In math, the fraction is nothing but a ratio. Ascending order means arranging the fractions from the smallest to the greatest in value. We have two simple methods to arrange fractions in ascending order namely LCM Method and the Visualization Method. Get a detailed explanation of those methods along with the solved examples on how to write fractions in ascending order on this page.

**More Related Articles:**

- Comparison of Fractions having the Same Numerator
- Comparison of Like Fractions
- Comparison of Unlike Fractions

## Fractions in Ascending Order

A fraction is a part of a whole. The simple parts of the fraction are numerator, denominator and both are separated by division symbol (/). Ascending order of fractions means arranging the fractions in the order from the smallest to greatest of their value. The examples of the fractions in ascending order are provided here.

**Example:**

The ascending order of the fractions is \(\frac { 1 }{ 2 } \), \(\frac { 3 }{ 2 } \), \(\frac { 5 }{ 2 } \)

### How to Order Fractions in Ascending Order?

Get step by step procedure to find the ascending order of the fractions in the following sections.

**LCM Method:**

- Check out the fractions.
- Find the L.C.M of denominators of all fractions to make the denominators same.
- To make the given fractions as like fractions, divide the obtained L.C.M by the denominator of fractions, and then multiply both numerator and denominator with a number after dividing by L.C.M.
- Compare the like fractions by comparing their numerators.
- Arrange the given fractions in order from least to the greatest value.

**Visualization Method:**

- Draw a graph for each of the given fraction.
- Observe the drawn images carefully.
- The graph which has the highest shaded region is the greatest fraction and the graph which has the lowest shaded region is the least fraction.
- Now, arrange the fractions in ascending order.

### Arranging Fractions in Ascending Order Examples

**Question 1:**

Arrange the given fractions in ascending order using the L.C.M method.

(i) \(\frac { 5 }{ 6 } \), \(\frac { 1 }{ 2 } \), \(\frac { 1 }{ 4 } \), \(\frac { 4 }{ 7 } \)

(ii) \(\frac { 7 }{ 10 } \), \(\frac { 1 }{ 8 } \), \(\frac { 6 }{ 5 } \), \(\frac { 5 }{ 3 } \)

**Solution:**

(i) The given fractions are

\(\frac { 5 }{ 6 } \), \(\frac { 1 }{ 2 } \), \(\frac { 1 }{ 4 } \), \(\frac { 4 }{ 7 } \)

Find the L.C.M of denominators

L.C.M of 6, 2, 4, and 7 is 84

Make the given fractions as like fractions

84 ÷ 6 = 14

\(\frac { 5 }{ 6 } \) x \(\frac { 14 }{ 14 } \) = \(\frac { 70 }{ 84 } \)

84 ÷ 2 = 42

\(\frac { 1 }{ 2 } \) x \(\frac { 42 }{ 42 } \) = \(\frac { 42 }{ 84 } \)

84 ÷ 4 = 21

\(\frac { 1 }{ 4 } \) x \(\frac { 21}{ 21 } \) = \(\frac { 21 }{ 84 } \)

84 ÷ 7 = 12

\(\frac { 4 }{ 7 } \) x \(\frac { 12 }{ 12 } \) = \(\frac { 48 }{ 84 } \)

The obtained like fractions are \(\frac { 70 }{ 84 } \), \(\frac { 42 }{ 84 } \), \(\frac { 21 }{ 84 } \), \(\frac { 48 }{ 84 } \)

Compare the numerators

21 < 42 < 48 < 70

The order of fractions is \(\frac { 21 }{ 84 } \)< \(\frac { 42 }{ 84 } \)<\(\frac { 48 }{ 84 } \)<\(\frac { 70 }{ 84 } \)

So, the ascending order of fractions is \(\frac { 1 }{ 4 } \)< \(\frac { 1 }{ 2 } \) < \(\frac { 4 }{ 7 } \) < \(\frac { 5 }{ 6 } \).

(ii) The given fractions are

\(\frac { 7 }{ 10 } \), \(\frac { 1 }{ 8 } \), \(\frac { 6 }{ 5 } \), \(\frac { 5 }{ 3 } \)

Find the L.C.M of denominators

L.C.M of 10, 8, 5, 3 is 120

Make the given fractions as like fractions

120 ÷ 10 = 12

\(\frac { 7 }{ 10 } \) x \(\frac { 12}{ 12 } \) = \(\frac { 84 }{ 120 } \)

120 ÷ 8 = 15

\(\frac { 1 }{ 8 } \) x \(\frac { 15}{ 15 } \) = \(\frac { 15 }{ 120 } \)

120 ÷ 5 = 24

\(\frac { 6 }{ 5 } \) x \(\frac { 24}{ 24 } \) = \(\frac { 144 }{ 120 } \)

120 ÷ 3 = 40

\(\frac { 5 }{ 3 } \) x \(\frac { 40}{ 40 } \) = \(\frac { 200 }{ 120 } \)

The obtained like fractions are \(\frac { 84 }{ 120 } \), \(\frac { 15 }{ 120 } \), \(\frac { 144 }{ 120 } \), and \(\frac { 200 }{ 120 } \)

Compare the numerators

15 < 84 < 144 < 200

The order of fractions is \(\frac { 15 }{ 120 } \) < \(\frac { 84 }{ 120 } \) < \(\frac { 144 }{ 120 } \) < \(\frac { 200 }{ 120 } \)

So, the ascending order of fractions is \(\frac { 1 }{ 8 } \) < \(\frac { 7 }{ 10 } \) < \(\frac { 6 }{ 5 } \) < \(\frac { 5 }{ 3 } \)

**Question 2:**

Find the ascending order of the following fractions.

\(\frac { 5 }{ 16 } \), \(\frac { 6 }{ 8 } \), \(\frac { 9 }{ 11 } \)

**Solution:**

The given fractions are \(\frac { 5 }{ 16 } \), \(\frac { 6 }{ 8 } \), \(\frac { 9 }{ 11 } \)

Draw a graph for each fraction.

By observing the shaded region of the fractions the order is \(\frac { 5 }{ 16 } \) < \(\frac { 6 }{ 8 } \) < \(\frac { 9 }{ 11 } \).