Fraction Calculator
Calculate with two fractions using any of the four operations. Enter simple fractions or mixed numbers, choose an operation, and get the answer reduced to lowest terms, shown as a mixed number, decimal, and percentage. The step-by-step panel explains every calculation including the LCM and GCF.
Formula
Worked example
1/2 + 1/3: LCD = 6, so 3/6 + 2/6 = 5/6 (GCF = 1, already simplified). As a decimal: 0.833333. As a percentage: 83.33%.
Adding and subtracting fractions using the LCD
To add or subtract fractions, you first need a common denominator. The most efficient common denominator is the Least Common Denominator (LCD), which is the Least Common Multiple of the two denominators. For 1/4 + 1/6, the LCD is 12. You convert 1/4 to 3/12 and 1/6 to 2/12, then add the numerators to get 5/12. Using the LCD (rather than simply multiplying denominators together) keeps the numbers smaller and often avoids a simplification step. This calculator always uses the LCD for addition and subtraction.
Multiplying and dividing fractions
Multiplication is the simplest fraction operation: multiply the numerators together and the denominators together, giving (a/b) x (c/d) = ac/bd. Division means multiplying by the reciprocal: keep the first fraction, flip the second, then multiply. So (a/b) / (c/d) = (a/b) x (d/c) = ad/bc. After multiplying you simplify by dividing both numerator and denominator by their GCF. You can also cross-cancel before multiplying, which is dividing a numerator and a diagonal denominator by their GCF before the multiplication step.
Mixed numbers and improper fractions
A mixed number such as 2 3/4 combines a whole part and a proper fraction. To compute with mixed numbers, convert them to improper fractions first: multiply the whole number by the denominator and add the numerator, keeping the same denominator. So 2 3/4 becomes (2x4+3)/4 = 11/4. After the operation, convert the improper result back to a mixed number by dividing numerator by denominator, the quotient is the whole part and the remainder over the denominator is the fractional part. This calculator handles mixed-number inputs directly in the Whole Number fields.
Simplifying fractions using the GCF
A fraction is in lowest terms (fully simplified) when the numerator and denominator share no common factor other than 1. The GCF (Greatest Common Factor), also called GCD (Greatest Common Divisor), is the largest number that divides both evenly. Divide both parts by the GCF to get the simplified fraction. For 18/24, GCF = 6, so 18/24 = 3/4. You can find the GCF by listing factors or by using the Euclidean algorithm, which repeatedly replaces the larger number with the remainder of dividing by the smaller until the remainder is 0.
Converting fractions to decimals and percentages
Any fraction n/d converts to a decimal simply by dividing: 3/4 = 0.75. To convert to a percentage, multiply the decimal by 100: 0.75 x 100 = 75%. Some fractions produce terminating decimals (like 1/4 = 0.25) while others produce repeating decimals (like 1/3 = 0.3333...). The number of decimal places a fraction terminates at depends on whether its denominator, once fully simplified, has only 2 and 5 as prime factors. Use the "Fraction to decimal and percent" mode to see the conversion with full precision.
Fraction operation reference
| Operation | Rule | Example | Result |
|---|---|---|---|
| Add | a/b + c/d = (a*LCD/b + c*LCD/d) / LCD | 1/4 + 1/6 | 5/12 |
| Subtract | a/b - c/d = (a*LCD/b - c*LCD/d) / LCD | 3/4 - 1/3 | 5/12 |
| Multiply | a/b x c/d = ac/bd | 2/3 x 3/4 | 1/2 |
| Divide | a/b / c/d = a/b x d/c | 3/4 / 3/8 | 2 |
| Simplify | n/d - (n/GCF)/(d/GCF) | 18/24 | 3/4 |
| To decimal | n / d | 5/8 | 0.625 |
Quick reference for the rules behind each operation.
Frequently asked questions
How do I add fractions with different denominators?
Find the Least Common Denominator (LCD) of the two denominators, which is their Least Common Multiple. Rewrite each fraction using the LCD as the new denominator, then add the numerators and keep the LCD as the denominator. Finally, simplify the result by dividing numerator and denominator by their GCF. Example: 1/4 + 1/6. LCD = 12. Convert: 3/12 + 2/12 = 5/12.
How do I divide two fractions?
Keep the first fraction unchanged, flip the second fraction (swap its numerator and denominator to get its reciprocal), and then multiply. This "keep, change, flip" rule works because dividing by a number is the same as multiplying by its reciprocal. For example, (3/4) / (2/5) = (3/4) x (5/2) = 15/8 = 1 7/8.
What is a mixed number and how do I convert it to an improper fraction?
A mixed number combines a whole number and a proper fraction, like 2 3/4. To convert it to an improper fraction, multiply the whole number by the denominator and add the numerator: 2 x 4 + 3 = 11, so 2 3/4 = 11/4. To go the other direction, divide the numerator by the denominator: the quotient is the whole part and the remainder becomes the new numerator.
What is the difference between GCF and LCD?
GCF (Greatest Common Factor) and LCD (Least Common Denominator) are used for opposite purposes. The GCF is the largest number that divides into both numerator and denominator, used when simplifying a fraction to lowest terms. The LCD is the smallest number that both denominators divide into evenly, used when adding or subtracting fractions so they share a common denominator.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 3/8 = 0.375, and 0.375 x 100 = 37.5%. Use the "Fraction to decimal and percent" mode to see the exact decimal and percentage together.
Why does this calculator use the LCD instead of just multiplying denominators?
Multiplying the two denominators always gives a valid common denominator but not always the smallest one. Using the LCD keeps the numbers smaller, which makes the arithmetic simpler and often means the result is already in lowest terms (or requires less simplification). For 1/4 + 1/6, multiplying denominators gives 24, but the LCD is only 12, keeping the numerators smaller throughout.