Quick facts
- •To add fractions with different denominators, first find a common denominator. 1/2 + 1/3 = 3/6 + 2/6 = 5/6, never 2/5.
- •Multiplying needs no common denominator. Multiply the tops, multiply the bottoms, then simplify.
- •Dividing by a fraction means multiplying by its reciprocal: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
- •Simplifying changes how a fraction looks, not its value. 2/4 and 1/2 are the same number.
- •A fraction is a division: 3/4 means 3 ÷ 4 = 0.75.
Quick reference
| Operation | Method | Example |
|---|---|---|
| Add | Find a common denominator, then add the numerators | 1/2 + 1/3 = 3/6 + 2/6 = 5/6 |
| Subtract | Common denominator, then subtract the numerators | 3/4 − 1/4 = 2/4 = 1/2 |
| Multiply | Multiply numerators and denominators | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Multiply by the reciprocal of the second fraction | 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9 |
Worked examples
A recipe needs 3/4 cup of flour. I want to make half. How much flour?
3/8 cup
Half of 3/4 is 3/4 × 1/2 = 3/8. Multiplying needs no common denominator.
I have 1/2 of a pizza and my friend has 1/3. How much do we have together?
5/6 of a pizza
Use a common denominator of 6: 1/2 = 3/6 and 1/3 = 2/6. Then add the tops: 3/6 + 2/6 = 5/6.
A 5/8 inch board is cut into 3 equal pieces. How thick is each?
5/24 inch
5/8 ÷ 3 = 5/8 × 1/3 = 5/24. Dividing by a whole number is the same as multiplying by its reciprocal.
What is 2 1/2 + 1 3/4?
4 1/4
Convert to improper fractions: 5/2 + 7/4 = 10/4 + 7/4 = 17/4. Dividing 17 by 4 gives 4 remainder 1, so the answer is 4 1/4.
Adding tops and bottoms straight across
The mistake
Writing 1/2 + 1/3 = 2/5 by adding both numerators and both denominators.
Do this instead
Find a common denominator first. 1/2 becomes 3/6 and 1/3 becomes 2/6. Add only the numerators: 3/6 + 2/6 = 5/6.
Why it matters
The wrong method gives 2/5, which is 0.4. The correct answer, 5/6, is about 0.833, more than double.
Why a fraction calculator matters
The common denominator step
- •You can only add or subtract fractions once they share the same bottom number.
- •For 1/2 + 1/3 the common denominator is 6, which gives 3/6 + 2/6 = 5/6.
- •Skipping the step gives answers like 2/5, which look fine but are wrong.
- •This calculator shows the converted fractions every time.
Multiplying versus dividing
- •Multiplying fractions is straightforward: tops together, bottoms together.
- •Dividing asks you to flip the second fraction first and then multiply.
- •Mixing the two methods up gives an answer that may look reasonable but is wrong.
- •Each operation here shows its own steps.
Always simplify
- •Teachers and exams normally expect fractions in lowest terms.
- •6/8 and 3/4 are the same value, but 3/4 is the finished answer.
- •Divide the top and bottom by their greatest common factor to simplify.
- •The calculator reduces the result and can show the unsimplified form first.
What makes this fraction calculator useful
Common denominator shown
Every addition and subtraction shows the converted fractions, which is where most mistakes happen.
Automatic simplification
Results are reduced to lowest terms, and the unsimplified form is shown too.
All four operations
Add, subtract, multiply and divide, each with its own steps.
Mixed numbers
Enter a mixed number such as 2 1/2. The working uses an improper fraction and the answer comes back in both forms.
Professional applications
Education
Teachers use step-by-step answers to show how a common denominator works.
1/2 + 1/3 becomes 3/6 + 2/6 = 5/6, written one line at a time.
Cooking
Cooks scale recipes up and down by multiplying every ingredient by a fraction.
Going from 4 servings to 6 means multiplying each amount by 3/2.
Construction and woodworking
Imperial measurements use fractions of an inch, so adding and comparing them is routine.
5/16 inch and 3/8 inch are different sizes: 5/16 is smaller, because 3/8 = 6/16.
Historical context
Frequently asked questions
How do I add fractions with different denominators?+
Convert both to a common denominator, then add the numerators. For 1/2 + 1/3, use 6: 3/6 + 2/6 = 5/6. The least common multiple of the denominators gives the smallest answer to simplify. Multiplying the two denominators also works, but you may need to simplify more.
How do I multiply fractions?+
Multiply the numerators together and the denominators together. 2/3 × 3/4 = 6/12, which simplifies to 1/2. You do not need a common denominator.
How do I divide fractions?+
Multiply by the reciprocal of the second fraction. 2/3 ÷ 3/4 becomes 2/3 × 4/3 = 8/9.
How do I turn an improper fraction into a mixed number?+
Divide the numerator by the denominator. The whole number part is the quotient and the remainder goes over the denominator. 41/10 is 4 remainder 1, so 4 1/10. The calculator shows both forms.
What this calculator cannot do+
It does not handle decimals, irrational numbers or algebraic fractions, and it shows steps without explaining the theory. Practise the steps by hand so you can do them in an exam.