What is the Half of a Fraction Calculator?
This calculator finds exactly half of any fraction you enter. Halving a fraction means dividing it by 2, which is the same as multiplying it by 1/2. The result is automatically reduced to its lowest terms and also shown as a decimal so you can see its true value at a glance.
How to use it
Enter the numerator (the top number, \(a\)) and the denominator (the bottom number, \(b\)) of your fraction, then read off the answer. The tool displays the simplified half-fraction, the unsimplified intermediate result, and a decimal equivalent. It works with whole-number numerators and denominators, including negatives.
The formula explained
To divide a fraction by 2, you keep the numerator and double the denominator: $$\frac{1}{2} \times \frac{a}{b} = \frac{a}{2 \times b}$$ This works because dividing by 2 is identical to multiplying by 1/2, and multiplying fractions means multiplying tops and bottoms: $$\frac{a}{b} \times \frac{1}{2} = \frac{a \times 1}{b \times 2} = \frac{a}{2b}$$ The calculator then divides both numbers by their greatest common divisor to simplify.
Worked example
Take \(\frac{3}{4}\). Doubling the denominator gives \(\frac{3}{8}\). Since 3 and 8 share no common factor greater than 1, the result is already simplified: half of \(\frac{3}{4}\) is \(\frac{3}{8}\), or 0.375 as a decimal. For \(\frac{6}{4}\), half is \(\frac{6}{8}\), which simplifies to $$\frac{3}{4} = 0.75$$
FAQ
Does halving always double the denominator? Yes, but the result may then simplify if the numerator is even — for example half of \(\frac{2}{3}\) is \(\frac{2}{6} = \frac{1}{3}\).
Can I enter an improper fraction? Absolutely. Half of \(\frac{9}{2}\) is \(\frac{9}{4} = 2.25\).
What about negative fractions? Negatives are supported; the sign is kept on the numerator and the denominator is shown positive.
