Fractions Definition and Types

Definition and Notation

• A fraction is a way to represent a part of a whole.
• It consists of a numerator (top number) and a denominator (bottom number) separated by a horizontal line.
• The notation for a fraction is: a/b where a is the numerator and b is the denominator.

Types of Fractions

• Proper Fraction: A fraction where the numerator is less than the denominator. Example: 1/2
• Improper Fraction: A fraction where the numerator is greater than or equal to the denominator. Example: 3/2
• Mixed Number: A combination of a whole number and a proper fraction. Example: 2 1/3

Operations with Fractions

• Addition: To add fractions, they must have the same denominator. Then, add the numerators and keep the same denominator.
• Subtraction: To subtract fractions, they must have the same denominator. Then, subtract the numerators and keep the same denominator.
• Multiplication: To multiply fractions, multiply the numerators and multiply the denominators.
• Division: To divide fractions, invert the second fraction (i.e., flip the numerator and denominator) and then multiply.

Simplifying Fractions

• A fraction is in its simplest form when the numerator and denominator have no common factors.
• To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

Equivalent Fractions

• Equivalent fractions are fractions that have the same value.
• They can be created by multiplying or dividing both the numerator and denominator by the same number.

Comparing Fractions

• To compare fractions, convert them to equivalent fractions with the same denominator.
• The fraction with the larger numerator is the larger fraction.

Definition and Notation

• A fraction represents a part of a whole, consisting of a numerator and a denominator separated by a horizontal line.
• The notation for a fraction is a/b, where a is the numerator and b is the denominator.

Types of Fractions

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

Operations with Fractions

• To add fractions, they must have the same denominator; add the numerators and keep the same denominator.
• To subtract fractions, they must have the same denominator; subtract the numerators and keep the same denominator.
• To multiply fractions, multiply the numerators and multiply the denominators.
• To divide fractions, invert the second fraction and then multiply.

Simplifying Fractions

• A fraction is in its simplest form when the numerator and denominator have no common factors.
• To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

Equivalent Fractions

• Equivalent fractions have the same value and can be created by multiplying or dividing both the numerator and denominator by the same number.

Comparing Fractions

• To compare fractions, convert them to equivalent fractions with the same denominator.
• The fraction with the larger numerator is the larger fraction.