Question

Which of the following are improper fractions?
\[\dfrac{3}{2}\], \[\dfrac{5}{6}\], \[\dfrac{9}{4}\], \[\dfrac{8}{8}\], \[3\], \[\dfrac{{27}}{{16}}\], \[\dfrac{{23}}{{31}}\], \[\dfrac{{19}}{{18}}\], \[\dfrac{{10}}{{13}}\], \[\dfrac{{26}}{{26}}\]

Answer 1

Hint: The given question is to be approached by the basic concept of fractions. The condition for a fraction to be an improper fraction is that the numerator value must be greater than or equal to the denominator value. So, we will one by one check each fraction to find the improper fractions.

Complete step by step answer:
We know that any fractional value can be represented in the form of \[\dfrac{p}{q}\], where \[p\] is the numerator and \[q\] is the denominator and also \[q \ne 0\]. Now, for a fractional value to be an improper fraction, the value of the numerator must be greater than or equal to the value of the denominator. So, to find the improper fraction out of the given numbers, we need to find out which one of the given numbers has a numerator value greater than or equal to the denominator value. Here, we can see that in \[\dfrac{3}{2}\], \[\dfrac{9}{4}\], \[\dfrac{8}{8}\], \[3\] i.e., \[\dfrac{3}{1}\], \[\dfrac{{27}}{{16}}\], \[\dfrac{{19}}{{18}}\] and \[\dfrac{{26}}{{26}}\] has numerator value greater than or equal to the denominator value.

Therefore, \[\dfrac{3}{2}\], \[\dfrac{9}{4}\], \[\dfrac{8}{8}\], \[3\], \[\dfrac{{27}}{{16}}\], \[\dfrac{{19}}{{18}}\] and \[\dfrac{{26}}{{26}}\] are improper fractions.

Note: A number which represents a part of a whole body which is divided into equal parts are called fractional numbers. Fractions can be easily converted into decimals when the numerator is divided by the denominator. Also, a fraction cannot have \[0\] in the denominator as the value of such fractions would be \[\infty \] or undefined.