What is the lowest term of a fraction?
The lowest term (or simplest form) of a fraction is when the numerator and denominator share no common factor greater than 1. For example, 3/4 is the lowest term of 9/12, because dividing both by their GCF of 3 gives 3/4. See also our Proportion Calculator.
How do I find the lowest term of a fraction?
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example, to simplify 18/24, the GCD is 6, so 18÷6 = 3 and 24÷6 = 4, giving the lowest term 3/4.
Which fraction is expressed in lowest term?
A fraction is in lowest terms when the only common factor between the numerator and denominator is 1. For example, 3/7, 5/8, and 11/13 are all in lowest terms. A fraction like 6/9 is not, because both share a common factor of 3.
What is the lowest term of 3/16?
The GCD of 3 and 16 is 1, which means 3/16 is already in its lowest terms — there is no common factor greater than 1 to divide by.
What is an improper fraction, and how does it simplify?
An improper fraction has a numerator larger than its denominator, such as 9/4. When simplified, it can also be expressed as a mixed number — 9/4 becomes 2 and 1/4. This calculator shows both the simplified improper fraction and its mixed number form.
What is the Euclidean algorithm used for simplifying fractions?
The Euclidean algorithm finds the GCD by repeatedly replacing the larger number with the remainder of dividing the two numbers until the remainder is 0. The last non-zero remainder is the GCD. For example, GCD(18, 24): 24 mod 18 = 6, then 18 mod 6 = 0, so GCD = 6.
Can I simplify negative fractions or fractions with large numbers?
Yes. Negative fractions follow the same simplification rules — the GCD is always positive, and the negative sign is preserved on the numerator. For very large numbers, the Euclidean algorithm still works correctly and efficiently.