Fraction Calculator
What is 2/3 + 3/4? Add, subtract, multiply, or divide any two fractions and see every step — the common denominator, the GCD simplification, the mixed number, and the decimal.
Simplified
17/12
lowest terms
Mixed number
1 5/12
whole + fraction
Decimal
1.4167
4 decimal places
Steps
2/3 + 3/4 → common denominator: LCD of 3 and 4 is 12 = 8/12 + 9/12 = 17/12 already in lowest terms: GCD(17, 12) = 1
Dividing by a fraction multiplies by its reciprocal because division asks “how many of these fit?” — two halves fit in every whole, so 7/8 ÷ 1/2 doubles to 14/8 = 7/4. Simplifying never changes the value: 17/12 and 1 5/12 are the same number written two ways.
How Fraction Arithmetic Works
Adding and subtracting need a common denominator: 2/3 + 3/4 rewrites over the LCD of 3 and 4, which is 12, giving 8/12 + 9/12 = 17/12 — the improper fraction 1 5/12, or about 1.4167. Multiplication just goes straight across, and division flips the second fraction: 7/8 ÷ 1/2 = 7/8 × 2/1 = 14/8, which a GCD of 2 simplifies to 7/4 = 1 3/4.
The four rules
Add: a/b + c/d = (ad + bc)/bd 2/3 + 3/4 = 17/12 = 1 5/12 Subtract: a/b − c/d = (ad − bc)/bd 3/4 − 2/3 = 1/12 Multiply: a/b × c/d = ac/bd 2/3 × 3/4 = 6/12 = 1/2 Divide: a/b ÷ c/d = a/b × d/c 7/8 ÷ 1/2 = 14/8 = 7/4 Always finish by dividing top and bottom by their GCD.
Frequently Asked Questions
How do I add fractions with different denominators?
Rewrite both over a common denominator first — the LCD is the least common multiple of the two denominators. For 2/3 + 3/4 the LCD of 3 and 4 is 12, so it becomes 8/12 + 9/12 = 17/12, which is the mixed number 1 5/12. Only the numerators add; the denominator stays put.
Why do you flip the second fraction when dividing?
Dividing asks how many of the divisor fit into the dividend, and multiplying by the reciprocal answers exactly that. 7/8 ÷ 1/2 asks how many halves fit in 7/8 — two fit in every whole, so it equals 7/8 × 2/1 = 14/8, which simplifies to 7/4 = 1 3/4.
How do I simplify a fraction to lowest terms?
Divide the numerator and denominator by their greatest common divisor. For 14/8 the GCD is 2, giving 7/4; for 6/12 the GCD is 6, giving 1/2. When the GCD is 1 — like 17/12 — the fraction is already in lowest terms.
What's the difference between an improper fraction and a mixed number?
They're the same value written two ways: 17/12 is improper (numerator larger than denominator), 1 5/12 is the mixed form (whole part plus a proper fraction). Mixed numbers read better in answers and measurements; improper fractions are easier to keep multiplying and dividing.