Nico And Lorena Used Different Methods To Determine The Product Of Three Fractions.Nico's Method$[ \begin{align*} &\text{(2)}\left(\frac{1}{6}\right)\left(-\frac{4}{5}\right) \ &=

Mar 13, 2025 by ADMIN 180 views

**Nico and Lorena's Methods for Determining the Product of Three Fractions**

Introduction

In mathematics, the product of fractions is a fundamental concept that is used extensively in various mathematical operations. Two students, Nico and Lorena, were tasked with determining the product of three fractions using different methods. In this article, we will explore Nico's method and Lorena's method for determining the product of three fractions.

Nico's Method

Nico's method for determining the product of three fractions involves multiplying the numerators and denominators of the fractions separately. The formula for this method is:

\left(\frac{a}{b}\right)\left(\frac{c}{d}\right)\left(\frac{e}{f}\right) = \frac{a \cdot c \cdot e}{b \cdot d \cdot f}

where $a$ , $b$ , $c$ , $d$ , $e$ , and $f$ are the numerators and denominators of the fractions.

Let's consider an example to illustrate Nico's method. Suppose we want to find the product of the following three fractions:

\left(\frac{1}{6}\right)\left(-\frac{4}{5}\right)\left(\frac{3}{8}\right)

Using Nico's method, we can multiply the numerators and denominators separately:

\left(\frac{1}{6}\right)\left(-\frac{4}{5}\right)\left(\frac{3}{8}\right) = \frac{1 \cdot (-4) \cdot 3}{6 \cdot 5 \cdot 8}

Simplifying the expression, we get:

\frac{1 \cdot (-4) \cdot 3}{6 \cdot 5 \cdot 8} = \frac{-12}{240}

Reducing the fraction to its simplest form, we get:

\frac{-12}{240} = -\frac{1}{20}

Discussion

Nico's method for determining the product of three fractions is a straightforward and efficient approach. However, it requires careful attention to the signs of the fractions and the order of operations. It is essential to multiply the numerators and denominators separately to avoid errors.

Lorena's Method

Lorena's method for determining the product of three fractions involves multiplying the fractions together directly. The formula for this method is:

\left(\frac{a}{b}\right)\left(\frac{c}{d}\right)\left(\frac{e}{f}\right) = \frac{a \cdot c \cdot e}{b \cdot d \cdot f}

However, Lorena's method involves a different approach. She multiplies the fractions together by multiplying the numerators and denominators together:

\left(\frac{1}{6}\right)\left(-\frac{4}{5}\right)\left(\frac{3}{8}\right) = \frac{1 \cdot (-4) \cdot 3}{6 \cdot 5 \cdot 8}

But instead of simplifying the expression, Lorena multiplies the fractions together directly:

\left(\frac{1}{6}\right)\left(-\frac{4}{5}\right)\left(\frac{3}{8}\right) = \frac{1 \cdot (-4) \cdot 3}{6 \cdot 5 \cdot 8} = \frac{-12}{240}

However, Lorena's method is not as efficient as Nico's method. It requires more steps and can be prone to errors.

Comparison of Methods

Both Nico's and Lorena's methods for determining the product of three fractions are valid approaches. However, Nico's method is more efficient and less prone to errors. It requires careful attention to the signs of the fractions and the order of operations, but it is a straightforward and efficient approach.

Conclusion

In conclusion, Nico and Lorena's methods for determining the product of three fractions are both valid approaches. However, Nico's method is more efficient and less prone to errors. It requires careful attention to the signs of the fractions and the order of operations, but it is a straightforward and efficient approach.

Final Answer

The final answer to the problem is:

-\frac{1}{20}

References

[1] "Multiplication of Fractions" by Math Open Reference
[2] "Multiplying Fractions" by Khan Academy

Additional Resources

[1] "Fractions" by Math Is Fun
[2] "Multiplication of Fractions" by Purplemath
Nico and Lorena's Methods for Determining the Product of Three Fractions: Q&A ====================================================================

Introduction

In our previous article, we explored Nico's method and Lorena's method for determining the product of three fractions. In this article, we will answer some frequently asked questions about these methods.

Q: What is the product of three fractions?

A: The product of three fractions is the result of multiplying three fractions together. It is a fundamental concept in mathematics that is used extensively in various mathematical operations.

Q: How do I multiply three fractions together?

A: There are two methods for multiplying three fractions together: Nico's method and Lorena's method. Nico's method involves multiplying the numerators and denominators of the fractions separately, while Lorena's method involves multiplying the fractions together directly.

Q: What is Nico's method for multiplying three fractions?

A: Nico's method for multiplying three fractions involves multiplying the numerators and denominators of the fractions separately. The formula for this method is:

\left(\frac{a}{b}\right)\left(\frac{c}{d}\right)\left(\frac{e}{f}\right) = \frac{a \cdot c \cdot e}{b \cdot d \cdot f}

Q: What is Lorena's method for multiplying three fractions?

A: Lorena's method for multiplying three fractions involves multiplying the fractions together directly. The formula for this method is:

\left(\frac{a}{b}\right)\left(\frac{c}{d}\right)\left(\frac{e}{f}\right) = \frac{a \cdot c \cdot e}{b \cdot d \cdot f}

However, Lorena's method involves a different approach. She multiplies the fractions together by multiplying the numerators and denominators together:

\left(\frac{1}{6}\right)\left(-\frac{4}{5}\right)\left(\frac{3}{8}\right) = \frac{1 \cdot (-4) \cdot 3}{6 \cdot 5 \cdot 8}

Q: Which method is more efficient?

A: Nico's method is more efficient than Lorena's method. It requires fewer steps and is less prone to errors.

Q: How do I simplify a fraction?

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

Q: What is the final answer to the problem?

A: The final answer to the problem is:

-\frac{1}{20}

Q: Where can I find more information about multiplying fractions?

A: You can find more information about multiplying fractions on websites such as Math Open Reference, Khan Academy, and Purplemath.