Basic Fractions
5 tools for basic fractions operations.
About Basic Fraction Operations
Basic fraction arithmetic — adding, subtracting, multiplying, dividing, and simplifying — forms the foundation of all fraction work. Whether you are helping a student with homework, verifying a calculation, or working through a recipe that involves fractional quantities, these tools handle every basic fraction operation instantly with step-by-step explanations.
How Fraction Arithmetic Works
Adding and subtracting fractions requires a common denominator. To add 1/3 + 1/4, find the least common denominator (12), convert both fractions (4/12 + 3/12), then add the numerators to get 7/12. Multiplication is simpler: multiply numerators together and denominators together (1/3 × 2/5 = 2/15). Division inverts the second fraction and multiplies (1/3 ÷ 2/5 = 1/3 × 5/2 = 5/6). The Fraction Calculator handles all four operations and shows each step.
Mixed Numbers and Improper Fractions
A mixed number combines a whole number and a proper fraction (e.g., 2 3/4). An improper fraction has a numerator larger than its denominator (e.g., 11/4). To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator: 2 3/4 = (2×4 + 3)/4 = 11/4. To convert back, divide the numerator by the denominator: 11 ÷ 4 = 2 remainder 3, giving 2 3/4. The Mixed Number Calculator and Improper to Mixed converter automate both directions.
Simplifying Fractions
A fraction is in its simplest (or lowest) form when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. For example, 18/24: GCD(18,24) = 6, so 18/24 = 3/4. The Simplify Fraction tool uses the Euclidean algorithm to compute the GCD efficiently, even for large numbers.
Equivalent Fractions
Two fractions are equivalent if they represent the same value. 1/2, 2/4, 3/6, and 50/100 are all equivalent. To generate equivalent fractions, multiply (or divide) both numerator and denominator by the same non-zero number. This is essential for finding a common denominator when adding fractions. The Equivalent Fractions tool generates a list of equivalent fractions and verifies whether two given fractions are equivalent.
Frequently Asked Questions
How do you add fractions with different denominators?
Find the least common denominator (LCD) of the two fractions. Convert each fraction to an equivalent fraction with the LCD as denominator. Then add the numerators and keep the denominator. Example: 1/4 + 1/6. LCD = 12. 1/4 = 3/12, 1/6 = 2/12. Sum = 5/12.
How do you multiply a fraction by a whole number?
Write the whole number as a fraction with denominator 1, then multiply numerators and denominators. Example: 3 × 2/5 = 3/1 × 2/5 = 6/5 = 1 1/5. Equivalently, just multiply the numerator by the whole number: 3 × 2 = 6, keep denominator 5, giving 6/5.
What is the simplest form of 36/48?
GCD(36, 48) = 12. Divide both by 12: 36/12 = 3, 48/12 = 4. Simplest form is 3/4.