Using the calculator
Type a mixed number with a space between the whole number and the fraction, like 3 2/5, and the improper fraction appears straight away. To go the other way, press swap and type an improper fraction like 17/5. Both directions show the steps, the simplest form when it can be simplified, the decimal, and fraction bars.
Mixed number to improper fraction
Multiply the whole number by the bottom of the fraction, add the top, and put the total over the same bottom. For 3 2/5, 3 × 5 = 15, plus 2 is 17, so it's 17/5.
The fraction bars show why. Each whole is 5 fifths, so 3 wholes are 15 fifths, and the extra 2 fifths make 17 fifths. Improper fractions are easier to multiply and divide with, which is why the fraction calculator turns mixed numbers into them first.
Improper fraction to mixed number
Divide the top by the bottom. The whole-number answer is the whole number, and the remainder goes over the same bottom. 17 ÷ 5 is 3 remainder 2, so 17/5 = 3 2/5. If there's no remainder, the fraction is a whole number, so 15/5 is 3.
An improper fraction is one whose top is at least as big as its bottom, so it's worth 1 or more. That's improper only in name, and 17/5 is a perfectly good number, and in algebra it's usually preferred to 3 2/5.
Questions
What is 2 1/2 as an improper fraction?
5/2. 2 × 2 = 4, plus 1 is 5, over 2.
What about negative mixed numbers?
The minus applies to the whole thing: −2 1/2 means −(2 + 1/2), which is −5/2. Convert as if it were positive, then put the minus back.
Should I simplify first?
It doesn't matter for the conversion. 10/4 gives 2 2/4, which simplifies to 2 1/2, the same as 5/2 gives. The calculator shows the simplest form too.
Sources
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