This fraction calculator adds, subtracts, multiplies, or divides two fractions, then simplifies the result. Enter both numerators and denominators, pick an operation, and read the reduced fraction. The default path adds 1/2 and 1/3 to get 5/6.
Students use it for homework checks. Adults use it for recipes, shop measurements, and quick share math. For related number skills, try the long division calculator or the mean median mode range calculator.
How the formula works
Addition and subtraction use a common denominator: (n1×d2 ± n2×d1) over (d1×d2). Multiplication multiplies tops and bottoms. Division multiplies the first fraction by the reciprocal of the second. After each path, divide numerator and denominator by their greatest common divisor so the answer is in lowest terms.
Worked example
Defaults: 1/2 + 1/3. Common denominator 6. Numerators become 3 and 2. Sum is 5/6, already reduced.
| Input | Value |
|---|---|
| Fraction 1 | 1/2 |
| Fraction 2 | 1/3 |
| Operation | Add |
| Result | 5/6 |
How to use the fields
- Numerator 1 and denominator 1 define the first fraction.
- Numerator 2 and denominator 2 define the second fraction.
- Operation chooses add, subtract, multiply, or divide.
When fraction math beats decimals
Exact shares stay exact in fraction form. A repeating decimal can hide error when you round early. Keep fraction form through the steps, then convert to a decimal only if a display or measurement needs it.
Common mistakes
- Adding numerators and denominators separately instead of using a common denominator
- Forgetting to flip the second fraction when dividing
- Leaving a result unsimplified when the teacher wants lowest terms
- Entering a zero denominator
Recipes and household use
Scaling a recipe from 2/3 cup to a half batch is fraction multiplication. Combining leftover paint amounts is often addition. Run the calculator once, then write the simplified amount on your shopping list so you do not rework the arithmetic at the store.
Classroom habits that stick
Write both fractions, name the operation, show the unreduced form, then reduce. That habit makes errors easier to spot. If the unreduced numerator and denominator share no factors other than 1, you already have lowest terms.
Negative fractions
If a result is negative, the tool keeps the sign on the numerator after reduction and keeps the denominator positive. That matches common classroom style and avoids double sign confusion.
Comparing results
After you simplify, cross multiply to compare two fractions, or convert both to a shared denominator. The calculator gives you the operated result; comparison of two final answers is a second step you can do by eye once both are reduced.
Practice with other operations
After you trust addition, switch the operation to subtract and compare 1/2 minus 1/3. The common denominator is still 6, and the result reduces to 1/6. Multiply next: 1/2 times 1/3 is 1/6 before or after reducing. Divide 1/2 by 1/3 by multiplying by 3/1 to get 3/2.
Working all four operations on the same pair builds fluency. Write the unreduced form once, then reduce, so you can see where a slip happened if the final answer looks wrong.
Sharing and fair splits
Fraction language shows up whenever people share a bill, a pizza, or a project bonus. If three people split two identical cakes evenly, each person gets 2/3 of a cake. If you already ate 1/2 of your share, you have 1/3 of a cake left. Tools like this keep those steps honest when mental math gets messy.
In construction and crafts, fractional inches are still common. Adding 3/8 and 5/16 needs a common denominator of 16. Enter 3/8 as 3 and 8, then 5 and 16, choose add, and read the simplified total before you mark a cut line.
From fractions to percents
Once you have a reduced fraction, you can convert to a decimal by dividing numerator by denominator, then to a percent by multiplying by 100. Keep the fraction for exact work and convert only when a percent display helps stakeholders. Do not round early if later steps still need exact values.
If two reduced fractions look different but might be equal, cross multiply. Equal products mean equal fractions. That check is faster than converting both to long decimals.
Teaching tips for parents and tutors
Ask the learner to estimate before calculating. One half plus one third should land between one half and one, so an answer like 5/6 passes a sanity check while 5/2 does not. Estimation catches operation mix ups faster than staring at algebra alone.
Keep a short error log: wrong operation, forgot to flip for division, or stopped before reducing. Patterns in that log tell you which habit to practice next session.
Limitations
This page works with two integer fractions and one operation at a time. Long expression chains need stepwise entry. Mixed numbers should be converted to improper fractions before you type them in.