Types of Fractions

Kinds of Fractions

1. Proper Fractions

   • Definition: Numerator is less than the denominator.
   • Example: 3/4, 2/5

2. Improper Fractions

   • Definition: Numerator is greater than or equal to the denominator.
   • Example: 5/4, 7/7

3. Mixed Numbers

   • Definition: A whole number combined with a proper fraction.
   • Example: 2 1/3, 4 5/6

4. Like Fractions

   • Definition: Fractions that have the same denominator.
   • Example: 1/4, 3/4, 2/4

5. Unlike Fractions

   • Definition: Fractions that have different denominators.
   • Example: 1/3, 1/4

6. Equivalent Fractions

   • Definition: Different fractions that represent the same value.
   • Example: 1/2 is equivalent to 2/4 and 3/6

7. Decimal Fractions

   • Definition: Fractions where the denominator is a power of ten, typically expressed in decimal form.
   • Example: 0.5 (1/2), 0.25 (1/4)

8. Simplest Form

   • Definition: A fraction is in simplest form when the numerator and the denominator are coprime (have no common factors other than 1).
   • Example: 4/8 simplified to 1/2

9. Complex Fractions

   • Definition: A fraction where the numerator, the denominator, or both contain fractions.
   • Example: (1/2)/(3/4)

10. Unit Fractions

    • Definition: Fractions with a numerator of 1.
    • Example: 1/5, 1/10

Types of Fractions

• Proper Fractions: Numerator is less than the denominator; examples include 3/4 and 2/5, indicating values less than one.

• Improper Fractions: Numerator is greater than or equal to the denominator; examples include 5/4 and 7/7, representing values that are equal to or greater than one.

• Mixed Numbers: Combination of a whole number and a proper fraction; examples include 2 1/3 and 4 5/6, representing values greater than one expressed with both whole and fractional parts.

• Like Fractions: Share the same denominator; examples are 1/4, 3/4, and 2/4, facilitating straightforward addition and subtraction.

• Unlike Fractions: Have different denominators; examples include 1/3 and 1/4, requiring a common denominator for operations.

• Equivalent Fractions: Different fractions that depict the same value; 1/2 is equivalent to 2/4 and 3/6, showing fractions can be simplified or altered while retaining value.

• Decimal Fractions: Fractions with a denominator that is a power of ten, usually represented in decimal form; examples include 0.5 (1/2) and 0.25 (1/4).

• Simplest Form: A fraction is in simplest form when the numerator and denominator are coprime with no common factors besides one; for instance, 4/8 simplifies to 1/2.

• Complex Fractions: Fractions where the numerator, the denominator, or both are fractions themselves; for example, (1/2)/(3/4), illustrating a more intricate structure of fractions.

• Unit Fractions: Fractions with a numerator of one; examples like 1/5 and 1/10 represent a single part of a whole divided into equal segments.