Fractions Definition and Types

Study Notes

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.

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

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.

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

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

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.

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).

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.

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

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