Fraction Calculator

Add, subtract, multiply or divide two fractions, mixed numbers or whole numbers. The answer is simplified automatically and shown as a proper fraction, a mixed number and a decimal — with every step explained the way NCERT textbooks teach it. Switch to “Improper ↔ mixed” to turn 17/5 into 3 2/5 or 3 2/5 back into 17/5.

First fraction

Operation

Second fraction

Examples: 3/4 · 2 1/3 (mixed) · -5/6 · 7 · 0.25

Simplest form

17/12

Mixed number

1 5/12

Decimal

1.416667

Step-by-step solution

LCM of denominators 3 and 4 = 12
Convert: 2/3 = 8/12, 3/4 = 9/12
Add numerators: 8 + 9 = 17 → 17/12
17/12 is already in its simplest form
As a mixed number: 1 5/12

How to use the fraction calculator

Type the first fraction, e.g. 3/4, a mixed number like 2 1/3, a whole number or a decimal.
Choose the operation: +, −, × or ÷.
Type the second fraction. The simplified answer and full working appear instantly.
To convert, choose “Improper ↔ mixed” and type 17/5 or 3 2/5 — the calculator converts it the other way.

Formulas

Addition	`a/b + c/d = (a·d + c·b) / (b·d)` The calculator uses the LCM of the denominators, as taught in school.
Subtraction	`a/b − c/d = (a·d − c·b) / (b·d)`
Multiplication	`a/b × c/d = (a·c) / (b·d)`
Division	`a/b ÷ c/d = a/b × d/c`
Mixed → improper	`w n/d = (w·d + n) / d`
Improper → mixed	`n/d = q r/d, where n = q·d + r` Divide: the quotient is the whole number, the remainder the new numerator.

Solved examples

Example 1: Add 2/3 and 3/4.

LCM of 3 and 4 = 12
2/3 = 8/12, 3/4 = 9/12
8/12 + 9/12 = 17/12

Answer: 17/12 = 1 5/12

Example 2: Divide 1 1/2 by 3/4.

1 1/2 = 3/2
3/2 ÷ 3/4 = 3/2 × 4/3 = 12/6

Answer: 2

Example 3: Multiply 5/6 by 9/10.

(5 × 9) / (6 × 10) = 45/60
HCF of 45 and 60 = 15 → 3/4

Answer: 3/4

How to add fractions with different denominators

You can only add or subtract fractions when they have the same denominator. Find the LCM of the denominators, rewrite each fraction with that LCM as its denominator, then add or subtract the numerators. Finally, simplify by dividing the numerator and denominator by their HCF.

Using the LCM (rather than simply multiplying the denominators) keeps the numbers small and is the method expected in NCERT answers.

Proper, improper and mixed fractions

A proper fraction has a numerator smaller than its denominator (3/5). An improper fraction has a numerator equal to or larger than its denominator (7/4). A mixed number combines a whole number and a proper fraction (1 3/4). Always convert mixed numbers to improper fractions before multiplying or dividing.

🎯 Asked in competitive exams

This topic regularly appears in the quantitative aptitude section of:

SSC CGL & CHSL
RRB NTPC & Group D
Campus placement aptitude tests

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Frequently asked questions

How do I enter a mixed number?

Type the whole number, a space, then the fraction — for example 2 1/3. Negative mixed numbers work too, like -1 1/2.

How do I convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5. To go back, multiply the whole number by the denominator and add the numerator: (3 × 5 + 2)/5 = 17/5.

How do I simplify a fraction?

Divide the numerator and the denominator by their HCF (highest common factor). For 45/60, the HCF is 15, so 45/60 = 3/4. The calculator does this automatically.

How do I divide fractions?

Keep the first fraction, change ÷ to ×, and flip the second fraction (use its reciprocal). Then multiply numerators and denominators.

Can I use decimals?

Yes. A decimal like 0.25 is converted to 25/100 and then simplified to 1/4 in the result.

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. The calculator shows the decimal value of every answer, rounded to 6 decimal places.