How to add & subtract fractions
For fractions with different denominators, you must find a common denominator first. The Least Common Denominator (LCD) is the smallest number that both denominators divide into evenly.
Example: 2/3 + 1/4
- Find LCD: smallest multiple of both 3 and 4 = 12
- Convert: 2/3 = 8/12 (multiply by 4/4), 1/4 = 3/12 (multiply by 3/3)
- Add numerators: 8/12 + 3/12 = 11/12
- Already in simplest form (GCD(11, 12) = 1)
For fractions with the same denominator, just add or subtract the numerators: 2/7 + 3/7 = 5/7. No conversion needed.
How to multiply & divide fractions
Multiplication
a/b × c/d = (a×c)/(b×d)
Multiply straight across. 2/3 × 4/5 = 8/15. No need for a common denominator.
Division
a/b ÷ c/d = a/b × d/c
"Keep, change, flip." 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
How to simplify fractions
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by the GCD.
simplified = numerator ÷ GCD / denominator ÷ GCD
Example: Simplify 24/36
- Find GCD(24, 36): factors of 24 = 24, factors of 36 = 36. Largest common = 12
- Divide both: 24 ÷ 12 = 2, 36 ÷ 12 = 3
- Result: 2/3 (GCD(2, 3) = 1, so this is lowest terms)
Mixed numbers explained
A mixed number is a whole number combined with a proper fraction: 2 3/4 means "2 and 3/4."
Mixed → Improper
new_numerator = whole × denom + num
2 3/4 → (2 × 4 + 3)/4 = 11/4
Improper → Mixed
whole = num ÷ denom, rem = leftover
11/4 → 11 ÷ 4 = 2 remainder 3 → 2 3/4
For math operations, convert mixed numbers to improper fractions first, then convert the answer back to mixed form if it's larger than 1.
Common fraction, decimal & percent equivalents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.667… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.167 | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/16 | 0.0625 | 6.25% |
Improper fractions vs mixed numbers
A proper fraction has a numerator smaller than its denominator (3/4). An improper fraction has a numerator ≥ denominator (7/4, 5/5). They're equivalent: 7/4 = 1 3/4.
Math textbooks and calculations typically prefer improper fractions (easier to multiply and divide). Everyday use (recipes, construction, fabric) typically uses mixed numbers (2 1/2 cups, 3 3/4 inches). Know how to convert between them — our calculator shows both.
Frequently asked questions
How do I add fractions with different denominators?
Find the Least Common Denominator (LCD), convert each fraction to an equivalent fraction with the LCD, then add the numerators. Example: 1/3 + 1/4. LCD of 3 and 4 is 12. Convert: 1/3 = 4/12, 1/4 = 3/12. Add: 4/12 + 3/12 = 7/12. The result 7/12 is already simplified. For subtraction, follow the same process but subtract the numerators instead of adding.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. 1/8 = 1 ÷ 8 = 0.125. 1/3 = 1 ÷ 3 = 0.333… (repeating). Some fractions terminate (have finite decimal representations); others repeat forever. Fractions where the denominator (after simplifying) only has factors of 2 and 5 always terminate: 1/2, 1/4, 1/5, 1/8, 1/10, 1/16, etc. Others produce repeating decimals.
What is a mixed number?
A mixed number combines a whole number with a proper fraction, like 2 3/4 (read 'two and three-fourths'). It's equivalent to the improper fraction 11/4 (multiply whole × denominator + numerator, keep the denominator). Mixed numbers are easier to visualize (2 3/4 cups vs 11/4 cups). For calculations, convert to improper fractions first, then convert back to mixed if the answer is larger than 1.
How do I simplify a fraction?
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by the GCD. Example: 24/36. GCD(24, 36) = 12. Divide both: 24÷12 = 2, 36÷12 = 3. Simplified: 2/3. Use the Euclidean algorithm to find GCD, or our calculator does it automatically. A fraction is in lowest terms when the GCD is 1.
How do I divide fractions?
Flip the second fraction (take its reciprocal) and multiply. 'Keep, change, flip.' Example: 2/3 ÷ 4/5. Keep 2/3, change ÷ to ×, flip 4/5 to 5/4: 2/3 × 5/4 = 10/12 = 5/6. This works because dividing by a fraction is the same as multiplying by its reciprocal. For mixed numbers, convert to improper fractions first.
What is the LCD (Least Common Denominator)?
The Least Common Denominator is the smallest number that all the denominators divide into evenly. For 1/3 and 1/4, the LCD is 12 (because 12 ÷ 3 = 4 and 12 ÷ 4 = 3). Finding the LCD is necessary to add or subtract fractions. Fastest method: find the Least Common Multiple (LCM) of the denominators. For small numbers, multiply the denominators and then simplify.
How do I convert a decimal to a fraction?
Count the decimal places, then write the number over a power of 10. Example: 0.375. Three decimal places → denominator 1000. Numerator is 375. Fraction: 375/1000. Simplify using GCD(375, 1000) = 125. Result: 3/8. For repeating decimals like 0.333…, algebra is needed (let x = 0.333, then 10x = 3.333, subtract to get 9x = 3, so x = 3/9 = 1/3).
What is an improper fraction?
An improper fraction has a numerator greater than or equal to its denominator, like 7/4 or 11/3. It represents a value ≥ 1. Improper fractions can be converted to mixed numbers: 7/4 = 1 3/4 (divide numerator by denominator: 7 ÷ 4 = 1 remainder 3). Improper fractions are preferred for calculations; mixed numbers are preferred for everyday use and reading.
What is 3/8 as a decimal?
3/8 = 0.375. Calculation: 3 ÷ 8 = 0.375. Related conversions: 1/8 = 0.125, 2/8 = 0.25, 3/8 = 0.375, 4/8 = 0.5, 5/8 = 0.625, 6/8 = 0.75, 7/8 = 0.875. Eighths all terminate because 8 = 2³ (denominator has only factors of 2). Sixteenths, thirty-seconds, and sixty-fourths also always terminate.
How do I multiply mixed numbers?
Convert each mixed number to an improper fraction, then multiply straight across (numerator × numerator, denominator × denominator), then simplify and convert back to mixed if needed. Example: 2 1/2 × 1 1/3. Convert: 2 1/2 = 5/2, 1 1/3 = 4/3. Multiply: (5 × 4)/(2 × 3) = 20/6 = 10/3 = 3 1/3. Do NOT just multiply the whole numbers and the fractions separately — that gives the wrong answer.