How a fraction is simplified
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. Dividing both by their greatest common divisor gets there in one step:
The value does not change, because dividing the top and the bottom by the same number is the same as dividing by .
Worked example: 48/64
These are the calculator's default numbers.
- Find the GCD with Euclid's method: 64 = 1 × 48 + 16, then 48 = 3 × 16 + 0. The GCD is 16.
- Divide both by 16: 48 ÷ 16 = 3 and 64 ÷ 16 = 4.
- GCD(3, 4) = 1, so 3/4 is in lowest terms. As a decimal it is 0.75, or 75%.
When to simplify
- Final answers: schoolwork and exams expect answers in lowest terms, so 6/8 is usually marked as 3/4.
- Comparing fractions: 15/25 and 21/35 look different, but both simplify to 3/5.
- Ratios and scores: 18 correct out of 24 is 3/4 of the questions, which is easier to read as 75%.
Frequently asked questions
How do you simplify a fraction to lowest terms?
Find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. 48/64 has GCD 16, so it simplifies to 3/4. If the GCD is 1, the fraction is already in lowest terms.
How do you find the GCD of two numbers?
Divide the larger number by the smaller and keep the remainder, then repeat with the smaller number and that remainder until the remainder is 0. The last non-zero remainder is the GCD. For 64 and 48: 64 = 1 × 48 + 16, then 48 = 3 × 16 + 0, so the GCD is 16.
Does simplifying change the value of a fraction?
No. Dividing the top and bottom by the same number is the same as dividing by 1, so 48/64 and 3/4 are exactly equal. Only the way the number is written changes.
Can you simplify by dividing by small numbers one at a time?
Yes. Halving 48/64 gives 24/32, then 12/16, then 6/8, then 3/4. You reach the same answer as dividing once by the GCD, just in more steps. Stop when no number other than 1 divides both.
How do you simplify a negative fraction?
Simplify the sizes as usual and keep one minus sign in front or on the numerator: -6/8 = -3/4. A minus sign on both the numerator and the denominator cancels out, so -6/-8 = 3/4.