The four operations
Adding and subtracting
Fractions can only be added or subtracted when they share a denominator. Convert both to a common denominator first, then add or subtract the numerators and leave the denominator alone.
Using b × d always works, though it does not always give the smallest denominator. Simplifying afterwards fixes that.
Multiplying
The easy one. Multiply the numerators together and the denominators together.
Dividing
Invert the second fraction and multiply. This works because dividing by a number is the same as multiplying by its reciprocal.
A worked example
As a decimal, 0.8333. As a percentage, 83.33%.
Simplifying to lowest terms
Divide both numerator and denominator by their greatest common divisor. For 18⁄24, the GCD is 6, so it reduces to 3⁄4. The calculator does this automatically using the Euclidean algorithm.
Proper, improper and mixed
| Type | Definition | Example |
|---|---|---|
| Proper | Numerator smaller than denominator | 3⁄4 |
| Improper | Numerator at or above the denominator | 7⁄4 |
| Mixed | A whole number plus a proper fraction | 1 3⁄4 |
Improper and mixed forms are equivalent — 7⁄4 and 1 3⁄4 are the same quantity. To convert an improper fraction to mixed, divide and keep the remainder: 7 ÷ 4 = 1 remainder 3, so 1 3⁄4. To go the other way, multiply the whole number by the denominator and add the numerator: 1 × 4 + 3 = 7, so 7⁄4.
Frequently asked questions
How do I add fractions with different denominators?
Convert both to a common denominator, then add the numerators. Multiplying the denominators together always gives a valid common denominator: ½ + ⅓ becomes 3⁄6 + 2⁄6 = 5⁄6.
Using the lowest common denominator gives smaller numbers to work with, but simplifying at the end reaches the same answer either way.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 18⁄24 the GCD is 6, giving 3⁄4.
If the GCD is 1, the fraction is already in lowest terms.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3⁄4 = 3 ÷ 4 = 0.75.
Some fractions produce repeating decimals — ⅓ is 0.333… — which is exactly why fractions remain useful for exact work.
Why can a denominator never be zero?
Division by zero is undefined. A fraction means "numerator divided by denominator", so a zero denominator asks for something with no answer.
The calculator will flag this rather than returning a value.