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Chapter 1: Problem 353

Simplify. $$ -\frac{3 x}{12 y} $$

Short Answer

Expert verified
-\frac{x}{4y}

Step by step solution

01

- Identify Common Factors

Examine the fraction \( -\frac{3x}{12y} \) and identify common factors between the numerator and the denominator. Notice that both 3 and 12 have a common factor of 3.
02

- Divide by Common Factor

Divide the numerator and the denominator by the common factor, 3. This simplifies \( -\frac{3x}{12y} \) to \( -\frac{x}{4y} \).

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Key Concepts

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

common factors
To simplify a fraction, it's essential to find what are called 'common factors' between the numerator and the denominator. A common factor is a number that divides evenly into both the top and bottom parts of the fraction. In the given problem, we have the fraction \( -\frac{3x}{12y} \). First, look closely at the numbers 3 (numerator) and 12 (denominator). The greatest common factor (GCF) between them is 3. Identifying common factors helps us determine how we can simplify the fraction.
numerator and denominator
When dealing with fractions, it's important to understand the terms 'numerator' and 'denominator'. The numerator is the top part of the fraction, and the denominator is the bottom part. For example, in \( -\frac{3x}{12y} \), 3x is the numerator, and 12y is the denominator. Recognizing these terms can make it easier to follow steps for simplifying fractions and performing other operations. It's like having a map when you're navigating a new city!
dividing by common factor
Once you identify the common factor, the next step is to divide both the numerator and the denominator by this factor. In the example \( -\frac{3x}{12y} \), we found that 3 is a common factor for both 3 and 12. By dividing the numerator (3x) by 3, we get x. Similarly, dividing the denominator (12y) by 3, we get 4y. Therefore, the simplified fraction is \( -\frac{x}{4y} \). This process of dividing by the common factor helps reduce fractions to their simplest forms, making them easier to work with.

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