A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar.
For example, in the fraction 3/4, 3 is the numerator representing three equal parts, and 4 is the denominator indicating that the whole is divided into four equal parts. Fractions are essential in mathematics for representing quantities that are not whole numbers.
Addition: Find a common denominator, convert both fractions, add the numerators, and simplify.
Subtraction: Find a common denominator, convert both fractions, subtract the numerators, and simplify.
Multiplication: Multiply the numerators together and multiply the denominators together, then simplify.
Division: Multiply the first fraction by the reciprocal of the second fraction (flip the second fraction), then simplify.
Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b - c/d = (ad - bc) / bd
Multiplication: a/b × c/d = ac / bd
Division: a/b ÷ c/d = a/b × d/c = ad / bc
Problem: 1/2 + 1/3 = ?
Solution:
A proper fraction has a numerator smaller than the denominator (e.g., 3/4). Its value is always less than 1.
An improper fraction has a numerator greater than or equal to the denominator (e.g., 7/4). Its value is greater than or equal to 1.
Divide both the numerator and denominator by their greatest common divisor (GCD). For example, 8/12 simplifies to 2/3 by dividing both by 4.