Calculate Fractions with Step-by-Step Solutions & Simplification

Add, subtract, multiply & divide fractions with step-by-step solutions. Simplify fractions to lowest terms & convert to decimals. Free math calculator for homework & cooking.

Calculate fraction operations including addition, subtraction, multiplication, and division with step-by-step solutions. Automatically simplifies results and shows equivalent forms.

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Understanding Fractions

A fraction represents a part of a whole, written as numerator/denominator. The numerator (top number) shows how many parts we have, while the denominator (bottom number) shows how many equal parts make up the whole.

Fraction Operations

Types of Fractions

Finding Common Denominators

To add or subtract fractions, you need a common denominator:

Equivalent Fractions

Fractions that represent the same value:

Converting Between Forms

Real-World Applications

Note: This calculator automatically simplifies fractions to their lowest terms using the Greatest Common Divisor (GCD). Mixed numbers are shown when the result is an improper fraction. All calculations show step-by-step solutions to help with learning.

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Frequently Asked Questions

How does the fraction calculator simplify fractions to lowest terms?

Fraction calculators simplify by finding the Greatest Common Divisor (GCD) of the numerator and denominator, then dividing both by the GCD. For example, 12/18 has GCD of 6, so 12÷6 = 2 and 18÷6 = 3, giving simplified fraction 2/3. The calculator uses algorithms like Euclidean method to find GCD efficiently. Proper fractions have numerators smaller than denominators, while improper fractions (like 7/3) can be converted to mixed numbers (2 1/3). Simplification makes fractions easier to understand and work with in further calculations.

What's the process for adding and subtracting fractions with different denominators?

Adding/subtracting fractions requires common denominators. Find the Least Common Multiple (LCM) of denominators, convert each fraction to equivalent fraction with common denominator, then add/subtract numerators while keeping the common denominator. Example: 1/4 + 1/6. LCM of 4 and 6 is 12. Convert: 1/4 = 3/12 and 1/6 = 2/12. Add: 3/12 + 2/12 = 5/12. For subtraction, follow same process but subtract numerators. Always simplify final answers when possible.

How do I multiply and divide fractions?

Multiplication is straightforward: multiply numerators together and denominators together, then simplify. Example: 2/3 × 4/5 = (2×4)/(3×5) = 8/15. Division uses "multiply by reciprocal" rule: flip the second fraction and multiply. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = (2×5)/(3×4) = 10/12 = 5/6 simplified. Cross-canceling before multiplying can simplify calculations—cancel common factors between any numerator and any denominator before multiplying.

How do I work with mixed numbers in fraction calculations?

Convert mixed numbers to improper fractions before calculating. For mixed number a b/c, the improper fraction is (a×c + b)/c. Example: 2 1/3 = (2×3 + 1)/3 = 7/3. Perform calculations with improper fractions, then convert final answer back to mixed number if desired. To convert improper fraction back to mixed number, divide numerator by denominator—quotient becomes whole number, remainder becomes new numerator over original denominator. Example: 11/4 = 2 3/4 (since 11÷4 = 2 remainder 3).

What are some practical applications for fraction calculations?

Common applications include cooking (adjusting recipe quantities), construction (measuring lumber, calculating dimensions), finance (calculating portions of investments), time calculations (1 1/2 hours = 1.5 hours), and academic work (algebra, physics problems). Cooking example: doubling recipe calling for 2/3 cup flour requires 2/3 × 2 = 4/3 = 1 1/3 cups. Construction: if board is 8 1/4 inches and you cut 2 3/8 inches, remaining length is 8 1/4 - 2 3/8 = 5 7/8 inches. Understanding fractions improves problem-solving in many practical situations.