Fractions Basics

Definitions

• A fraction is a way to represent a part of a whole as a ratio of two numbers.
• The top number is called the numerator (tells how many equal parts).
• The bottom number is called the denominator (tells how many parts the whole is divided into).

Types of Fractions

• Proper fraction: numerator is less than the denominator (e.g. 1/2, 3/4).
• Improper fraction: numerator is greater than or equal to the denominator (e.g. 3/2, 5/4).
• Mixed number: a combination of a whole number and a proper fraction (e.g. 2 1/2, 3 3/4).

Operations with Fractions

• Addition: add numerators, keep denominators the same (e.g. 1/4 + 1/4 = 2/4).
• Subtraction: subtract numerators, keep denominators the same (e.g. 2/4 - 1/4 = 1/4).
• Multiplication: multiply numerators and denominators separately (e.g. 1/2 × 3/4 = 3/8).
• Division: invert and multiply (e.g. 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3).

Simplifying Fractions

• Simplification: reducing a fraction to its simplest form (e.g. 4/8 = 1/2).
• Greatest common divisor (GCD): find the largest number that divides both numerator and denominator.

Equivalent Fractions

• Equivalent fractions: fractions that have the same value (e.g. 1/2, 2/4, 3/6).
• Multiplying by 1: a convenient way to create equivalent fractions (e.g. 1/2 = 1/2 × 2/2 = 2/4).

Comparing Fractions

• Comparing fractions: determining which fraction is larger or smaller.
• Cross-multiplication: a method to compare fractions (e.g. 1/2 vs 2/3: 1×3 = 3, 2×2 = 4, so 2/3 is larger).

Fractions

• A fraction represents a part of a whole as a ratio of two numbers: the numerator (top number) and the denominator (bottom number).

Numerator and Denominator

• The numerator tells how many equal parts.
• The denominator tells how many parts the whole is divided into.

Types of Fractions

• A proper fraction has a numerator less than the denominator (e.g. 1/2, 3/4).
• An improper fraction has a numerator greater than or equal to the denominator (e.g. 3/2, 5/4).
• A mixed number is a combination of a whole number and a proper fraction (e.g. 2 1/2, 3 3/4).

Operations with Fractions

• To add fractions, add numerators and keep denominators the same (e.g. 1/4 + 1/4 = 2/4).
• To subtract fractions, subtract numerators and keep denominators the same (e.g. 2/4 - 1/4 = 1/4).
• To multiply fractions, multiply numerators and denominators separately (e.g. 1/2 × 3/4 = 3/8).
• To divide fractions, invert and multiply (e.g. 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3).

Simplifying Fractions

• Simplification reduces a fraction to its simplest form (e.g. 4/8 = 1/2).
• The greatest common divisor (GCD) is the largest number that divides both numerator and denominator.

Equivalent Fractions

• Equivalent fractions have the same value (e.g. 1/2, 2/4, 3/6).
• Multiplying by 1 is a convenient way to create equivalent fractions (e.g. 1/2 = 1/2 × 2/2 = 2/4).

Comparing Fractions

• Comparing fractions determines which fraction is larger or smaller.
• Cross-multiplication is a method to compare fractions (e.g. 1/2 vs 2/3: 1×3 = 3, 2×2 = 4, so 2/3 is larger).