Add, subtract, multiply, and divide fractions
A fraction represents a part of a whole or a ratio between two numbers. It consists of a numerator (top number) and a denominator (bottom number). Fractions are fundamental in mathematics and are used extensively in cooking, construction, science, and everyday life.
a/b + c/d = (a×d + b×c) / (b×d)
| Calculation | Expression | Result |
|---|---|---|
| Add fractions | 1/2 + 1/4 | 3/4 |
| Subtract fractions | 3/4 - 1/2 | 1/4 |
| Multiply fractions | 2/3 × 3/4 | 1/2 |
| Divide fractions | 1/2 ÷ 1/4 | 2 |
| Mixed to improper | 2 1/2 | 5/2 |
First, find the least common denominator (LCD) of both fractions. Convert each fraction to an equivalent fraction with the LCD. Then add the numerators and keep the common denominator. For example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12
Multiply the numerators together and the denominators together. Then simplify if possible. For example: 2/3 × 3/4 = 6/12 = 1/2. You can also simplify before multiplying by canceling common factors.
Multiply the first fraction by the reciprocal (flip) of the second fraction. For example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2⅔. Remember: Keep, Change, Flip.
A proper fraction has a numerator smaller than its denominator (e.g., 3/4), representing less than one whole. An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/4), representing one or more wholes. Mixed numbers combine whole numbers with fractions (e.g., 1¾).
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions result in repeating decimals, like 1/3 = 0.333... (written as 0.3̄).
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, to simplify 12/18: GCD of 12 and 18 is 6, so 12/18 = 2/3.