Fraction Calculator
Your details
Result
Answer
- As a mixed number
- 1 7/12
- As a decimal
- 1.583333
- Before simplifying
- 38/24
- Working
- 3/4 + 5/6 = (3×6 + 5×4) / (4×6) = 38/24
- As a percentage
- 158.3333%
- The least common denominator of 4 and 6 is 12, not 24. Cross-multiplying always works and is easier to remember, but using the LCD keeps the numbers smaller — 12 here instead of 24.
- 38/24 simplifies to 19/12 by dividing both parts by 2.
- 19/12 is an improper fraction — the numerator is larger than the denominator — which is why it also has a mixed-number form.
Common fraction equivalents
The decimal and percentage for fractions that come up constantly.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333 | 33.33% |
| 2/3 | 0.6667 | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.50% |
| 3/8 | 0.375 | 37.50% |
| 5/8 | 0.625 | 62.50% |
| 1/16 | 0.0625 | 6.25% |
How do you add fractions?
To add fractions, give them a common denominator by cross-multiplying, then add the numerators. For 3/4 + 5/6, multiply to get 18/24 + 20/24, which is 38/24, and simplify to 19/12. Multiplying fractions needs no common denominator — multiply the tops and the bottoms.
a/b + c/d = (ad + cb)/bd a/b × c/d = ac/bd a/b ÷ c/d = ad/bc- a, c
- The numerators — the top numbers
- b, d
- The denominators — the bottom numbers
Addition and subtraction need the two fractions to describe parts of the same size, which is what a common denominator provides. Cross-multiplying onto b×d always works and is the easiest rule to remember, though it can produce larger numbers than necessary — the least common denominator of 4 and 6 is 12, not 24, so 3/4 + 5/6 can be done as 9/12 + 10/12 instead of 18/24 + 20/24. Both reach 19/12. Multiplication is the simplest of the four and the one people expect to be harder: multiply the numerators, multiply the denominators, done — no common denominator required. Division is multiplication by the reciprocal, which is the same rule with the second fraction flipped. Simplifying at the end means dividing both parts by their greatest common divisor, and it is not optional in most schoolwork: 38/24 and 19/12 are the same number, but only one is in lowest terms.
- To add or subtract, find a common denominator for both fractions.
- Multiply each numerator by the other fraction's denominator.
- Add or subtract the numerators, keeping the denominator.
- To multiply, multiply the numerators and the denominators.
- To divide, flip the second fraction and multiply instead.
- Divide both parts by their greatest common divisor to simplify.
Worked example: Adding 3/4 and 5/6
Adding 3/4 and 5/6
The denominators 4 and 6 differ, so the fractions describe parts of different sizes and cannot be added directly. Cross-multiplying puts both over 4 × 6 = 24: the first becomes 3 × 6 = 18 over 24, and the second becomes 5 × 4 = 20 over 24. Now the parts match, so add the numerators: 18 + 20 = 38, giving 38/24. That is not in lowest terms — the greatest common divisor of 38 and 24 is 2, so dividing both gives 19/12. Because 19 is larger than 12 it is an improper fraction, which as a mixed number is 1 7/12, and as a decimal 1.583333. Using the least common denominator of 12 instead of 24 reaches the same place with smaller numbers: 9/12 + 10/12 = 19/12 directly, with no simplifying step needed.
What each fraction input means
- Operation
- What to do with the two fractions. Addition and subtraction need a common denominator first.
- First numerator
- The top number of the first fraction.
- First denominator
- The bottom number of the first fraction. Cannot be zero.
- Second numerator
- The top number of the second fraction.
- Second denominator
- The bottom number of the second fraction. Cannot be zero.
What this fraction does not account for
- A denominator of zero is undefined, not infinity. A fraction is a division, and division by zero has no value.
- Dividing by a fraction whose numerator is zero is division by zero, which this calculator rejects rather than returning a misleading result.
- Cross-multiplying always works but does not always give the least common denominator. The answer is the same once simplified; the intermediate numbers are just larger.
- Negative fractions are handled with the sign kept on the numerator, so the result reads −1/2 rather than 1/−2. Both mean the same thing, but only one is conventional.
- Repeating decimals are shown to six places and truncated. One third is 0.333333, not exactly — the fraction is the precise form, which is why fractions are preferred in exact work.
- This handles two fractions at a time. For a longer expression, work left to right respecting the usual order of operations.
Frequently asked questions
How do you add fractions with different denominators?
Give them a common denominator first. Multiply each numerator by the other's denominator and both denominators together: 3/4 + 5/6 becomes 18/24 + 20/24 = 38/24, which simplifies to 19/12.
How do you multiply fractions?
Multiply the numerators together and the denominators together. No common denominator is needed, which makes multiplication simpler than addition: 3/4 × 5/6 = 15/24, which simplifies to 5/8.
How do you divide fractions?
Flip the second fraction and multiply. Dividing by 5/6 is the same as multiplying by 6/5, so 3/4 ÷ 5/6 = 3/4 × 6/5 = 18/20, which simplifies to 9/10.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 38/24 that divisor is 2, giving 19/12. If the only common factor is 1, the fraction is already in lowest terms.
What is an improper fraction?
One where the numerator is larger than the denominator, like 19/12. It is a perfectly valid number and can be written as the mixed number 1 7/12 instead, which is often easier to picture.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. 19 ÷ 12 = 1.583333. Some fractions give exact decimals, like 3/4 = 0.75, while others repeat forever, which is why the fraction is the precise form.
Sources and review
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