Improper Fraction

Definition

An improper fraction is a fractional representation where the numerator is greater than the denominator. This type of fraction is used to express a value that is greater than one whole unit.

5 Must Know Facts For Your Next Test

1. Improper fractions are commonly used in the context of simplifying rational expressions, where the numerator may be a polynomial with a degree higher than the denominator.
2. When adding or subtracting rational expressions with a common denominator, the fractions must be converted to improper fractions before the operations can be performed.
3. Visualizing fractions, both proper and improper, is an important skill in understanding the relationship between the numerator and denominator.
4. Improper fractions can be converted to mixed numbers by dividing the numerator by the denominator and using the quotient as the whole number and the remainder as the numerator of the fractional part.
5. The value of an improper fraction is always greater than 1, whereas the value of a proper fraction is always less than 1.

Review Questions

• Explain how an improper fraction can be used to simplify a rational expression.
  • In the context of simplifying rational expressions (topic 8.1), an improper fraction is used when the numerator of the expression is a polynomial with a degree higher than the degree of the denominator. By converting the expression to an improper fraction, the numerator and denominator can be factored and simplified more easily, leading to a simpler, equivalent rational expression.
• Describe the process of adding or subtracting rational expressions with a common denominator, and how improper fractions are involved.
  • When adding or subtracting rational expressions with a common denominator (topic 8.3), the fractions must first be converted to improper fractions. This is because the numerators of the expressions need to be combined or subtracted, and the common denominator must remain the same. By converting the fractions to improper form, the numerators can be easily manipulated, and the result can then be simplified or converted back to a mixed number if necessary.
• Analyze how the concept of improper fractions is related to the visualization of fractions (topic 1.5) and the understanding of the relationship between the numerator and denominator.
  • Visualizing fractions, both proper and improper, is crucial for understanding the concept of improper fractions. An improper fraction represents a value greater than one whole unit, which can be difficult to visualize compared to a proper fraction. By understanding the relationship between the numerator and denominator, and how an improper fraction can be converted to a mixed number, students can develop a deeper understanding of the meaning and application of improper fractions in various mathematical contexts.

Related terms

Proper Fraction: A proper fraction is a fractional representation where the numerator is less than the denominator, indicating a value less than one whole unit.

Mixed Number: A mixed number is a combination of a whole number and a proper fraction, used to represent a value greater than one whole unit.

Simplifying Fractions: The process of reducing a fraction to its simplest form by dividing both the numerator and denominator by their greatest common factor.