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?
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3I agree with the teacher that to be called a fraction, it has to be written as $p/q$, where $p, q$ are integers. (If not, all numbers can be called a fraction as $x = x/1$). – Mar 23 '15 at 09:31
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The value is correct but her result is not normalized as probably intended by the teacher. So it depends a bit on how specific the question was asked. – mvw Mar 23 '15 at 09:40
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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 $\frac{11}{80}$.
N. F. Taussig
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Clément Guérin
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1Yes, of course, my mental calculus is not as good as it used to be, I am changing it right now. – Clément Guérin Mar 23 '15 at 09:41
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It might be helpful to explain that $\mathbb{Z}$ is the set of integers and that $\mathbb{N}^*$ is the set of positive integers. – N. F. Taussig Mar 23 '15 at 10:31