How do you multiply fractions?

To multiply fractions, multiply the numerators together and multiply the denominators together. Then simplify. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can simplify before multiplying by cancelling common factors between any numerator and any denominator.

How do you divide fractions?

To divide fractions, multiply the first fraction by the reciprocal of the second fraction (flip the second fraction). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

How do you simplify a fraction?

To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. Example: 18/24. GCF(18,24) = 6. 18÷6 = 3, 24÷6 = 4. Simplified fraction: 3/4. A fraction is fully simplified when the GCF of numerator and denominator is 1.

How do you convert a decimal to a fraction?

Count the decimal places and use that power of 10 as the denominator. Example: 0.75 has two decimal places, so 0.75 = 75/100. Then simplify by dividing by GCF(75,100) = 25: 75/100 = 3/4. For repeating decimals like 0.333..., set x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 1/3.

Fraction Calculator 2026 - Add, Subtract, Multiply, Divide & Simplify Fractions

Fraction Calculator

Add, subtract, multiply, or divide two fractions. Shows simplified result and step-by-step solution.

Result

Mixed Numbers Calculator

Add, subtract, multiply, or divide mixed numbers (whole number + fraction). Enter the whole number and fractional parts separately.

Result

Simplify Fractions Calculator

Reduce any fraction to its simplest form by dividing both numerator and denominator by their greatest common factor (GCF).

Simplified

Decimal to Fraction Calculator

Convert any decimal number to a fraction in simplest form. Works for terminating and repeating decimals.

Fraction

Fraction to Decimal Calculator

Convert any fraction or mixed number to its decimal equivalent. Shows both exact decimal and rounded result.

Decimal

Big Number Fraction Calculator

Handles very large integer numerators and denominators using BigInt arithmetic. No rounding errors.

Result

Adding and Subtracting Fractions

Fractions can only be added or subtracted when they share a common denominator. The cleanest approach is to find the Least Common Multiple (LCM) of the two denominators, convert each fraction, then add or subtract the numerators.

a/b + c/d = (ad + bc) / bd Then simplify by dividing numerator and denominator by GCF(ad+bc, bd) Better: use LCM(b,d) as the common denominator 1/4 + 1/6: LCM(4,6) = 12 1/4 = 3/12 · 1/6 = 2/12 · 3/12 + 2/12 = 5/12

Using the LCM rather than the product of denominators gives smaller numbers to work with and often produces a result that is already in simplest form. The LCM method is the standard approach taught in schools from year 5 onward.

Subtraction

Subtraction follows exactly the same process. After finding a common denominator, subtract the second numerator from the first. The result may be negative if the first fraction is smaller than the second, which is mathematically valid.

a/b - c/d = (ad - bc) / bd Example: 3/4 - 1/6 = (18-4)/24 = 14/24 = 7/12

Multiplying and Dividing Fractions

Multiplication is the most straightforward fraction operation because no common denominator is needed. You simply multiply across: numerator times numerator, denominator times denominator.

a/b × c/d = (a×c) / (b×d) Example: 3/4 × 2/5 = 6/20 = 3/10

A useful shortcut before multiplying is cross-cancellation: divide any numerator and any denominator by their GCF before multiplying. This keeps numbers smaller and often eliminates the need to simplify at the end.

Division

Dividing by a fraction is equivalent to multiplying by its reciprocal. Flip the second fraction (exchange numerator and denominator), then multiply.

a/b ÷ c/d = a/b × d/c = (a×d) / (b×c) Example: 3/4 ÷ 1/6 = 3/4 × 6/1 = 18/4 = 9/2 = 4 1/2

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The mnemonic "Keep-Change-Flip" (KCF) is often used for fraction division: Keep the first fraction, Change the operation to multiplication, Flip the second fraction. The mathematical justification is that multiplying by d/c is the same as dividing by c/d because (c/d) × (d/c) = 1.

Simplifying Fractions: GCF Method

A fraction is in its simplest form when the only positive integer that divides both the numerator and denominator evenly is 1. To simplify, find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by it.

Finding the GCF: Euclidean Algorithm

The Euclidean algorithm is the most efficient method for finding the GCF of two numbers. Repeatedly apply the rule: GCF(a, b) = GCF(b, a mod b), until the remainder is zero. The last non-zero remainder is the GCF.

GCF(48, 36): 48 = 1×36 + 12 → GCF(48,36) = GCF(36,12) 36 = 3×12 + 0 → GCF(36,12) = 12 Simplify 48/36: divide both by 12 → 4/3 (or 1 1/3)

Fraction	GCF	Simplified	Mixed Number
4/8	4	1/2	0.5
12/18	6	2/3	0.667…
36/48	12	3/4	0.75
100/250	50	2/5	0.4
220/440	220	1/2	0.5
17/51	17	1/3	0.333…

Mixed Numbers

A mixed number combines a whole number and a proper fraction, like 2 3/4. To perform arithmetic on mixed numbers, first convert each to an improper fraction (where the numerator is larger than the denominator), carry out the operation, then convert back.

Convert mixed to improper: w + n/d = (w×d + n) / d Example: 2 3/4 = (2×4 + 3) / 4 = 11/4 Convert improper to mixed: n/d = q remainder r = q r/d Example: 11/4 = 2 remainder 3 = 2 3/4

The calculator above handles this conversion automatically. You enter the whole and fractional parts separately, and the result is shown both as an improper fraction and as a simplified mixed number.

Mixed Number Addition Example

1 1/2 + 2 1/3 Convert: 3/2 + 7/3 LCM(2,3) = 6: 9/6 + 14/6 = 23/6 Back to mixed: 3 5/6

Decimal and Fraction Conversion

Decimal to Fraction

Count the decimal places, use the corresponding power of 10 as the denominator, write the digits after the decimal point as the numerator, then simplify.

0.625: 3 decimal places → 625/1000 GCF(625, 1000) = 125 → 5/8

Repeating Decimals

For a repeating decimal like 0.333..., use algebra. Let x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. For 0.142857142857... (repeating block of 6 digits): multiply by 10^6, subtract, simplify.

Fraction to Decimal

Divide the numerator by the denominator. If the denominator's only prime factors are 2 and 5, the decimal terminates. Otherwise it repeats. Examples: 1/4 = 0.25 (terminates); 1/3 = 0.333... (repeats); 1/7 = 0.142857142857... (6-digit repeating block).

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Every fraction with integer numerator and denominator produces either a terminating or repeating decimal. Irrational numbers like π and √2 cannot be expressed as fractions and have non-terminating, non-repeating decimal expansions.

Equivalent Fractions and Comparing Fractions

Two fractions are equivalent if they represent the same value. You can generate equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero integer.

Original	×2	×3	×5	×10	Decimal
1/2	2/4	3/6	5/10	10/20	0.5
1/3	2/6	3/9	5/15	10/30	0.333…
2/3	4/6	6/9	10/15	20/30	0.666…
3/4	6/8	9/12	15/20	30/40	0.75
1/5	2/10	3/15	5/25	10/50	0.2

Comparing Fractions

To compare two fractions, convert them to a common denominator and compare numerators. Or convert both to decimals. The fraction with the larger numerator (after common denominator conversion) is larger.

Compare 3/5 and 5/8: LCM(5,8) = 40 3/5 = 24/40 · 5/8 = 25/40 25/40 > 24/40, so 5/8 > 3/5

Cross-multiplication is a shortcut: for a/b vs c/d, compare a×d with b×c. If a×d > b×c, then a/b > c/d. For 3/5 vs 5/8: 3×8 = 24 and 5×5 = 25. Since 24 < 25, we confirm 3/5 < 5/8.

Frequently Asked Questions

How do you add fractions with different denominators?

Find the LCM of the denominators. Multiply each fraction's numerator and denominator to reach that LCM as the denominator, then add the numerators. Example: 1/3 + 1/4. LCM(3,4) = 12. Convert: 4/12 + 3/12 = 7/12. If you do not want to find the LCM, multiply the numerators and denominators crosswise: (1×4 + 1×3) / (3×4) = 7/12. Both methods give the same answer; LCM gives smaller numbers.

What is an improper fraction?

An improper fraction has a numerator greater than or equal to its denominator, like 7/4 or 9/3. It represents a value of 1 or more. Improper fractions are mathematically valid and often easier to work with during calculations. When presenting a final answer, they are often converted to mixed numbers: 7/4 = 1 3/4. The calculators above show results in both forms.

Why can't a fraction have a denominator of zero?

Division by zero is undefined in mathematics. A fraction a/b represents "a divided into b equal parts." If b = 0, there are no parts - the operation has no meaning. In the real number system, a/0 is simply undefined. In limits (calculus), expressions that approach division by zero are said to diverge or approach infinity, but that is a different concept from the arithmetic value of a fraction.

What is the difference between LCM and GCF?

The GCF (Greatest Common Factor, also called GCD) is the largest number that divides both values evenly. It is used to simplify fractions. The LCM (Least Common Multiple) is the smallest number that is a multiple of both values. It is used to find a common denominator for adding or subtracting fractions. They are related: for any two integers a and b, LCM(a,b) × GCF(a,b) = a × b. For example, GCF(4,6) = 2 and LCM(4,6) = 12, and indeed 2 × 12 = 4 × 6 = 24.

When does a fraction simplify to a terminating decimal?

A fraction in its simplest form produces a terminating decimal if and only if the denominator has no prime factors other than 2 and 5. Examples: 1/4 = 1/(2²) = 0.25 (terminates); 1/8 = 1/(2³) = 0.125 (terminates); 3/20 = 3/(4×5) = 0.15 (terminates); 1/3 (denominator has factor 3) = 0.333… (repeats); 1/7 (denominator has factor 7) = 0.142857… (repeats with 6-digit period).