fraction calculator

Add, subtract, multiply, and divide fractions. Convert mixed numbers, improper fractions, and decimals with step-by-step visual models.

Math Calculators

Result

2 14Improper9/4

Decimal2.25

Show Your Work

How to Use the Fraction Calculator (Step-by-Step)

Master fraction arithmetic, mixed numbers, step-by-step simplification, and imperial tape measure conversions.

Enter Fractions or Mixed Numbers

Type proper fractions (e.g. 3/4), improper fractions (e.g. 7/4), or mixed numbers with whole parts (e.g. 1 1/2 or 2 3/8). Negative values like -1/2 or -1 3/4 are fully supported.

Select an Arithmetic Operation (+, -, ×, ÷)

Combine fractions using addition (+), subtraction (-), multiplication (*), or division (/). Expressions are evaluated according to standard algebraic fraction rules.

Read Instant Mixed & Improper Results

View the computed answer formatted both as a simplified mixed number (e.g. 2 1/4) and as an irreducible improper fraction (e.g. 9/4), alongside its exact decimal equivalent.

Inspect Step-by-Step Mathematical Work

Click 'Show Your Work' to explore every mathematical step: converting mixed numbers to improper fractions, finding the Least Common Denominator (LCD / LCM), and reducing via GCD.

Convert to Tape Measure & Imperial Ruler

Toggle 'Tape Measure' to round any decimal result to the nearest standard 1/16-inch fraction (e.g. 1 5/16"), ideal for woodworking, carpentry, and architectural drafting.

Examine Visual Diagrams & Copy Steps

Analyze the interactive fraction bar diagram illustrating the proportional parts, and click 'Copy Steps' to export the complete breakdown directly to your clipboard.

Frequently Asked Questions (FAQ)

Mathematical fundamentals, fraction arithmetic rules, and practical woodworking applications.

QHow do you add and subtract fractions with different denominators?

To add or subtract fractions with unlike denominators, first find the Least Common Multiple (LCM) of the denominators to determine the Least Common Denominator (LCD). Next, multiply the numerator and denominator of each fraction by the necessary factor so both share the LCD. Finally, add or subtract the numerators while keeping the common denominator, and reduce the resulting fraction to lowest terms.

QHow does fraction multiplication and division work?

For multiplication, multiply the numerators together and multiply the denominators together: (a/b) * (c/d) = (a*c)/(b*d). For division, multiply the first fraction by the reciprocal (the inverted form) of the second fraction: (a/b) / (c/d) = (a/b) * (d/c) = (a*d)/(b*c).

QHow do you convert a mixed number into an improper fraction and vice versa?

To convert a mixed number (Whole Num/Den) to an improper fraction, multiply the whole number by the denominator and add the numerator: (Whole * Den + Num) / Den. To convert an improper fraction back to a mixed number, perform integer division: the quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator.

QWhy is fraction simplification necessary and how is GCD used?

Simplifying expresses a fraction in its lowest terms (irreducible form). This is done by dividing both numerator and denominator by their Greatest Common Divisor (GCD / GCF). A simplified fraction is clearer, easier to interpret, and standard across scientific and engineering disciplines.

QWhat is the Tape Measure fraction feature and how does 1/16" rounding work?

Standard imperial rulers and measuring tapes are calibrated in halves, quarters, eighths, and sixteenths of an inch. The Tape Measure feature rounds any decimal outcome to the nearest 1/16-inch increment and simplifies it (e.g., 10/16" simplifies to 5/8"), making it indispensable for woodworkers, machinists, and builders.

QCan this calculator handle negative fractions and signs?

Yes. You can enter negative fractions such as -3/4 or negative mixed numbers such as -1 1/2. The negative sign is factored into the numerator during algebraic computations and preserved in the final simplified answer according to the laws of signs.

QWhat happens if a denominator is zero?

Division by zero is undefined in mathematics. If zero is entered as a denominator (e.g., 5/0), the calculator flags the expression as invalid and prompts you to enter non-zero denominators.

QCan I use this fraction calculator for cooking recipes and craft projects?

Yes! Scaling kitchen recipes (such as doubling 3/4 cup of flour or halving 1 1/2 teaspoons of salt) and calculating exact board cuts in carpentry are two of the most popular everyday uses for this tool.

Addition:

a b

c d

ad + bc bd

Subtraction:

a b

c d

ad - bc bd

Multiplication:

a b

c d

ac bd

Division:

a b

c d

ad bc

Numerator: The top part of the fraction.
Denominator: The bottom part (cannot be zero).

What is fraction calculator?

Solve and simplify fractions instantly with this step-by-step solver and visual fractions calculator. Whether you are adding mixed numbers or dividing complex fractions, this engine breaks down the math. It visually represents the problem using colored blocks to help you understand the proportions. The RESULT panel displays the simplified mixed number, the IMPROPER fraction, and its Decimal equivalent. For practical measuring, you can click Show Tape Measure (16ths). The hidden workspace details every step: Convert to Improper Fractions, Find Least Common Multiple (LCM), Apply Operation, and Simplify the Result. Use Copy Steps to export the entire process for homework or project documentation.

Practical Calculation Example

A carpenter in Seattle is cutting trim for a custom cabinet. He needs to add a 1 1/2 inch board to a 3/4 inch spacer. He enters the fractions into the calculator. The system instantly gives him 2 1/4 inches. By using the Show Tape Measure (16ths) feature, he can see exactly where to mark his cut on his physical measuring tape, completely avoiding costly cutting mistakes. He then uses Copy Steps to paste the math into his project ledger.

Reference Zones

Interface Element	Mathematical Function	Practical Application
IMPROPER	Fraction Format	Displays the top-heavy version of a fraction before it is simplified into a mixed number.
Show Tape Measure (16ths)	Visual Aid	Translates the abstract fraction into a real-world position on a standard imperial measuring tape.
Find Least Common Multiple	Common Denominator	The core mathematical step ensuring the bottom numbers match before adding or subtracting.
Copy Steps	Export Data	Copies the entire step-by-step breakdown to your clipboard for easy sharing.

History and Origin

The use of fractions dates back to ancient Egypt, where the Eye of Horus was used to represent fractional parts of volume. However, the modern notation with the horizontal bar separating the numerator and denominator is largely attributed to the Arab mathematician Al-Hassar in the 12th century. This notation later became the universal standard in English mathematics through the translation of Middle Eastern algebraic texts.