Fraction Calculator
Add, subtract, multiply, and divide fractions with automatic simplification.
The Formula
Subtraction: a/b − c/d = (ad − bc) / bd
Multiply: a/b × c/d = ac / bd
Divide: a/b ÷ c/d = ad / bc
= (3×5 + 2×4) / (4×5)
= (15 + 8) / 20
= 23/20
= 1 and 3/20
How to Calculate Fractions
Adding/Subtracting: Find a common denominator, then add or subtract numerators. Multiplying: Multiply numerators together and denominators together. Dividing: Multiply by the reciprocal of the second fraction (flip and multiply). All results are automatically simplified to lowest terms.
Frequently Asked Questions
How do I add fractions with different denominators?
Find a common denominator (the easiest is to multiply both denominators together), convert each fraction to that denominator, then add the numerators. For 1/3 + 1/4: common denominator is 12. Convert: 4/12 + 3/12 = 7/12. The LCM of the denominators gives the smallest common denominator, which keeps the numbers smaller.
How do I simplify a fraction?
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For 18/24: GCD(18, 24) = 6, so 18/6 = 3 and 24/6 = 4, giving 3/4. If you're not sure of the GCD, keep dividing by small primes (2, 3, 5, 7) until no common factors remain.
How do I divide fractions?
Keep, change, flip: keep the first fraction as is, change the division sign to multiplication, then flip the second fraction (swap numerator and denominator). So (2/3) ÷ (4/5) becomes (2/3) x (5/4) = 10/12 = 5/6. This works because dividing by a fraction is the same as multiplying by its reciprocal.
What is a reciprocal?
The reciprocal of a fraction is simply the fraction flipped upside down — numerator and denominator swapped. The reciprocal of 3/4 is 4/3. The reciprocal of 5 (which is 5/1) is 1/5. Multiplying a number by its reciprocal always equals 1: (3/4) x (4/3) = 12/12 = 1. Reciprocals are central to division and the concept of multiplicative inverse.
How do fractions relate to decimals and percentages?
All three represent parts of a whole. To convert a fraction to a decimal, divide the numerator by the denominator: 3/4 = 0.75. To convert to a percentage, multiply the decimal by 100: 0.75 = 75%. Going back: a percentage divided by 100 gives a decimal (75% = 0.75), and a decimal can be written as a fraction by using the place value as the denominator (0.75 = 75/100 = 3/4).