Related Tags

project euler

# What are ordered fractions?

Kainat Asif

Ordered fractions are fractions that are sorted in ascending order.

## Methods of ordering

The common methods for ordering fractions are:

### Method 1: Common denominator

Find the LCMleast common multiple of the denominators of all fractions. This will be the common denominator of all fractions.

Multiply and divide a number with all fractions so that their denominator becomes equal to the common denominator, as shown in the figure below:

After all of the fractions have an equal denominatori.e., the common denominator, sort the fractions on the basis of their numerators.

The fraction with the largest numerator is the largest fraction, and the fraction with the smallest numerator is the smallest fraction. The ordered fractions after the sorting are the sorted fractions.

 Fractions Common Denominator 1/2 15/30 2/5 12/30 5/3 50/30

Fractions: 1/2, 2/5, 5/3

Common denominators: 15/30, 12/30, 50/30

Sorted numerators: 12/30, 15/30, 50/30

Ordered fractions: 2/5, 1/2, 5/3

### Method 2: Common numerators

Find the LCM of the numerators of all fractions. This will be the common numerator of all fractions.

Multiply and divide a number with all fractions so that their numerator becomes equal to the common numerator, as shown in the figure below:

After all of the fractions have an equal numeratori.e., the common numerator, sort the fractions on the basis of their denominators.

The fraction with the largest denominator is the smallest fraction, and the fraction with the smallest denominator is the largest fraction. The ordered fractions after the sorting are the sorted fractions.

 Fractions Equivalent Decimals 9/4 630/280 7/2 630/180 2/3 630/945 5/11 630/1386

Fractions: 9/4, 7/2, 2/3, 5/11

Common numerators: 630/280, 630/180, 630/945, 630/1386

Sorted denominators: 630/1386, 630/945, 630/280, 630/180

Ordered fractions: 5/11, 2/3, 9/4, 7/2

### Method 3: Changing to fractions

Change all of the fractions to their decimal equivalents and sort them. The resulting fractions after sorting are the sorted fractions.

 Fractions Equivalent Decimals 1/9 0.11 2/7 0.29 5/3 1.67 7/11 0.64 2/9 0.22

Fractions: 1/9, 2/7, 5/3, 7/11, 2/9

Equivalent decimals: 0.11, 0.29, 1.67, 0.64, 0.22

Sorted equivalent decimals: 0.11, 0.22, 0.29, 0.64, 1.67

Ordered fractions: 1/9, 2/9, 2/7, 7/11, 5/3

RELATED TAGS

project euler

CONTRIBUTOR

Kainat Asif