Fraction - to be or not to be?

Question

In a recent year 6 maths test my daughter was asked to write a fraction equal to half of 11/40. Her response was 5.5/40 which was not accepted as a correct answer- the model answer used for marking was 11/80. Does the numerator or denominator in a fraction necessarily have to be a whole number? If it isn't and examples such as 5.5/40 are acceptable, what type of fraction is it?

Answer 1

From the definition of the rational numbers, you can always put every rational number $r\in\mathbb{Q}$ in the form :

$$r=\frac{n}{d} \text{ where } n\in\mathbb{Z}\text{ and } d\in\mathbb{N}^*\text{ with } \gcd(n,d)=1 $$

Any time, in a math test someone is asked to compute a (numerical) fraction, it is implicit that this is the form that is needed. Your daughter's answer is technically right but in that case she could also have answered :

$$\frac{0.55}{4}=\frac{0.11}{0.8}=\frac{0.00011}{0.0008} $$

which are not as clear as $\frac{11}{80}$.