Fraction calculator
Mixed numbers and fractions, with a simplified answer and the steps.
The four operations on fractions
| Operation | How | Example |
|---|---|---|
| Add | Common denominator, add the tops | 1/2 + 1/3 = 3/6 + 2/6 = 5/6 |
| Subtract | Common denominator, subtract the tops | 3/4 − 1/6 = 9/12 − 2/12 = 7/12 |
| Multiply | Tops times tops, bottoms times bottoms | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Flip the second, then multiply | 3/4 ÷ 1/2 = 3/4 × 2 = 3/2 |
Mixed numbers are turned into improper fractions first: 1½ is 3/2, because 1 whole is 2 halves. At the end, an improper answer is turned back into a mixed number by dividing: 7/2 is 3 remainder 1, so 3½.
Questions
How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the tops. For ½ + ⅓ the smallest common denominator is 6: ½ = 3/6 and ⅓ = 2/6, so the sum is 5/6. The calculator shows these steps for your numbers.
How do I divide fractions?
Flip the second fraction upside down and multiply: ¾ ÷ ½ = ¾ × 2/1 = 6/4 = 1½. Dividing by a fraction is the same as multiplying by its reciprocal.
How do I enter a mixed number like 2¾?
Put 2 in the whole-number box, 3 on top and 4 on the bottom. For a negative mixed number such as −2¾, put the minus sign on the whole number only; it applies to the whole thing.
What does simplifying a fraction mean?
Dividing the top and bottom by their greatest common factor, so the fraction uses the smallest whole numbers possible: 18/12 simplifies to 3/2 by dividing both by 6. Every answer here is fully simplified.
Why can’t the denominator be 0?
The bottom number says how many equal parts the whole is split into, and you can’t split something into zero parts. Dividing by a fraction equal to zero is undefined for the same reason.
Is the decimal exact?
The fraction is always exact (the calculator uses whole-number arithmetic with no size limit). Its decimal is shown to up to 10 places; when the decimal repeats forever, like 1/3 = 0.333…, it is rounded and marked with ≈.
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