## Arrange fractions from least to greatest

$$\frac{15}{4}\,\,\,\,\,\frac{17}{6}\,\,\,\,\,\frac{11}{2}\,\,\,\,\,\frac{7}{3}$$

How do you sort improper fractions from least to greatest? One method is to convert them into mixed numbers and then arrange them.

1. Change each improper fraction into a mixed number:

$$\frac{15}{4}\,=\,3\frac{3}{4}$$

$$\frac{17}{6}\,=\,2\frac{5}{6}$$

$$\frac{11}{2}\,=\,5\frac{1}{2}$$

$$\frac{7}{3}\,=\,2\frac{1}{3}$$

2. Arrange the mixed numbers:

$$2\frac{1}{3}\,<\,2\frac{5}{6}\,<\,3\frac{3}{4}\,<\,5\frac{1}{2}$$

3. Switch the mixed numbers back into impropers:

$$\frac{7}{3}\,\,\,\,\,\frac{17}{6}\,\,\,\,\,\frac{15}{4}\,\,\,\,\,\frac{11}{2}$$

In the above example, we converted each fraction into a mixed number in order to compare the numbers. In this next example, none of the fractions are improper, so we will have to find common denominators in order to compare the fractions.

Arrange these fractions from least to greatest.

$$\frac{3}{4}\,\,\,\,\,\frac{5}{6}\,\,\,\,\,\frac{1}{2}\,\,\,\,\,\frac{2}{3}$$

1. To solve this problem, first rename the four fractions with a common denominator. In this case, 12 is a common denominator.

$$\frac{3}{4}\,=\,\frac{9}{12}$$

$$\frac{5}{6}\,=\,\frac{10}{12}$$

$$\frac{1}{2}\,=\,\frac{6}{12}$$

$$\frac{2}{3}\,=\,\frac{8}{12}$$

2. Now arrange the fractions:

$$\frac{6}{12}\,<\,\frac{8}{12}\,<\,\frac{9}{12}\,<\,\frac{10}{12}$$

3. Switch the fractions back to their original form"

$$\frac{1}{2}\,<\,\frac{2}{3}\,<\,\frac{3}{4}\,<\,\frac{5}{6}$$

 Directions: Sort the fractions from least to greatest. Place the fractions in the center of each circle. Once the fractions are correctly sorted, a message will pop up letting you know that you are correct. Duane Habecker, Created with GeoGebra

# Self-Check

 Question 1 Sort from least to greatest: $$\frac{5}{12}\,\,\,\,\,\frac{5}{6}\,\,\,\,\,\frac{5}{21}$$ [show answer] $$\frac{5}{21}\,<\,\frac{5}{12}\,<\,\frac{5}{6}$$

 Question 2 Sort from least to greatest: $$\frac{98}{99}\,\,\,\,\,\frac{45}{46}\,\,\,\,\,\frac{5}{6}$$ [show answer] $$\frac{5}{6}\,<\,\frac{45}{46}\,<\,\frac{98}{99}$$

 Question 3 Sort from least to greatest: $$\frac{5}{7}\,\,\,\,\,\frac{2}{5}\,\,\,\,\,\frac{6}{12}$$ [show answer] $$\frac{2}{5}\,<\,\frac{6}{12}\,<\,\frac{5}{7}$$