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Chapter 4: Problem 64

Simplify by dividing. See Examples 14 through 19. $$\frac{-14}{-14}$$

Short Answer

Expert verified
The simplified form of \( \frac{-14}{-14} \) is 1.

Step by step solution

01

Identify the Numerator and Denominator

In the expression \( \frac{-14}{-14} \), the numerator is \(-14\) and the denominator is \(-14\).
02

Recognize Common Factors

Both the numerator and the denominator are the same number, \(-14\). This means they share a common factor.
03

Divide the Numerator by the Denominator

Since the numerator is equal to the denominator, divide \(-14\) by \(-14\). Using the property of division, when a number is divided by itself, we get 1. Therefore, \( \frac{-14}{-14} = 1 \).

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Key Concepts

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

Understanding the Numerator
In a fraction, the top number is called the numerator. It represents the number of parts we have. In the expression \( \frac{-14}{-14} \), the numerator is \(-14\). This indicates "negative fourteen parts" of a whole. Recognizing the numerator helps you understand how much you are dealing with in a fraction. By focusing on the numerator alone, you grasp half of the fraction's identity. Simplifying fractions always starts with identifying both the numerator and the denominator correctly.
Comprehending the Denominator
The denominator is the bottom number in a fraction. It shows the total number of equal parts into which the whole is divided. In \( \frac{-14}{-14} \), \(-14\) serves as the denominator as well. It's essential to understand that the denominator sets the scale or size of each part. Even though both the numerator and denominator are \(-14\) here, usually, they can differ. This understanding is key to mastering simplifying fractions.
Identifying the Common Factor
A common factor is a number that divides exactly into two or more numbers. When simplifying fractions, finding a common factor between the numerator and denominator is crucial. In \( \frac{-14}{-14} \), the common factor is clearly the number itself, \(-14\). Recognizing common factors can simplify fractions faster, as it shows how both parts of the fraction share a similar base. You divide the numerator and denominator by their greatest common factor to simplify the fraction.
Applying the Division Property
The division property in mathematics states that any number divided by itself equals one. This is a fundamental property used to simplify fractions. In \( \frac{-14}{-14} \), dividing the numerator by the denominator, both being \(-14\), directly applies the division property. Thus, the fraction simplifies to \(1\). The division property is a powerful tool for simplification. It aids in quickly reducing fractions to their simplest form by applying straightforward division. It's handy whenever the numerator and denominator are identical or share common factors.

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Most popular questions from this chapter

Write each mixed number as an improper fraction. See Example 20. $$114 \frac{2}{7}$$

Solve. See the Concept Checks in this section. Habitat for Humanity is a nonprofit organization that helps provide affordable housing to families in need. Habitat for Humanity does its work of building and renovating houses through 1500 local affiliates in the United States and 80 international affiliates. What fraction of the total Habitat for Humanity affiliates are located in the United States? (Hint: First find the total number of affiliates.) (Source: Habitat for Humanity International)

Write each mixed number as an improper fraction. See Example 20. $$166 \frac{2}{3}$$

Simplify the following. $$\frac{1-\frac{x}{4}}{2+\frac{3}{8}}$$

Write each mixed number as an improper fraction. See Example 20. $$10 \frac{14}{27}$$
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