How to Add and Subtract Fractions
Adding and subtracting fractions requires a common denominator. If the denominators already match, add or subtract the numerators and keep the denominator. 3/8 + 2/8 = 5/8. Done.
When the denominators differ, find the least common denominator (LCD). For 1/3 + 1/4, the LCD of 3 and 4 is 12. Convert each fraction: 1/3 = 4/12 and 1/4 = 3/12. Now add: 4/12 + 3/12 = 7/12. Subtraction works the same way — convert to the common denominator, then subtract the numerators.
Common mistake: adding denominators. 1/3 + 1/4 is not 2/7. The denominator tells you the size of each piece. You can only combine pieces of the same size, which is why you need a common denominator first.
| Problem | LCD | Converted | Result |
|---|---|---|---|
| 1/3 + 1/4 | 12 | 4/12 + 3/12 | 7/12 |
| 2/5 + 1/3 | 15 | 6/15 + 5/15 | 11/15 |
| 3/4 - 1/6 | 12 | 9/12 - 2/12 | 7/12 |
| 5/6 - 1/4 | 12 | 10/12 - 3/12 | 7/12 |
How to Multiply and Divide Fractions
Multiplying fractions is simpler than adding them. Multiply the numerators together, multiply the denominators together, then simplify. 2/3 × 4/5 = 8/15. No common denominator needed.
Dividing fractions uses the “keep, change, flip” rule. Keep the first fraction, change the division sign to multiplication, flip the second fraction (take its reciprocal). 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. This works because dividing by a fraction is the same as multiplying by its inverse.
Pro tip for multiplication: cross-cancel before you multiply to keep numbers small. In 3/4 × 2/9, the 3 and 9 share a factor of 3 (simplify to 1/4 × 2/3 = 2/12 = 1/6), and the 2 and 4 share a factor of 2 (simplify to 1/2 × 1/3 = 1/6). Same answer, smaller numbers along the way.
| Operation | Rule | Example | Result |
|---|---|---|---|
| Multiply | Top × Top, Bottom × Bottom | 2/3 × 4/5 | 8/15 |
| Multiply | Cross-cancel first | 3/4 × 2/9 | 1/6 |
| Divide | Keep, Change, Flip | 2/3 ÷ 4/5 | 5/6 |
| Divide | Keep, Change, Flip | 5/8 ÷ 1/2 | 5/4 = 1 1/4 |
How to Simplify Fractions
A fraction is simplified (or “reduced”) when the numerator and denominator share no common factor other than 1. To simplify, find the greatest common divisor (GCD) of both numbers and divide both by it. 8/12: GCD of 8 and 12 is 4, so 8/12 = 2/3.
Quick method: if both numbers are even, divide both by 2. Repeat until at least one is odd. Then check for common factors of 3, 5, 7, and so on. For 18/24: both even → 9/12, now 9 is odd. GCD of 9 and 12 is 3 → 3/4. The calculator does this automatically using the Euclidean algorithm, which finds the GCD in a few division steps regardless of how large the numbers are.
Converting Improper Fractions to Mixed Numbers
An improper fraction has a numerator larger than its denominator: 11/4, 7/3, 15/8. To convert to a mixed number, divide the numerator by the denominator. The quotient is the whole number part. The remainder becomes the new numerator over the original denominator.
Example: 11/4. Divide 11 ÷ 4 = 2 remainder 3. So 11/4 = 2 3/4. Another: 7/3. Divide 7 ÷ 3 = 2 remainder 1. So 7/3 = 2 1/3. The calculator shows this conversion automatically whenever the result is an improper fraction.
To go the other direction (mixed number to improper fraction): multiply the whole number by the denominator, add the numerator. 2 3/4 = (2 × 4 + 3)/4 = 11/4.
Common Fraction-to-Decimal Conversions
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1667 | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/4 | 0.75 | 75% |
| 2/3 | 0.6667 | 66.67% |
For converting fractions to percentages or working with decimal equivalents, the percentage calculator handles those conversions directly. For exponents and powers (like squaring a fraction), use the exponent calculator.