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Tool: Fraction Calculator — Add, Subtract, Multiply & Divide | Printed on:
Fraction Calculator — Add, Subtract, Multiply & Divide
Add, subtract, multiply, and divide fractions with step-by-step reduction and mixed numbers.
Fraction Arithmetic & Simplification
Fraction Arithmetic Operations
Transparent mathematical methodology explained in plain English.
(a/b) ± (c/d) = (ad ± bc) / bd | (a/b) × (c/d) = ac / bd | (a/b) ÷ (c/d) = ad / bc Finds common denominators for addition and subtraction, and multiplies straight across for multiplication and reciprocal division.
Variables Explained:
- a, c: Numerators.
- b, d: Denominators (non-zero).
Adding 3/4 + 2/3
Finding least common denominator and reducing.
- Find common denominator: 4 × 3 = 12.
- Convert fractions: 3/4 = 9/12, and 2/3 = 8/12.
- Add numerators: 9 + 8 = 17.
- Result: 17/12.
- Convert to mixed fraction: 1 5/12 (approx. 1.4167).
Frequently Asked Questions: Fraction Calculator
Click any question below to expand quick answers, formulas, and expert tips.
How do you add or subtract fractions with unlike denominators?
Find the Least Common Denominator (LCD) of both fractions. Multiply the numerator and denominator of each fraction by the factor needed to match the LCD, add or subtract the numerators while keeping the denominator the same, and reduce to simplest form.
How do you multiply fractions?
Multiply the numerators together, then multiply the denominators together (Formula: [a/b] × [c/d] = [a×c] / [b×d]). For example: 2/3 × 4/5 = 8/15. Simplify the final fraction if possible.
How do you divide fractions using the reciprocal method (Keep, Change, Flip)?
Keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down (its reciprocal). For example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole number quotient becomes the whole number part, the remainder becomes the new numerator, and the denominator stays the same. For example, 17/5 = 3 with a remainder of 2, so 3 2/5.
How do you reduce or simplify a fraction to its lowest terms?
Find the Greatest Common Factor (GCF) of both numerator and denominator, then divide both numbers by that GCF. For example, for 18/24, the GCF is 6: 18÷6 / 24÷6 = 3/4.
What is the Least Common Denominator (LCD) and how do you find it?
The LCD is the Least Common Multiple (LCM) of the denominators. To find it, list multiples of each denominator or use prime factorization to find the smallest number both denominators divide into evenly.
How do you convert a fraction to a decimal and percentage?
Divide the top numerator by the bottom denominator to get a decimal (e.g., 3 ÷ 4 = 0.75). Multiply the decimal by 100 to convert to a percentage (0.75 × 100 = 75%).
Can you perform operations with mixed fractions?
Yes. First convert the mixed fractions into improper fractions (multiply whole number by denominator and add numerator), perform the arithmetic operation, and then convert the result back to a mixed number.