when multiplying negative fractions, the result is always positive and that we need to simplify the expression by evaluating the numerator and denominator separately. By following these steps, you can evaluate any expression involving negative fractions and simplify it to its simplest form.

Additional Resources

For more information on multiplying fractions and negative numbers, check out the following resources:

Khan Academy: Multiplying Fractions
Mathway: Multiplying Negative Fractions
Wolfram Alpha: Multiplying Negative Fractions

Evaluating Expressions with Exponents
Simplifying Fractions with Variables
Solving Linear Equations with Fractions

Comments

Do you have any questions or comments about this article? Please feel free to leave a comment below.

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Introduction

In our previous article, we evaluated the expression $${-\frac{3}{8} \times \left(-\frac{12}{5}\right)}$$ and explored the concept of multiplying negative fractions. In this article, we will answer some of the most frequently asked questions about multiplying negative fractions.

Q&A

Q: What is the rule for multiplying negative fractions?

A: When multiplying negative fractions, the result is always positive. This is because the negative sign is a placeholder that indicates the direction of the number on the number line.

Q: How do I multiply two negative fractions?

A: To multiply two negative fractions, you need to multiply the numerators and denominators separately and then simplify the expression. For example, $${-\frac{3}{8} \times \left(-\frac{12}{5}\right) = \frac{(-3) \times (-12)}{8 \times 5} = \frac{36}{40} = \frac{9}{10}}$$.

Q: What is the difference between multiplying positive and negative fractions?

A: When multiplying positive fractions, the result is always positive. However, when multiplying negative fractions, the result is always positive. This is because the negative sign is a placeholder that indicates the direction of the number on the number line.

Q: Can I multiply a negative fraction by a positive fraction?

A: Yes, you can multiply a negative fraction by a positive fraction. The result will be a negative fraction. For example, $${-\frac{3}{8} \times \frac{12}{5} = \frac{(-3) \times 12}{8 \times 5} = \frac{-36}{40} = \frac{-9}{10}}$$.

Q: How do I simplify a fraction after multiplying the numerators and denominators?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, $\frac{36}{40} = \frac{36 \div 4}{40 \div 4} = \frac{9}{10}$ .

Q: What is the greatest common divisor (GCD) of 36 and 40?

A: The GCD of 36 and 40 is 4.

Q: Can I multiply a negative fraction by a negative fraction?

A: Yes, you can multiply a negative fraction by a negative fraction. The result will be a positive fraction. For example, $${-\frac{3}{8} \times \left(-\frac{12}{5}\right) = \frac{(-3) \times (-12)}{8 \times 5} = \frac{36}{40} = \frac{9}{10}}$$.

Q: How do I know if a fraction is positive or negative?

A: To determine if a fraction is positive or negative, you need to look at the sign of the numerator and denominator. If both the numerator and denominator are positive, the fraction is positive. If both the numerator and denominator are negative, the fraction is positive. If one of the numerator or denominator is negative, the fraction is negative.