How to solve it
- Multiply the whole part by the denominator.
- Add the numerator to the product.
- The result is the new numerator.
- Keep the denominator.
3 2/5 = (3 × 5 + 2)/5 = 17/5
Result: 17/5
Common mistake:Wrong: 2 3/4 = 5/4.Right: 2 3/4 = 11/4.Adding the whole part and the numerator ignores that each whole has several parts: 2 wholes are 8 quarters.
Enter the sign, the whole part, the numerator and the denominator, and the calculator returns the improper fraction with the work that justifies it. To go the other way, use improper fraction to mixed number.
Worked example: 2 3/5
A board is 2 3/5 feet long, and you want the length as a single fraction of a foot. What is it?
- Multiply the whole number by the denominator. 2 × 5 = 10.
- Add the numerator. 10 + 3 = 13.
- Keep the denominator: the 5 does not change, so you get 13/5.
- Reduce if possible. 13 is prime and does not divide 5, so the fraction is already in lowest terms.
Result: 13/5 of a foot.
Check: 13 ÷ 5 gives quotient 2 and remainder 3, which are the whole part and the numerator again. As decimals, both equal 2.6.
Why you multiply the whole number by the denominator
Each whole unit contains as many parts as the denominator says. With fifths, one unit is 5/5, so 2 units are 10/5. Add the 3 parts from the fraction to those 10 and the total is 13 fifths. The multiplication only counts the parts inside the wholes, which is why the denominator does not change: each part stays the same size.
A mixed number is a whole number plus a fraction, and the English Wikipedia describes it as the sum of a non-zero integer and a proper fraction, with the improper fraction as an equivalent form. Writing it as an improper fraction lets you multiply, divide or raise to a power without splitting the two parts. The mixed number calculator does that conversion and the operation in one step.
What changes with the sign, zero and a common factor
The rule is always the same, but in three cases the result looks different. The table shows the calculation for each and what the calculator returns.
| Case | Calculation | Result |
|---|---|---|
| Negative mixed number: −4 1/3 | −(4 × 3 + 1)/3 | −13/3 |
| Can be reduced: 1 2/4 | (1 × 4 + 2)/4 = 6/4 | 3/2 |
| Zero fraction part: 3 0/7 | (3 × 7 + 0)/7 = 21/7 | 3 |
In the reducible case, 6 and 4 share the factor 2, and 6/4 and 3/2 have the same value. Reducing changes the digits you write, not the amount. With a whole part of 0, as in 0 3/8, the calculation is (0 × 8 + 3)/8 = 3/8, and the mixed number was already the fraction 3/8. If you only want to reduce a fraction you already have, use simplify fractions.
The fraction part must be proper, with the numerator smaller than the denominator, and the denominator cannot be 0. The input accepts whole-number digits only, up to 100 per field; if your mixed number has a decimal, convert it first with decimal to fraction.
If you need a different conversion
To go the other way, from an improper fraction to a mixed number, use the improper fraction to mixed number calculator. The improper fractions and mixed numbers worksheets let you practice the conversion and its check, with answers. The guide to types of fractions explains when a fraction counts as proper, improper or mixed, and the fraction calculator uses the resulting fraction in any operation.
Source: English Wikipedia, article Fraction, section “Mixed numbers”, which defines a mixed number as the sum of a non-zero integer and a proper fraction and explains how to convert it to an improper fraction.
Frequently asked questions
How do I turn an amount like 2 hours 15 minutes into a fraction?
Write the minutes as a fraction of an hour: 2 hours 15 minutes is 2 15/60 hours. With the rule, (2 × 60 + 15)/60 = 135/60, which reduces to 9/4 of an hour. To go the other way, use fraction of an hour to minutes.
What do I do if the fraction part is greater than 1, as in 1 7/5?
That entry is not a mixed number, because the fraction in a mixed number is proper. Add the two parts: 1 + 7/5 = 5/5 + 7/5 = 12/5. You can also first write 7/5 as 1 2/5 and get 2 2/5, which gives the same fraction.
How do I turn a mixed number into a decimal?
Convert to a fraction first and divide the numerator by the denominator. With 1 3/4 you get 7/4 = 1.75. You can also divide only the fraction part, 3 ÷ 4 = 0.75, and add it to the whole number. For repeating decimals, such as 1/6 = 0.1666… (0.16 with a bar over the 6), see fraction to decimal.