How do you add or subtract fractions with unlike denominators?

To add or subtract fractions with different denominators, first find the Least Common Multiple (LCM) of the denominators to create a common denominator. Convert both fractions to equivalent fractions using this common denominator, perform addition or subtraction on the numerators, and simplify the result to lowest terms.

How do you multiply two fractions?

Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator (e.g., (a/b) * (c/d) = (a*c)/(b*d)). Then divide both numbers by their Greatest Common Divisor (GCD) to reduce to lowest terms.

How do you divide fractions?

To divide by a fraction, multiply by its reciprocal (flip the second fraction upside down): (a/b) ÷ (c/d) = (a/b) * (d/c) = (a*d)/(b*c), then reduce to simplest form.

What is a mixed fraction vs an improper fraction?

An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/4). A mixed number combines a whole integer with a proper fraction (e.g., 1 3/4). They represent the exact same mathematical value.

Fraction Calculator with Steps: Add, Subtract, Multiply & Divide Fractions

How to Use the Free Online Fraction Calculator

Fractions represent parts of a whole and are fundamental to arithmetic, engineering, carpentry, cooking, chemistry, and financial analysis. This fraction calculator with steps automatically computes addition, subtraction, multiplication, and division for proper fractions, improper fractions, and mixed numbers, delivering exact simplified fraction results alongside decimal and percentage equivalents.

Mathematical Formulas for Fraction Operations

1. Adding Fractions: (a/b) + (c/d)

If denominators are identical, simply add the numerators: a/d + c/d = (a + c)/d. If denominators differ, find the Least Common Multiple (LCM) of b and d:

Addition: (a/b) + (c/d) = [(a × d) + (c × b)] / (b × d)

2. Subtracting Fractions: (a/b) − (c/d)

Convert both fractions to have equivalent common denominators and subtract the second numerator from the first:

Subtraction: (a/b) − (c/d) = [(a × d) − (c × b)] / (b × d)

3. Multiplying Fractions: (a/b) × (c/d)

Multiply across horizontally—multiply numerators together and denominators together:

Multiplication: (a/b) × (c/d) = (a × c) / (b × d)

4. Dividing Fractions: (a/b) ÷ (c/d)

Multiply the first fraction by the reciprocal of the second fraction (invert and multiply):

Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c)

Step-by-Step Worked Examples

Example 1: Adding Unlike Fractions (3/4 + 1/6)
Step 1: Find the LCM of 4 and 6 → LCM(4, 6) = 12.
Step 2: Scale first fraction: 3/4 × 3/3 = 9/12.
Step 3: Scale second fraction: 1/6 × 2/2 = 2/12.
Step 4: Add numerators: 9/12 + 2/12 = 11/12.
Decimal equivalent: 0.9167 (91.67%).

Example 2: Dividing Mixed Fractions (2 1/2 ÷ 3/4)
Step 1: Convert 2 1/2 to improper fraction → (2 × 2 + 1)/2 = 5/2.
Step 2: Invert the divisor 3/4 → 4/3.
Step 3: Multiply: (5 × 4) / (2 × 3) = 20/6.
Step 4: Simplify by dividing by GCD(20, 6) = 2 → 10/3.
Mixed Number: 3 1/3 | Decimal: 3.3333.

Fraction Comparison Table

Fraction	Fraction Type	Decimal Equivalent	Percentage
1/8	Proper	0.125	12.5%
1/4	Proper	0.25	25.0%
1/3	Proper (Repeating)	0.3333...	33.33%
1/2	Proper	0.50	50.0%
3/4	Proper	0.75	75.0%
5/4 (1 1/4)	Improper / Mixed	1.25	125.0%

Frequently Asked Questions

Yes, you can enter negative whole numbers or negative numerators. The calculator preserves proper algebraic sign conventions across all operations.

To convert any fraction into a percentage, divide the numerator by the denominator to find the decimal value, then multiply by 100 and append the % sign (e.g., 3/4 = 0.75 = 75%).

In mathematics, division by zero is undefined because no real number multiplied by 0 can yield a non-zero numerator. Our tool automatically alerts you if zero is entered in the denominator.