How to Use This Calculator
Enter the Fractions
Type the numerator and denominator of each fraction. Use Space to jump from whole → numerator, / to jump to denominator, and Enter to advance to the next term.
Select the Operation
Click the color-coded operator button between terms to cycle through addition (+), subtraction (−), multiplication (×), and division (÷).
Read the Simplified Result
The answer appears instantly as a simplified mixed number. Switch visualization tabs to see a bar model, circle chart, or number line. Export to CSV or share a link.
Formula & Methodology
Fraction Addition
Find a common denominator, then add the numerators and simplify.
Fraction Multiplication
Multiply numerators together and denominators together, then simplify.
Fraction Division
Invert the divisor (flip & multiply). This is the Keep-Change-Flip method.
Fraction Operations at a Glance
| Operation | Formula | Example | Result |
|---|---|---|---|
| Addition | (ad+bc)/bd | 1/3 + 1/4 | 7/12 |
| Subtraction | (ad−bc)/bd | 3/4 − 1/3 | 5/12 |
| Multiplication | (ac)/(bd) | 2/5 × 3/7 | 6/35 |
| Division | (ad)/(bc) | 5/6 ÷ 2/3 | 5/4 |
Key Terms
- Numerator
- The top number in a fraction, representing how many parts are taken.
- Denominator
- The bottom number, representing the total number of equal parts.
- Improper Fraction
- A fraction where the numerator is greater than or equal to the denominator, such as 7/4.
- Mixed Number
- A whole number combined with a proper fraction, such as 1 3/4.
- Greatest Common Divisor (GCD)
- The largest positive integer that divides both numerator and denominator evenly; used to simplify.
- Least Common Multiple (LCM)
- The smallest positive integer that is divisible by two given integers. Used to find common denominators.
Real-World Examples
Combining Recipe Ingredients
3/4 + 2/3
17/12 = 1 5/12 — combining three-quarters and two-thirds cup of flour
Dividing Pizza Slices
3/8 ÷ 1/4
3/2 = 1 1/2 — how many quarter-pizza portions fit in three-eighths
Lumber Measurement
5/8 × 3/4
15/32 inch — finding the area of a cross-section cut
Mastering Fraction Arithmetic
Why Fractions Still Matter
Despite the prevalence of decimals in technology, fractions remain essential in cooking, construction (where measurements are in eighths and sixteenths of an inch), music (time signatures like 3/4), and higher mathematics. Fractions express exact values that decimals can only approximate, such as 1/3, which equals the repeating decimal 0.333...
Simplification and Common Denominators
Simplifying a fraction means dividing both the numerator and denominator by their greatest common divisor. For example, 12/18 simplifies to 2/3 by dividing both by 6. When adding or subtracting fractions, finding the least common denominator (LCD) minimizes the size of the numbers you work with.
Converting Between Fractions and Decimals
To convert a fraction to a decimal, divide the numerator by the denominator. To convert a terminating decimal to a fraction, place the decimal digits over the appropriate power of ten and simplify. For repeating decimals, algebraic techniques derive the exact fraction — 0.666... equals 2/3.