Fractions are easy to mangle by hand, especially with different denominators or mixed numbers. This calculator adds, subtracts, multiplies and divides fractions, mixed numbers and decimals, then gives the answer in lowest terms, as a mixed number where that applies, and as a decimal. It handles negatives and refuses to divide by zero.
How to use it
- Enter the first fraction, such as 3/4, 1 1/2 or 0.75.
- Choose add, subtract, multiply or divide.
- Enter the second fraction.
- Read the simplified answer, mixed number and decimal.
When it helps
- Checking maths homework.
- Scaling recipe amounts.
- Adding measurements in woodworking or sewing.
- Teaching how fractions combine.
Good to know
- Write mixed numbers with a space, like 2 1/4.
- Decimals are turned into exact fractions before any maths happens, so 0.75 is treated as exactly 3/4.
- The answer is always reduced as far as it can go.
How fractions are combined
To add or subtract, convert to a common denominator: 1/2 plus 2/3 becomes 3/6 plus 4/6, which is 7/6. To multiply, multiply the tops and the bottoms: 1/2 times 2/3 is 2/6, or 1/3. To divide, flip the second fraction and multiply: 1/2 divided by 2/3 is 1/2 times 3/2, or 3/4.
The tool then reduces the result using the greatest common divisor, and converts improper fractions to mixed numbers.
Worked example: a recipe
A recipe needs 3/4 cup of milk, and you want 1 and a half times as much. Multiply 3/4 by 3/2 to get 9/8, which is 1 1/8 cups. If you want half a recipe, multiply by 1/2 to get 3/8 of a cup.
For carpentry, adding 5/8 and 3/16 inch gives 13/16, the kind of sum that's easy to slip on by hand.
Mixed numbers and decimals
A mixed number such as 2 1/4 is converted to the improper fraction 9/4 before calculating. Decimals are converted exactly: 0.75 becomes 3/4, and 0.125 becomes 1/8. That avoids rounding errors you'd get from working in decimals.
Results show the decimal value too, useful when you need a measurement on a ruler or a spreadsheet.
Common mistakes
Adding the tops and bottoms separately is the classic error: 1/2 plus 1/3 is not 2/5. Another is forgetting to flip when dividing. Always simplify at the end, and check your answer is sensible: adding two positive fractions should give something bigger than either.
Dividing by zero isn't allowed, and the tool will say so.
Fractions in daily life
Recipes, tools, music and sewing all use fractions. A socket set in inches runs 1/4, 5/16, 3/8, 7/16 and so on. Time signatures in music are fractions, and discounts such as one third off are fractions too.
A reliable calculator saves time and prevents measurement mistakes that cost materials.
Estimating first
Before calculating, estimate the answer. If you add two fractions that are each a little over one half, expect a little over one. An estimate helps you spot input mistakes.
Questions
How does it add fractions with different bottoms?
It finds a common denominator for you.
Why does it reject a zero on the bottom?
A fraction with a zero denominator isn't defined.