Revising Fractions

Introduction to Fractions

• A fraction is a part of a whole, representing one or more equal parts of a whole object.
• Example: Three-fourth (3/4)
  • Numerator: The number above the line, indicating the number of equal parts considered.
  • Fraction Bar: The line separating the numerator and denominator.
  • Denominator: The number below the line, indicating the total number of equal parts the whole is divided into.

Fractions as Part of a Set

• Example: In a set of four bottles, if three are red and one is green, three-fourth (3/4) of the bottles are red.

Unit Fractions

• A fraction where the numerator is 1.
• Examples: 1/3, 1/7, 1/13.

Types of Fractions Based on Denominators

• Like Fractions: Fractions with the same denominators (e.g., 1/4, 3/4).
• Unlike Fractions: Fractions with different denominators (e.g., 5/8, 5/3, 2/7).

Types of Fractions

Proper Fractions

• The numerator is less than the denominator.
• Example: 2/8 (2 < 8).

Improper Fractions

• The numerator is greater than or equal to the denominator.
• Examples:
  • 5/2 (5 > 2).
  • 4/4 (4 = 4).

Mixed Fractions

• The sum of a natural number and a proper fraction.
• Example: 2 and 1/2.
  • Here, 2 is the natural number, and 1/2 is the proper fraction.

Conversions Between Fractions

Mixed Number to Improper Fraction

• Example: Convert 5 and 3/9 into an improper fraction.
  • Multiply the natural number by the denominator, then add the numerator to get the new numerator.
  • Write the denominator as is.
  • Calculation: 5 and 3/9 = (5 × 9) + 3 / 9
  • Result: 45 + 3 / 9 = 48/9

Improper Fraction to Mixed Number

• Example: Convert 9/2 into a mixed number.
  • Divide the numerator by the denominator.
  • Write the quotient plus the remainder over the divisor.
  • Calculation: 9 ÷ 2 = quotient 4, remainder 1
  • Result: 9/2 = 4 + 1/2 = 4 and 1/2