Question

Arrange the following in the ascending order:
$\dfrac{2}{9},\dfrac{7}{9},\dfrac{3}{9},\dfrac{4}{9},\dfrac{1}{9},\dfrac{6}{9},\dfrac{5}{9}$

Answer 1

Hint: Ascending order is to arrange the function in increasing order. The fraction having the same denominator are compared using their numerator. The fraction with the smallest numerator is the smallest and fraction with largest numerator is the largest.

Complete step-by-step answer:
Ascending order means to arrange numbers in increasing order that is from the smallest to the largest number. To arrange the numbers we need to first compare the numbers. In the care of fractions, we compare it on the basis of the denominator, if all the terms have the same denominator or not. We have been given the fraction.
$\dfrac{2}{9},\dfrac{7}{9},\dfrac{3}{9},\dfrac{4}{9},\dfrac{1}{9},\dfrac{6}{9},\dfrac{5}{9}$
From the above we can say that all the fractions have the same denominator. Thus for the fractions having the same denominator, the fraction with the smallest numerator is the smallest. From the given fractions we can say that in the fraction $\dfrac{1}{9}$ , the numerator is the smallest. Thus $\dfrac{1}{9}$ is the first fraction in the ascending order.
Similarly find the next smallest fraction after $\dfrac{1}{9}$ by comparing the numerator. Thus we can say that
$\dfrac{1}{9}<\dfrac{2}{9}<\dfrac{3}{9}<\dfrac{4}{9}<\dfrac{5}{9}<\dfrac{6}{9}<\dfrac{7}{9}$
Hence we can form the ascending order as,
$\dfrac{1}{9},\dfrac{2}{9},\dfrac{3}{9},\dfrac{4}{9},\dfrac{5}{9},\dfrac{6}{9},\dfrac{7}{9}$
Thus we got the required order.

Note: To find the descending order, which is the decreasing order is from highest to the smallest, just reverse the ascending order i.e.
$\dfrac{7}{9},\dfrac{6}{9},\dfrac{5}{9},\dfrac{4}{9},\dfrac{3}{9},\dfrac{2}{9},\dfrac{1}{9}$
If the numerator were different, then we would have to find the LCM of the denominators and express all the fractions such that they have the same denominator for easy comparison. We can also find the decimal form and then compare, but that is complex and time consuming.