ACT Math - How to order fractions from least to greatest or from greatest to least

Place the following fractions in increasing order:

$\frac{2}{3},\frac{1}{2},\frac{3}{8},\frac{4}{5},\frac{2}{15}$ .

$\frac{2}{15},\frac{3}8{,}\frac{1}{2},\frac{}2{}3, \frac{4}{5}$

$\frac{2}{15},\frac{}2{}3,\frac{3}8{,}\frac{1}{2}, \frac{4}{5}$

$\frac{4}{5},\frac{}2{}3, \frac{1}{2},\frac{3}8{,}\frac{2}{15}$

$\frac{4}{5},\frac{1}{2},\frac{3}8{,}\frac{}2{}3, \frac{2}{15}$

$\frac{2}{15},\frac{}2{}3, \frac{4}{5},\frac{3}8{,}\frac{1}{2}$

Explanation

To put these fractions in increasing order it is important to compare them as decimals, since fractions can often be deceiving. $\frac{2}{3}=0.6\bar{6};; \frac{1}{2}=0.5;; \frac{3}{8}=0.375;; \frac{4}{5}=0.8;; \frac{2}{15}=0.1\bar{3}$ .

Now that the value of each fraction is obvious we can sort then in increasing order:

$\frac{2}{15},\frac{3}8{,}\frac{1}{2},\frac{}2{}3, \frac{4}{5}$

Order the following fractions from least to greatest:

2/3, 3/4, 1/2

1/2, 2/3, 3/4

2/3, 3/4, 1/2

2/3, 1/2, 3/4

3/4, 1/2, 2/3

3/4, 2/3, 1/2

Explanation

1/2 is the least, then 2/3, then 3/4.

Order the following fractions from least to greatest: $\frac{5}{8} , \frac{1}{4},\frac{9}{10},\frac{1}{2}$

$\frac{1}{4},\frac{1}{2},\frac{5}{8},\frac{9}{10}$

$\frac{9}{10},\frac{5}{8},\frac{1}{2},\frac{1}{4}$

$\frac{1}{4},\frac{5}{8},\frac{1}{2},\frac{9}{10}$

$\frac{1}{4},\frac{1}{2},\frac{9}{10},\frac{5}{8}$

$\frac{5}{8},\frac{1}{4},\frac{1}{2},\frac{9}{10}$

Explanation

The most generic process of ordering fractions that can apply to all questions begins with finding the common denominator between all fractions, preferably the least common denominator. In this question, the LCD is 40. Therefore the fractions become: $\frac{25}{40},\frac{10}{40},\frac{36}{40},\frac{20}{40}$ . From this point, we can simply arrange the fractions based upon their numerators. This becomes: $\frac{10}{40},\frac{20}{40},\frac{25}{40},\frac{36}{40}$ . The final step is to reduce the fractions to their original denominators, which becomes: $\frac{1}{4},\frac{1}{2},\frac{5}{8},\frac{9}{10}$ .

If you are comfortable and competent in quickly converting fractions to decimals, then there is a quicker method than what is described above. Simply convert each fraction to a decimal, organize the decimals, and then convert the decimals back to fractions. In this question we can convert $\frac{5}{8} , \frac{1}{4},\frac{9}{10},\frac{1}{2}$ to . Then we can reorganize this to and convert back to $\frac{1}{4},\frac{1}{2},\frac{5}{8},\frac{9}{10}$ .

When approaching this kind of problem, choose the method in which you are more comfortable working with. There is no sense in trying to save time by choosing a method that you are not comfortable with and increasing your risk of answering the question incorrectly.

Place the following fractions in order from greatest to least.

$\frac{2}{5},\frac{4}{8},\frac{2}{10},\frac{3}{12}$