How to add and subtract fractions
- Turn mixed numbers into improper fractions: 1 ½ = (1 × 2 + 1) ÷ 2 = 3/2.
- Find a common denominator (the least common multiple of the denominators).
- Add or subtract the numerators; keep the denominator.
- Simplify by dividing top and bottom by their greatest common factor.
Example: 1 ½ + ¾ = 6/4 + 3/4 = 9/4 = 2 ¼.
Multiplying and dividing
a/b × c/d = (a × c) / (b × d) · a/b ÷ c/d = a/b × d/c
To divide, flip the second fraction and multiply (“keep, change, flip”). 1 ½ ÷ ¾ = 3/2 × 4/3 = 12/6 = 2.
Common mistakes
- Adding denominators (1/2 + 1/3 is not 2/5; it is 5/6).
- Forgetting to convert mixed numbers before multiplying.
- Leaving the answer unsimplified; most teachers want lowest terms.
Worked examples
- Adding: 1/3 + 1/4. The common denominator is 12, so 4/12 + 3/12 = 7/12.
- Subtracting mixed numbers: 2 1/2 − 1 3/4 = 5/2 − 7/4 = 10/4 − 7/4 = 3/4.
- Multiplying: 2/3 × 3/5 = 6/15 = 2/5.
- Dividing: flip the second fraction and multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 (1 1/2).
Simplifying
Divide the top and bottom by their greatest common factor. 18/24: both divide by 6, giving 3/4. The calculator always shows the simplest form and the mixed number.
Related calculators
- Decimal to Fraction Converter: Decimals to fractions and back.
- Ratio Calculator: Simplify ratios and solve proportions.
- Rounding Calculator: Round to decimals, tens or significant figures.
Questions people ask
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. 18/24: the GCF is 6, so it simplifies to 3/4.
How do I enter a negative fraction?
Put the minus sign on the whole number, or on the numerator if there is no whole number, for example numerator −3, denominator 4.
How do I turn a fraction into a decimal?
Divide the numerator by the denominator: 3/8 = 0.375. The answer box shows the decimal too, and the decimal to fraction converter goes the other way.
Formula checked October 2026 · How we calculate