Fraction Calculator
Add, subtract, multiply and divide fractions
How to use Fraction Calculator
Add, subtract, multiply and divide fractions. Automatic simplification. Mixed numbers supported. Free online fraction calculator.
When do you need to calculate with fractions?
Fractions represent exact values that decimals cannot always express precisely. 1/3 = 0.3333... (repeating) in decimal, but as a fraction it is exact. This precision matters in mathematics, cooking, and measurement.
- Cooking and recipe scaling: A recipe calls for 2/3 cup of flour and you want to triple it — 2/3 × 3 = 2 cups. Or halve 3/4 teaspoon — 3/4 ÷ 2 = 3/8. Fraction arithmetic keeps measurements exact.
- Mathematics and education: Students learning fractions, algebra, and number theory need to perform exact operations — adding, subtracting, multiplying, and dividing fractions and mixed numbers.
- Construction and carpentry: Imperial measurements use fractional inches — 3 and 5/8 inches, 7/16 inches. Adding and subtracting these requires fraction arithmetic.
- Music theory: Time signatures and note values are fractions — a half note is 1/2, a quarter note 1/4, an eighth note 1/8. Calculating polyrhythm patterns requires fraction operations.
- Finance: Stock prices historically quoted in fractions (1/8, 1/4 of a dollar). Interest rate calculations often involve fractional percentages.
Common operations: To add fractions, find the common denominator. 1/3 + 1/4 = 4/12 + 3/12 = 7/12. To multiply, multiply numerators and denominators: 2/3 × 3/4 = 6/12 = 1/2. To divide, multiply by the reciprocal: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Frequently Asked Questions
What is a mixed number and how do I convert it to a fraction?
A mixed number combines a whole number and a fraction: 2½. To convert: multiply the whole number by the denominator, add the numerator, keep the same denominator. 2½ = (2×2+1)/2 = 5/2. To convert back: divide numerator by denominator — quotient is the whole number, remainder is the new numerator.
How do I find the lowest common denominator?
The lowest common denominator (LCD) is the smallest number divisible by all the denominators. For 1/3 and 1/4: find the LCM of 3 and 4 = 12. Then convert: 1/3 = 4/12, 1/4 = 3/12, sum = 7/12. The LCM can be found by listing multiples or using the formula: LCM(a,b) = (a×b)/GCD(a,b).
What is simplifying (reducing) a fraction?
Simplifying means dividing numerator and denominator by their Greatest Common Divisor (GCD) to get the equivalent fraction in lowest terms. 6/8: GCD(6,8)=2, so 6/8 = 3/4. A fraction is fully simplified when GCD(numerator, denominator) = 1 — they share no common factors.
What is an improper fraction?
An improper fraction has a numerator larger than or equal to its denominator: 7/4, 9/3. Improper fractions are equivalent to mixed numbers: 7/4 = 1¾. Both forms are mathematically valid — improper fractions are often easier to multiply and divide; mixed numbers are more intuitive for real-world measurements.
Why do fractions matter when calculators use decimals?
Fractions represent exact rational numbers. 1/3 in decimal is 0.33333... (infinite). In calculations involving 1/3 + 2/3, using fractions gives exactly 1; using decimals (0.333 + 0.667 = 1.000) involves rounding. In algebra and symbolic mathematics, fractions are exact; decimals are approximations.
Fractions vs decimals vs percentages vs ratios
All four express proportional relationships. Fractions (3/4) are exact and natural for arithmetic. Decimals (0.75) are convenient for computing and comparison. Percentages (75%) are intuitive for human communication — discounts, statistics, interest rates. Ratios (3:4) compare two quantities directly — used in maps, recipes, and aspect ratios. The choice depends on context: fractions for precision, decimals for computation, percentages for communication, ratios for comparison.