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ยฝ Fraction Calculator

Fraction addition, subtraction, multiplication, division with auto-simplification

Result
5
6
= 0.83333333

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Fraction Calculator Guide

The Fraction Calculator is a professional math tool that supports addition, subtraction, multiplication, and division of two fractions, automatically completing the common denominator and simplification process. After entering the numerator and denominator, the system automatically calculates the result and displays it in both simplified fraction and decimal forms.

A fraction represents the relationship between a part and a whole, consisting of a numerator (top number), denominator (bottom number), and a fraction bar. Fraction operations are a core skill from elementary school through college mathematics. This tool is especially suitable for students checking homework, teachers preparing problems, and engineers performing precise fraction calculations.

Fraction Operation Formulas

ใ€Additionใ€‘a/b + c/d = (aร—d + cร—b) / (bร—d), then simplify
ใ€Subtractionใ€‘a/b - c/d = (aร—d - cร—b) / (bร—d), then simplify
ใ€Multiplicationใ€‘a/b ร— c/d = (aร—c) / (bร—d), then simplify
ใ€Divisionใ€‘a/b รท c/d = a/b ร— d/c = (aร—d) / (bร—c), then simplify

Simplification: Divide both numerator and denominator by their GCD

Practical Examples

๐Ÿ“‹
ใ€Example 1ใ€‘1/2 + 1/3 = ? Common denominator: 1/2 = 3/6, 1/3 = 2/6 Add: 3/6 + 2/6 = 5/6 Result: 5/6 โ‰ˆ 0.8333 ใ€Example 2ใ€‘2/3 ร— 3/4 = ? Multiply numerators: 2ร—3 = 6 Multiply denominators: 3ร—4 = 12 Simplify: 6/12 = 1/2 (divide by GCD=6) Result: 1/2 = 0.5 ใ€Example 3ใ€‘3/4 รท 1/2 = ? Convert to multiplication: 3/4 ร— 2/1 = 6/4 Simplify: 6/4 = 3/2 (divide by GCD=2) Result: 3/2 = 1.5

Important Notes

๐Ÿ’ก
- The denominator cannot be 0; this is an undefined operation in mathematics - When entering negative numbers, the sign of the result is automatically normalized (denominator stays positive) - Results are automatically simplified to lowest terms, e.g. 4/8 becomes 1/2 - When the result is a whole number (e.g. 4/2), it is displayed as an integer rather than a fraction - Fraction division is equivalent to multiplying by the reciprocal of the divisor (swap numerator and denominator)

Application Scenarios

  • - Math education: Students practice fraction arithmetic, verify homework answers
  • - Cooking & baking: Adjust recipe proportions (e.g. halve or double a recipe)
  • - Engineering measurement: Precise ratio conversions and material proportions in construction
  • - Financial calculations: Interest rate allocation, share ratios, discount splitting
  • - Scientific experiments: Chemical solution proportions, physical quantity ratio calculations

Fractions and Decimals

Fractions can be converted to decimal form (numerator รท denominator), but not all fractions can be expressed as terminating decimals. When the prime factors of the denominator include only 2 and 5, the fraction can be expressed as a terminating decimal; otherwise, it produces a repeating decimal. For example, 1/2=0.5, 1/3=0.333..., 1/7=0.142857142857...

In practice, choose the appropriate representation based on precision requirements: decimal form is convenient for comparing values in engineering calculations, while fraction form preserves exact values and avoids rounding errors in theoretical derivations.

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