Fraction basics
A fraction a/b has a numerator a (how many parts) and a denominator b (how many equal parts make a whole). A proper fraction is less than one (3/4), an improper fraction is one or more (7/4), and a mixed number writes an improper fraction as a whole number plus a proper fraction (1 3/4). To enter a mixed number above, put the whole number in its own box; for a simple fraction leave that box empty.
The four rules
| Operation | Rule | Example |
|---|---|---|
| Add | Use a common denominator, then add numerators | 1/2 + 1/3 = 3/6 + 2/6 = 5/6 |
| Subtract | Use a common denominator, then subtract numerators | 3/4 − 1/6 = 9/12 − 2/12 = 7/12 |
| Multiply | Multiply numerators and denominators | 3/4 × 2/5 = 6/20 = 3/10 |
| Divide | Multiply by the reciprocal of the second fraction | 2/3 ÷ 4/9 = 2/3 × 9/4 = 18/12 = 3/2 |
a/b + c/d = (a·d + c·b) ÷ (b·d) · a/b × c/d = (a·c) ÷ (b·d) · a/b ÷ c/d = (a·d) ÷ (b·c)
Simplifying to lowest terms
A fraction is in lowest terms when the numerator and denominator have no common factor other than 1. Divide both by their greatest common divisor (GCD). For 18/12 the GCD is 6, so 18/12 = 3/2. The calculator always simplifies the result, which is why 3/4 × 2/5 is shown as 3/10 rather than 6/20.
Worked example: least common denominator
To add 5/12 + 7/18, you could multiply the denominators (12 × 18 = 216), but the numbers stay smaller with the least common multiple of 12 and 18, which is 36.
- 5/12 = 15/36 (multiply top and bottom by 3)
- 7/18 = 14/36 (multiply top and bottom by 2)
- 15/36 + 14/36 = 29/36, already in lowest terms.
Using 216 gives 90/216 + 84/216 = 174/216, which simplifies to the same 29/36. Both routes are correct; the smaller denominator just means less simplifying at the end.
Worked example: mixed numbers
2 3/4 − 1 5/6. First convert each mixed number to an improper fraction: 2 3/4 = (2 × 4 + 3)/4 = 11/4 and 1 5/6 = (1 × 6 + 5)/6 = 11/6. The least common denominator is 12, so 33/12 − 22/12 = 11/12.
1 1/2 × 2 2/3. Convert: 3/2 × 8/3 = 24/6 = 4. A common mistake is to multiply the whole numbers and the fractions separately (1 × 2 and 1/2 × 2/3), which gives 2 1/3, the wrong answer.
Negative fractions
A minus sign on a mixed number applies to the whole value: −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2. Enter the minus sign on the whole number (or on the numerator when there is no whole number). For example, −1 1/2 + 1/4 = −6/4 + 1/4 = −5/4 = −1 1/4.
Fractions in daily life
- Cooking: halving a recipe that needs 3/4 cup of milk gives 3/4 × 1/2 = 3/8 cup. To scale whole recipes, the ratio calculator is quicker.
- Measurements: imperial tape measures use 1/16-inch steps, so adding 2 3/8 in and 1 7/16 in gives 3 13/16 in.
- Percentages: any fraction can be turned into a percentage by dividing and multiplying by 100, so 3/8 = 0.375 = 37.5%. See the percentage calculator.
Common mistakes
- Adding denominators: 1/2 + 1/3 is not 2/5. Always find a common denominator first.
- Flipping the wrong fraction when dividing: only the second fraction (the divisor) is turned upside down.
- Forgetting to convert mixed numbers before multiplying or dividing.
- Leaving answers unsimplified when a teacher or form expects lowest terms.
Converting a decimal to a fraction
Write the decimal over a power of ten with as many zeros as there are decimal places, then simplify. 0.375 = 375/1000; the GCD of 375 and 1000 is 125, so 0.375 = 3/8. Likewise 0.6 = 6/10 = 3/5 and 2.25 = 225/100 = 9/4 = 2 1/4. Repeating decimals need a different trick: 0.333… is exactly 1/3 and 0.1666… is 1/6, while 0.33 typed as a finite decimal is 33/100, slightly less than one third.
Comparing two fractions
To see which of two fractions is larger without a calculator, cross-multiply. For 5/8 and 3/5, compare 5 × 5 = 25 with 3 × 8 = 24; since 25 is larger, 5/8 is the larger fraction (0.625 against 0.6). The same check tells you whether two fractions are equal: 4/6 and 6/9 give 36 and 36, so they are equivalent, both simplifying to 2/3. Subtracting one fraction from the other in the calculator gives the size of the difference: 5/8 − 3/5 = 1/40.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions with a common denominator, add the numerators, and simplify. For 1/2 + 1/3, use sixths: 3/6 + 2/6 = 5/6.
How do you divide fractions?
Keep the first fraction, change division to multiplication, and flip the second fraction. 2/3 ÷ 4/9 = 2/3 × 9/4 = 18/12 = 3/2 = 1 1/2.
How do I turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator: 11/4 = 2 remainder 3, so 2 3/4.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 5/6 = 5 ÷ 6 ≈ 0.833333.
How do I convert 0.375 to a fraction?
Write it as 375/1000 and divide both by their GCD, 125, to get 3/8.
Sources
- Common Core State Standards for Mathematics, Number and Operations—Fractions (grades 3–6).
- Khan Academy, Fractions: adding, subtracting, multiplying and dividing.
Last reviewed 8 October 2026. Results are estimates; see our disclaimer.