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Chapter 7: Problem 359

In the following exercises, simplify. $$ \frac{0}{9} $$

Short Answer

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Step by step solution

01

Understand the fraction

The fraction to simplify is \( \frac{0}{9} \). Any fraction with a numerator of 0 is equal to 0, regardless of the denominator.
02

Simplify the fraction

Since the numerator is 0, the entire fraction \( \frac{0}{9} \) simplifies to 0.

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Key Concepts

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

numerator
The numerator is the top number in a fraction. It represents how many parts of the whole you have. In our example, the numerator is 0 in the fraction \(\frac{0}{9}\). When dealing with fractions, the numerator can tell you if the fraction equals zero. If the numerator is zero, the entire fraction simplifies to zero.
  • Think of the numerator as the number of pizzas you have if you have 0 pizzas out of 9.
  • It doesn鈥檛 matter how many slices a pizza is divided into if you have no pizzas.
Understanding that the numerator can zero out the fraction is crucial in simplifying fractions.
denominator
The denominator is the bottom number in a fraction. It shows into how many parts the whole is divided. In the fraction \(\frac{0}{9}\), the denominator is 9. Even though the denominator is 9, the fraction is considered 0 because the numerator is 0.
The denominator affects the fraction only if the numerator is a non-zero value. For example, in \(\frac{3}{9}\), you have 3 parts of 9 total parts.
  • The denominator helps in dividing the whole into equal parts.
  • It provides context to how much of the whole is considered.
But remember, if the numerator is 0, the fraction always simplifies to 0, no matter the denominator.
fraction simplification
Fraction simplification is the process of reducing a fraction to its simplest form. This can involve canceling out common factors in both the numerator and the denominator. However, in some special cases, simplification can be immediate and obvious.
In our example \(\frac{0}{9}\), since the numerator is 0, we don't need to look for common factors. The rule is simple: any fraction with a numerator of 0 simplifies directly to 0.
Here are a few key points for fraction simplification:
  • If the numerator is zero, the fraction equals zero.
  • If the numerator and denominator have common factors, divide them out.
  • Always check if the fraction can be simplified further.
Recognizing these rules makes fraction simplification straightforward and easy to manage.

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