How to use the fraction calculator
The Convert tab opens first: type a fraction, a mixed number, a decimal or a percent and it shows every other form at once, finds the closest simple fraction to a decimal, and shows the long division and simplifying steps. For arithmetic, open Calculate. Type your first fraction, pick plus, minus, times or divided by, and type the second. The answer appears at once as a simplified fraction, a mixed number, a decimal and a percent, and the list on the right writes out every step. Press Play under See it to watch the answer built from pieces. A third fraction is one button away. Multiplying and dividing are done before adding and subtracting, the same order a calculator follows, and the steps say so when it matters.
Two more tabs sit beside them. Tape measure finds the nearest mark for a length in inches or millimeters and splits it into equal parts. Chart prints a table of fractions of an inch with decimals and millimeters. Nothing you type leaves your device.
Adding and subtracting fractions
You can only add pieces that are the same size. Halves and thirds are different sizes, so first cut both into the same number of equal pieces. The best number to cut into is the smallest one that both bottoms divide into, the least common multiple. For 1/2 and 1/3 that number is 6.
1/2 = 3/6 (multiply top and bottom by 3)
1/3 = 2/6 (multiply top and bottom by 2)
3/6 + 2/6 = 5/6
Once the bottoms match, add or subtract the tops and keep the bottom. The pieces did not change size, so the bottom does not change. The calculator shows this as two bars re-cut into six pieces, then shaded pieces slid together into one row.
Multiplying and dividing fractions
Multiplying fractions needs no common bottom: multiply the tops together and the bottoms together. A picture shows why. Cut a square into columns for the first fraction and rows for the second, and the overlap is the answer. For 2/3 × 3/4, the overlap is 6 pieces out of 12, which is 1/2.
Dividing asks how many of the second fraction fit into the first. To work it out, flip the second fraction and multiply. The flip of 1/8 is 8/1, so 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. Six eighths-sized pieces fit into three quarters. You cannot divide by zero, and the calculator tells you so instead of giving a number.
Simplifying and the greatest common divisor
A fraction is in lowest terms when no whole number other than 1 divides both the top and the bottom. To simplify, find the greatest common divisor and divide both by it. The Euclidean algorithm finds it with repeated division: divide the larger number by the smaller, keep the remainder, and repeat until the remainder is zero. The last number you divided by is the answer. For 48 and 18, 48 ÷ 18 leaves 12, 18 ÷ 12 leaves 6, and 12 ÷ 6 leaves 0, so the greatest common divisor is 6 and 18/48 becomes 3/8. Press Show the simplifying steps on the Convert tab to see it for any fraction.
Mixed numbers and improper fractions
A mixed number is a whole number plus a fraction, like 2 3/8. An improper fraction has a top that is at least as big as its bottom, like 19/8. To change a mixed number to an improper fraction, multiply the whole by the bottom, add the top, and keep the bottom: 2 × 8 + 3 = 19, so 2 3/8 = 19/8. To go back, divide the top by the bottom. The quotient is the whole part and the remainder is the new top. Adding 1 3/4 and 5/8 gives 19/8, which is 2 3/8.
Fractions as decimals
To turn a fraction into a decimal, divide the top by the bottom by long division. Some fractions end, like 3/8 = 0.375. Others repeat forever, like 1/7 = 0.142857142857…, where the six digits 142857 repeat. A fraction in lowest terms ends exactly when its bottom has no prime factor other than 2 and 5. That is why every tape-measure fraction, whose bottoms are 2, 4, 8, 16, 32 and 64, has an exact decimal, and why thirds and sevenths never do. The calculator marks the repeating digits with a bar, and works with exact whole-number ratios, so 1/3 + 1/6 is exactly 1/2 and never 0.49999. The same idea explains a famous puzzle: three thirds make exactly 1, but three copies of 0.33 make 0.99, and three copies of 0.333 make 0.999. Each extra 3 shrinks the gap without closing it. Only a decimal whose 3s never stop equals 1/3, so a rounded decimal can never replace the fraction. The Convert tab has a short animation of this.
Fractions on a tape measure
A tape measure marks the inch by halving. Between each pair of inch marks sits a half-inch mark, then quarter marks, eighths, sixteenths, and on finer tapes thirty-seconds and sixty-fourths. Each size is made by cutting the one before it in two. The longest lines are the inches, and the lines get shorter as the fractions get smaller. Most tapes sold for building mark sixteenths along the whole blade, and some add 1/32 marks in the first foot.
An inch is exactly 25.4 millimeters, so converting is exact too: 5/8 of an inch is 15.875 millimeters, 1/16 is 1.5875 millimeters, and 1/64 is 0.396875 millimeters. When a length falls between marks, pick the nearest one. The Tape measure tab shows how far off each choice is, so you can decide whether 1/16 is close enough or whether you need a finer mark.
Mistakes that give the wrong answer
- Adding the tops and the bottoms. 1/2 + 1/3 is not 2/5. The pieces must be the same size first.
- Forgetting to flip when dividing. 3/4 ÷ 1/8 is 6, not 3/32.
- Reading a mixed number as a product. 2 3/8 is 2 + 3/8, not 2 × 3/8.
- Typing a decimal into a fraction box. Use the Convert tab for decimals.
- Rounding to a tape mark too early. Do the arithmetic exactly, then round once at the end.
- Mixing units. Inches and millimeters in one sum give nonsense until one is converted.
Where the numbers come from
- Inch and millimeter: one inch is exactly 25.4 millimeters (NIST SP 811, Appendix B.8, and NIST's SI units page for length).
- Greatest common divisor and the Euclidean algorithm: a standard method for finding the greatest common divisor, also used to reduce fractions to simplest form.
- Terminating and repeating decimals: a fraction repeats when its bottom has a prime factor other than 2 or 5 (the standard result on repeating decimals).
- Fraction rules for adding, subtracting, multiplying, dividing and mixed numbers are standard arithmetic.
- Decimal equivalents such as 1/8 = 0.125 and 1/64 = 0.015625 are exact division, and match published decimal-inch charts.
- Rounding to a tape mark: the page rounds to the nearest mark and sends an exact halfway to the larger one. This is this page's choice, not a published standard.
Questions
How do you add fractions with different bottoms?
Cut both into the same number of equal pieces, using the smallest number that both bottoms divide into, then add the tops and keep the bottom. For 1/2 + 1/3, use 6: 3/6 + 2/6 = 5/6.
How do you add mixed numbers?
Change each to an improper fraction, add as usual, then change back. 1 3/4 + 5/8 is 7/4 + 5/8 = 14/8 + 5/8 = 19/8, which is 2 3/8. The calculator shows these steps.
How do you divide fractions?
Flip the second fraction and multiply. 3/4 ÷ 1/8 = 3/4 × 8/1 = 6. It asks how many of the second fit into the first.
How do you simplify a fraction?
Divide the top and bottom by their greatest common divisor. 18/48 divided by 6 on both gives 3/8. If the only common divisor is 1, the fraction is already simplified.
Is the answer rounded?
No. The page uses exact whole-number ratios for every operation. The decimal shows repeating digits with a bar. Only the nearest tape mark is a rounded value, and it is labeled with how far off it is.
How big a number can I type?
Up to 30 digits in each box. Longer answers are shortened on screen with their digit count, and copy and share keep the full values you typed.
What is 5/8 of an inch in millimeters?
15.875 millimeters, because one inch is exactly 25.4 millimeters.
Can I share my sum?
Yes. Share saves only the fractions and the signs between them for 90 days so the link can show the sum and its answer. It makes a picture for Facebook and a short video for TikTok.