Fraction Calculator with Steps – Mixed Numbers & Decimals

Stuck on 2 ⅓ + 1 ¾, or wondering what 0.1666… is as a fraction? Type it into this fraction calculator and you’ll get the answer in its simplest form, plus the working behind it: the common denominator, the cancelling, the flip for division. Mixed numbers, negatives and repeating decimals all work, and every result is shown as a fraction, decimal and percent at once.

How to Type Fractions into the Calculator

• A plain fraction: leave the big box empty and fill in the top and bottom, like 3 over 4.
• A mixed number: put the whole number in the big box. For 2¾, type 2, then 3 over 4.
• A whole number: type it in the big box and leave the fraction empty.
• A negative: put the minus sign on the whole number (−1 ½) or on the top number (−2 over 5).
• A repeating decimal: on the Decimal tab, wrap the repeating part in brackets. 0.(3) means 0.333…, and 0.1(6) means 0.1666…

Press Enter to jump to the next box.

The Four Operations at a Glance

Adding and Subtracting: Find the Common Denominator

You can only add or subtract fractions when they’re cut into the same size pieces, so the bottom numbers must match first.

Take 5/12 + 3/8. The smallest number both 12 and 8 divide into is 24, the lowest common denominator. Multiply the top and bottom of each fraction to reach it: 5/12 becomes 10/24, and 3/8 becomes 9/24. Now add the tops and keep the bottom: 19/24.

Multiplying the two bottom numbers (12 × 8 = 96) also works, but you end up with bigger numbers to simplify later. The calculator always uses the lowest one.

Multiplying: Cancel First

To multiply fractions, multiply the tops together and the bottoms together. No common denominator needed.

It’s easier if you cancel before you multiply. In 4/9 × 3/8, the 4 and the 8 share a factor of 4, and the 3 and the 9 share a factor of 3. Cancel them and you’re left with 1/3 × 1/2 = 1/6. Multiplying straight through gives 12/72, which simplifies to the same answer with more work.

Dividing: Keep, Change, Flip

Dividing by a fraction is the same as multiplying by its reciprocal, the fraction turned upside down. Teachers often call it keep, change, flip:

1. Keep the first fraction: 3/4
2. Change ÷ to ×
3. Flip the second fraction: 2/5 becomes 5/2

3/4 × 5/2 = 15/8, which is 1 7/8 as a mixed number. Only the second fraction flips. Flipping the first one, or both, is the most common division mistake.

Mixed Numbers Without the Mess

Turn mixed numbers into improper fractions first, do the sum, then turn the answer back. To convert 2 ⅓, multiply the whole number by the bottom and add the top: 2 × 3 + 1 = 7, so 2 ⅓ = 7/3.

For 3 ¼ − 1 ⅔: that’s 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12. Working with improper fractions avoids the “borrowing” step that trips people up when the second fraction part is bigger than the first.

A negative mixed number is negative all the way through: −1 ½ means −(1 + ½), which is −3/2, not −1 + ½.

Simplifying with the Greatest Common Factor

A fraction is in simplest form when the top and bottom share no factor except 1. To get there, divide both by their greatest common factor (GCF).

For small numbers you can often spot it: 18/24 → both divide by 6 → 3/4. For bigger numbers, Euclid’s method finds it every time. For 84/36: 84 = 2 × 36 + 12, then 36 = 3 × 12 + 0. The last number you divided by, 12, is the GCF, so 84/36 = 7/3, or 2 ⅓. The Simplify tab shows this working for any fraction.

Decimals and Repeating Decimals to Fractions

Ending decimals: count the digits after the point and write the number over 10, 100, 1000 and so on. 0.75 has two digits, so it’s 75/100 = 3/4. 2.125 is 2125/1000 = 2 ⅛.

Repeating decimals need one more step. For 0.1666… (written 0.1(6) in the calculator):

1. Let x = 0.1666…
2. Multiply so the repeating parts line up: 100x = 16.666… and 10x = 1.666…
3. Subtract: 90x = 15, so x = 15/90 = 1/6.

This is why 0.333 and 0.333… aren’t the same. 0.333 is exactly 333/1000. Only the never-ending 0.333… equals 1/3.

Common Fractions as Decimals and Percents

Percents for repeating decimals are rounded to two places. Any fraction with only 2s and 5s as factors of its bottom number (like 8 or 20) gives a decimal that ends. Anything else, like 3, 7 or 9, repeats.

Where Fraction Answers Go Wrong

• Adding the bottoms. 1/2 + 1/3 isn’t 2/5. The bottoms tell you the piece size; they don’t get added. The answer is 5/6.
• Flipping the wrong fraction when dividing. Only the second one turns over.
• Forgetting to simplify. 6/8 is correct but not finished; 3/4 is.
• Losing the minus sign on a negative mixed number, as shown above.
• Treating a rounded decimal as exact. 0.33 × 3 = 0.99, not 1. Keep the fraction until the last step.

Frequently Asked Questions