Converting Improper Fractions to Mixed Numbers

Definition

• An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Examples

• 3/2, 5/3, 7/4 are all improper fractions.

Converting Improper Fractions to Mixed Numbers

• To convert an improper fraction to a mixed number, divide the numerator by the denominator to find the whole number part and the remainder.
• The remainder becomes the numerator of the fraction part.

Example

• Convert 7/4 to a mixed number:
  • 7 ÷ 4 = 1 with a remainder of 3
  • Mixed number: 1 3/4

Key Properties

• An improper fraction can always be written as a mixed number.
• An improper fraction is not in its simplest form.

Simplifying Improper Fractions

• To simplify an improper fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
• If the GCD is 1, the fraction is in its simplest form.

Example

• Simplify the improper fraction 12/8:
  • GCD of 12 and 8 is 4
  • Divide both numerator and denominator by 4: 3/2
  • Simplified improper fraction: 3/2

Improper Fractions

• An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Examples of Improper Fractions

• 3/2, 5/3, and 7/4 are improper fractions.

Converting to Mixed Numbers

• Divide the numerator by the denominator to find the whole number part and the remainder.
• The remainder becomes the numerator of the fraction part.

Mixed Number Conversion Example

• 7/4 converts to 1 3/4:
  • 7 ÷ 4 = 1 with a remainder of 3
  • The mixed number is 1 3/4.

Key Properties of Improper Fractions

• An improper fraction can always be written as a mixed number.
• An improper fraction is not in its simplest form.

Simplifying Improper Fractions

• Divide both the numerator and denominator by their greatest common divisor (GCD).
• If the GCD is 1, the fraction is in its simplest form.

Simplification Example

• 12/8 simplifies to 3/2:
  • The GCD of 12 and 8 is 4.
  • Divide both numerator and denominator by 4.