Types and Simplifying Fractions

Types of Fractions

• Fractions represent a part of a whole. They are composed of a numerator (the top number) and a denominator (the bottom number).
• Proper Fractions: The numerator is smaller than the denominator. Example: 2/3
• Improper Fractions: The numerator is equal to or larger than the denominator. Example: 5/3
• Mixed Numbers: Combine a whole number and a proper fraction. Example: 1 2/3 (which is equivalent to the improper fraction 5/3)

Equivalent Fractions

• Equivalent fractions represent the same portion of a whole, even though they use different numerators and denominators.
• Created by multiplying or dividing both the numerator and denominator by the same non-zero number.
• Example: 1/2 = 2/4 = 3/6

Simplifying Fractions

• Simplifying a fraction means expressing it in its lowest terms.
• Achieved by dividing both the numerator and denominator by their greatest common factor (GCF).
• The simplified form of a fraction is considered the "most reduced" or "lowest terms" form.
• Example: Simplifying 4/8 to 1/2

Types of Fractions Based on Denominator

• Unit Fractions: A fraction with a numerator of 1. Example: 1/5
• Like Fractions: Fractions with the same denominator. Example: 2/7, 3/7, and 4/7
• Unlike Fractions: Fractions with different denominators. Example: 1/3 and 1/5

Comparing Fractions

• Comparing fractions with the same denominator is straightforward; the larger numerator indicates the larger fraction.
• Comparing fractions with different denominators often requires finding a common denominator to determine their relative magnitudes.

Addition and Subtraction of Fractions

• Adding or subtracting fractions with the same denominator is done by performing the operation on the numerators and keeping the denominator the same.
• Adding and subtracting unlike fractions requires finding a common denominator first.
• Example: 1/4 + 3/4 = 4/4 (or 1 whole)

Multiplication of Fractions

• Multiplying fractions is done by multiplying the numerators together and the denominators together.
• Example: (2/3) * (1/4) = 2/12 (which simplifies to 1/6)

Division of Fractions

• Dividing fractions involves multiplying the first fraction by the reciprocal of the second.
• Example: (2/3) ÷ (1/4) = (2/3) * (4/1) = 8/3

Decimal Fractions

• Decimal fractions represent a portion of a whole, expressed using a decimal point.