Improper Fractions

Definition

An improper fraction is a fraction where the numerator is greater than the denominator. This means the value of the fraction is greater than 1. Improper fractions are an important concept in the context of adding and subtracting mixed numbers, as well as solving equations with fractions.

5 Must Know Facts For Your Next Test

1. Improper fractions can be converted to mixed numbers by dividing the numerator by the denominator and using the quotient as the whole number part, with the remainder as the numerator of the fractional part.
2. When adding or subtracting mixed numbers, it is often necessary to first convert any improper fractions to mixed numbers.
3. Improper fractions can be used to represent values greater than 1, which is important when solving equations with fractions.
4. Multiplying or dividing an improper fraction by another fraction or whole number will result in another improper fraction.
5. Simplifying an improper fraction involves reducing the numerator and denominator to their lowest terms.

Review Questions

• Explain how to convert an improper fraction to a mixed number.
  • To convert an improper fraction to a mixed number, you first divide the numerator by the denominator. The quotient becomes the whole number part, and the remainder becomes the numerator of the fractional part, with the original denominator remaining the same. For example, to convert the improper fraction 7/4 to a mixed number, you would divide 7 by 4, which gives you 1 with a remainder of 3. The mixed number representation would then be 1 3/4.
• Describe the role of improper fractions in the context of adding and subtracting mixed numbers.
  • When adding or subtracting mixed numbers, it is often necessary to first convert any improper fractions to mixed numbers. This is because the whole number and fractional parts need to be separated in order to perform the arithmetic operations. By converting improper fractions to mixed numbers, you can more easily combine the whole number and fractional parts, which is crucial for accurately adding and subtracting mixed numbers.
• Analyze how improper fractions are used in solving equations with fractions.
  • Improper fractions are important in solving equations with fractions because they allow you to represent values greater than 1. This is necessary when the solution to an equation involves a value that exceeds 1, such as 5/3 or 7/2. By using improper fractions, you can accurately represent and manipulate these values within the equation, leading to a correct solution. Improper fractions provide the flexibility to work with fractional quantities that are not limited to values less than 1.

Related terms

Mixed Number: A mixed number is a combination of a whole number and a proper fraction. For example, 3 1/2 is a mixed number.

Proper Fraction: A proper fraction is a fraction where the numerator is less than the denominator. The value of a proper fraction is less than 1.

Simplifying Fractions: Simplifying a fraction involves reducing it to its lowest terms by dividing the numerator and denominator by their greatest common factor.