Question

How do you write $\dfrac{1}{14},\dfrac{7}{9},\dfrac{4}{5}$ in order from least to greatest?

Answer 1

Hint: We first try to convert the fractions to their decimal forms. We try to compare their values of the digits after decimal. Then from the value of their decimals we find the relation between the original numbers.

Complete step by step answer:
The given three numbers which are in their fraction forms have to be arranged in the form of least to greatest.
We first try to convert the fractions to their decimal forms.
All the fractions will be converted using the multiplication form.
The fractions are equal to $\dfrac{1}{14}=0.07,\dfrac{7}{9}=0.\overline{7},\dfrac{4}{5}=0.8$.
The digits right after decimal decides the characteristics of being greater and lesser.
In case of digits being similar we move on to the very next digit to compare.
So, we can see the highest valued digit right after decimal is $0.8$. Then comes $0.\overline{7}$ and finally $0.07$. This gives $0.07 < 0.\overline{7} < 0.8$
The order for least to greatest will be $0.07 < 0.\overline{7} < 0.8$ which gives for actual valued numbers is \[\dfrac{1}{14} < \dfrac{7}{9} < \dfrac{4}{5}\].

Note:
We can also directly compare them in fractions. The comparison only for fractions would work as the digit values become equal for all fractions either in numerator or in denominator. Among $\dfrac{1}{14},\dfrac{7}{9},\dfrac{4}{5}$, the easiest way to compare is to make the numerators equal. Then we take the value of the denominator with least value being the greatest in comparison and the greatest value in denominator being the least in comparison.