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Fractions trip people up because each operation has its own rule — you can multiply straight across but you can’t add across, and dividing means flipping the second fraction. This calculator handles all four operations on two fractions and shows the answer three ways: fully reduced, as a mixed number, and as a decimal.
Enter the two fractions, pick an operation, and get the worked result.
Fraction Calculator: step-by-step worked example
Work out 3/4 + 5/6
- First numerator
- 3
- First denominator
- 4
- Operation
- + Add
- Second numerator
- 5
- Second denominator
- 6
- 1
Common denominator
Denominator = d₁ × d₂
4 × 6 = 24
- 2
Expand the numerators and add
Numerator = n₁ × d₂ + n₂ × d₁
3 × 6 + 5 × 4 = 38/24
- 3
Simplify by the GCF
Numerator ÷ GCF / Denominator ÷ GCF
38 ÷ 2 / 24 ÷ 2 = 19/12
- 4
Mixed number
Numerator ÷ Denominator → whole part and remainder
= 1 7/12
- 5
Decimal value
Numerator ÷ Denominator
19 ÷ 12 = 1.5833
- 3/40.7547.4%
- 5/60.833352.6%
Good to know: Never add tops and bottoms separately: 3/4 + 5/6 ≠ 8/10. Find a common denominator first; the least one is the LCM of the denominators (12 here), which keeps the numbers small.
Fraction Calculator — how it works
The four operations
| Operation | Rule |
|---|---|
| Multiply | Multiply numerators, multiply denominators: a⁄b × c⁄d = ac⁄bd |
| Divide | Flip the second, then multiply: a⁄b ÷ c⁄d = a⁄b × d⁄c |
| Add | Common denominator first: a⁄b + c⁄d = (ad + cb)⁄bd |
| Subtract | Same, subtracting: (ad − cb)⁄bd |
Addition and subtraction are the ones people get wrong — you can’t just add numerators and denominators. You need a common denominator first.
Simplifying the result
Every answer is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor. So 6⁄8 becomes 3⁄4, and 4⁄2 becomes 2⁄1 (a whole number).
Mixed numbers and decimals
An improper fraction like 3⁄2 is also shown as the mixed number 1 1⁄2 and the decimal 1.5, so you can use whichever form the task needs — mixed numbers for measurements and cooking, decimals for further calculation.
Worked example
To add 1⁄2 and 1⁄3, put both over a common denominator of 6: 1⁄2 = 3⁄6 and 1⁄3 = 2⁄6, so the sum is 5⁄6 (already in lowest terms), which is about 0.833 as a decimal. Multiplying instead is quicker — 1⁄2 × 1⁄3 = 1⁄6 — and dividing flips the second fraction: 1⁄2 ÷ 1⁄3 = 1⁄2 × 3⁄1 = 3⁄2, or 1 1⁄2.
Frequently asked questions
How do I add two fractions?+
Give them a common denominator, then add the numerators. For 1⁄2 + 1⁄3, rewrite as 3⁄6 + 2⁄6 = 5⁄6. You can’t simply add numerators and denominators together — that’s the most common fraction mistake. The calculator does the common-denominator step for you.
How do I divide fractions?+
Flip the second fraction (its reciprocal) and multiply. So 1⁄2 ÷ 1⁄3 becomes 1⁄2 × 3⁄1 = 3⁄2. The rule “keep, change, flip” captures it: keep the first, change ÷ to ×, flip the second.
What is a mixed number?+
A whole number combined with a proper fraction, like 1 1⁄2. It’s another way to write an improper fraction (one where the numerator exceeds the denominator): 3⁄2 equals 1 1⁄2. The calculator shows both forms.
How does it simplify the answer?+
It divides the numerator and denominator by their greatest common divisor, reducing the fraction to lowest terms. So 6⁄8 becomes 3⁄4. A result like 4⁄2 reduces to 2⁄1, which is just the whole number 2.
Can it handle negative fractions?+
Yes. Enter a negative numerator (or denominator) and the sign is handled correctly, with the result normalised so the sign sits on the numerator — for example 1⁄4 − 1⁄2 gives −1⁄4.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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