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Chapter 10: Problem 42

Multiply. \(-\frac{3}{5}\left(-\frac{2}{7}\right)\)

Short Answer

Expert verified
The result is \(\frac{6}{35}\).

Step by step solution

01

- Understand the Problem

We are asked to multiply two negative fractions: oaa: \(-\frac{3}{5}\) and \(-\frac{2}{7}\).
02

- Multiply the Numerators

Multiply the numerators of the two fractions: \(-3\) and \(-2\). Since multiplying two negative numbers results in a positive number, we get \(-3 \times -2 = 6\).
03

- Multiply the Denominators

Next, multiply the denominators of the two fractions: \(5\) and \(7\). This gives us \(5 \times 7 = 35\).
04

- Combine the Results

Combine the results from steps 2 and 3 to form the new fraction: \(\frac{6}{35}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Fractions
To understand how to multiply negative fractions, it's important to first understand what a negative fraction is. A negative fraction is a fraction where at least one part (numerator or denominator) is negative.
For example, \(-\frac{3}{5}\) has a negative numerator, which means the fraction itself is negative.
When we multiply two negative fractions, we end up with a positive result because multiplying two negative numbers makes a positive number. This is why \(-3 \times -2 = 6\).
Keep this rule in mind when working with negative fractions, and remember, the negativity cancels out!
Math Operations
Math operations are procedures we perform with numbers to get a result. For fraction multiplication, follow these steps:
1. Multiply the numerators.
2. Multiply the denominators.
This rule applies universally, whether the fractions are positive or negative. In our exercise, we start by multiplying the numerators: \(-3\) and \(-2\). Since \(-3 \times -2 = 6\), we get a positive 6. Then, we multiply the denominators: \5\ and \7\. This gives us \5 \times 7 = 35\. So, the result is \frac{6}{35}\.
Numerators and Denominators
Fractions have two main parts: the numerator and the denominator. The numerator is the top part, showing how many parts we have. The denominator is the bottom part, showing into how many parts the whole is divided.
For example, in \(-\frac{3}{5}\), \3\ is the numerator, and \[5\] is the denominator. When dealing with fractions in math operations, it's essential to handle numerators and denominators correctly. In multiplication:
1. Multiply the numerators together.
2. Multiply the denominators together.
This leads to the correct result of the fraction operation. In our exercise, combining the results of \6\ (numerator) and \[35\] (denominator) gives us \frac{6}{35}\.

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Most popular questions from this chapter

Multiply. \(4 \cdot(-4) \cdot(-5) \cdot(-12)\)

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