Question

What fraction is halfway between \[{}^{1}/{}_{3}\] and \[{}^{1}/{}_{5}\]?

Answer 1

Hint: For solving this question you should know about the fraction halfway between the fractions. The fraction halfway is calculated in the question by making the same denominators and then solve it by seeing the numerator. Then we can get the exact halfway for these fractions. But it will be more if the fractions denominator will be increased.

Complete step by step answer:
According to the question we have to calculate the fraction halfway between \[{}^{1}/{}_{3}\] and \[{}^{1}/{}_{5}\].
And for calculating the halfway between two fractions we will make some denominator of both and then we will look up at the numerator.
If we look at question then it is \[\dfrac{1}{3}\] and \[\dfrac{1}{5}\] so it is seeming that the halfway is \[{}^{1}/{}_{4}\].
But \[{}^{1}/{}_{4}\] is a wrong answer.
So, we find the equivalent fraction for \[\dfrac{1}{3}\] and \[\dfrac{1}{5}\] which have the same denominator.
LCM of both = 15
So, the fractions can be written as:
\[\Rightarrow \dfrac{1}{3}\] and \[\dfrac{1}{5}\to \dfrac{1}{3}\times \dfrac{5}{5}\] and \[\dfrac{1}{5}\times \dfrac{3}{3}\]
\[\Rightarrow \dfrac{1}{3}\] and \[\dfrac{1}{5}\to \dfrac{5}{15}\] and \[\dfrac{3}{15}\]
So, if we see then \[\dfrac{4}{15}\] is exact between them.
But if we choose a larger denominator, then we can find the other fractions:
Denominator of 30:
\[\Rightarrow \dfrac{1}{3}\] and \[\dfrac{1}{5}\to \dfrac{10}{30}\] and \[\dfrac{6}{30}\]
So, the fractions \[\dfrac{9}{30},\dfrac{8}{30}\] and \[\dfrac{7}{30}\] are between both.
Denominator 60:
\[\Rightarrow \dfrac{1}{3}\] and \[\dfrac{1}{5}\to \dfrac{20}{60}\] and \[\dfrac{12}{60}\]
So, the fractions: \[\dfrac{19}{60},\dfrac{18}{60},\dfrac{17}{60},\dfrac{16}{60},\dfrac{15}{60},\dfrac{14}{60},\dfrac{13}{60}\] are between both \[\dfrac{1}{3}\] and \[\dfrac{1}{5}\].

So, the fraction exactly between \[\dfrac{1}{3}\] and \[\dfrac{1}{5}\] is \[{}^{4}/{}_{15}\].

Note: While calculating the halfway fraction for any fractions you have to assure that both the fractions have the same denominator. And both have to be equivalent to each other if we change the fractions to make the same denominator. And then we calculate the halfway fractions.