Fractions, step by step
Fractions come up in recipes, measurements, homework and anywhere a whole gets split. The rules are simple, but there are a lot of small steps: find a common denominator, turn mixed numbers into improper fractions, flip the second fraction to divide, and simplify at the end. Miss one and the answer is wrong.
This fraction calculator does each step for you and shows it, so you can check your own work or learn the method. It handles mixed numbers like 1 3/4, negative fractions, simplifying and turning decimals into fractions.
How to use it
- Choose Two fractions, Simplify, or Decimal to fraction.
- For a mixed number like 1 3/4, put 1 in the whole number box, 3 on top and 4 on the bottom. For a plain fraction, leave the whole number at 0.
- Pick +, −, × or ÷ and fill in the second fraction.
- Read the answer as a mixed number and an improper fraction, with the decimal and the steps below.
The fraction rules
a/b + c/d = (a × d + c × b) ÷ (b × d)
a/b × c/d = (a × c) ÷ (b × d)
a/b ÷ c/d = a/b × d/c
mixed to improper: w n/d = (w × d + n)/dMixed numbers carry their sign on the whole number, so −1 1/2 means minus one and a half. For a negative fraction without a whole number, put the minus sign on the top number instead, like −3 over 4. The bottom number can never be 0, because nothing can be split into zero equal parts.
For adding and subtracting, the calculator uses the lowest common denominator rather than simply multiplying the two denominators, which keeps the numbers small. Every answer is simplified by dividing the top and bottom by their greatest common factor, so you always see the simplest form.
Worked example: 1 3/4 + 2/3
- Turn the mixed number into an improper fraction: 1 3/4 = 7/4
- Lowest common denominator of 4 and 3: 12
- Rewrite both: 7/4 = 21/12 and 2/3 = 8/12
- Add the tops: 21/12 + 8/12 = 29/12
- As a mixed number: 29 ÷ 12 = 2 remainder 5, so 2 5/12
The answer is 2 5/12, or 29/12 as an improper fraction, which is about 2.4167 as a decimal. Switch to Decimal to fraction and 0.375 becomes 3/8; switch to Simplify and 18/24 becomes 3/4.
Common fractions and decimals
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.3% |
| 1/4 | 0.25 | 25% |
| 3/8 | 0.375 | 37.5% |
| 2/3 | 0.666... | 66.7% |
| 3/4 | 0.75 | 75% |
| 5/8 | 0.625 | 62.5% |
Where fraction sums go wrong
- Adding the denominators. 1/2 + 1/3 is 5/6, not 2/5.
- Forgetting to convert mixed numbers before multiplying. 1 1/2 × 2 is 3, not 2 1/2.
- Flipping the wrong fraction when dividing. Flip the second one only.
- Leaving an answer unsimplified. 6/8 is right, but 3/4 is what most teachers expect.
- For more than two fractions or a long sum, the scientific calculator shows fraction answers when they are simple.
Frequently asked questions
How do I add fractions with different denominators?
Find the lowest common denominator, rewrite each fraction over it, then add the tops. For 1/4 + 1/6, the lowest common denominator is 12, so 3/12 + 2/12 = 5/12. The calculator shows the common denominator it used and simplifies the result for you.
How do I divide fractions?
Flip the second fraction upside down and multiply. 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8, which is 1 7/8 as a mixed number. With mixed numbers, turn them into improper fractions first. Choose ÷ above and each step is written out.
How do I turn a decimal into a fraction?
Write the decimal over 10, 100 or 1,000 depending on how many decimal places it has, then simplify. 0.375 has three places, so it is 375/1000, which simplifies to 3/8. Choose Decimal to fraction above to do it for any decimal up to nine places.
How do I simplify a fraction?
Divide the top and bottom by their greatest common factor, the largest number that divides both exactly. For 18/24 that number is 6, giving 3/4. Choose Simplify above; the calculator finds the factor, shows the division and gives the decimal as well.
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