Improper fraction calculator, drawn as bars.

An improper fraction calculator converts a fraction whose top is larger than its bottom, such as 17/5, into a mixed number, 3 2/5, and converts mixed numbers back into improper fractions. It writes out the division or the multiplication, simplifies the result, shows the value as a decimal, and draws it as bars so you can see how many wholes and how many parts it holds.

How to use the improper fraction calculator

1. Choose a direction under Convert: Improper to mixed or Mixed to improper.
2. Type the number in Fraction or mixed number. Write a fraction as 17/5 and a mixed number as 3 2/5.
3. Read the big answer and the cards beside it. The bars show each whole as a full bar and the leftover as a part bar.
4. Open The steps for the working, and use Copy result to take the answer with you.

Improper fraction to mixed number

Divide the top by the bottom. The whole number part of the answer is the new whole number, and the remainder goes over the same bottom number. For 17/5, 17 ÷ 5 = 3 with remainder 2, so the mixed number is 3 2/5. In the bars, that is three full bars of five parts and one bar with two parts filled.

If the remainder fraction can be simplified, do it last. 22/8 gives 22 ÷ 8 = 2 remainder 6, so 2 6/8, and dividing 6 and 8 by 2 gives 2 3/4. If there is no remainder, the answer is a whole number: 9/9 = 1.

Mixed number to improper fraction

Multiply the whole number by the bottom number, add the top, and keep the bottom. For 3 2/5, 3 × 5 = 15, and 15 + 2 = 17, so the answer is 17/5. For 6 3/7, 6 × 7 = 42 and 42 + 3 = 45, so 45/7.

Quarters as a pattern

Each time the top goes up by 4, one more whole is added. The remainder of 1, 2 or 3 sets the fraction. Negative values keep the same pattern with a minus sign in front: −11/4 is −2 3/4.

Check your answer

To check, convert back. 3 2/5 should give 3 × 5 + 2 = 17 over 5. If it does not, the remainder was put over the wrong bottom number, which is the most common slip.

Common problems

• The calculator does not change a fraction like 3/5, because its top is smaller than its bottom. That is a proper fraction and has no whole part.
• You get a different answer from your book for 22/8. Books often stop at 2 6/8 and some ask for lowest terms. The calculator gives the simplest form, 2 3/4.
• The picture is not drawn for large numbers. Bars are shown for bottoms up to 24 and up to 12 wholes.

To add, subtract, multiply or divide, use the mixed fraction calculator. To see the decimal for a mixed number, try mixed number to decimal.