**Comparing fractions** is an operation that we commonly find in mathematics. A fraction is a number that can be expressed in the form “a / b” where a is called the numerator while b is called the denominator. Examples of fractional numbers are 1/3 and 2/7.

When compared, the two fractions have different values. Comparing here means determining the relationship between the two fractions more than, less than, or equal to. To understand how to compare 2 fractions, we take the following example.

## BASIC EXAMPLE

For example, in your school, an election for the Student Council President was held and the following results were obtained.

■ 1/3 of the students in your school elect Candidate I.

■ 2/7 of the students in your school elect Candidate II.

Based on these results, one candidate had more votes than the other. To know who won, knowledge of **comparing fractions** is required. There are two things you need to know about fractions, namely similar fractions and dissimilar fractions.

**Comparing Similar Fractions and Similar Fractions**

Try to pay attention to the two fractional models below. Attached figure 10.1. From this model, it can be concluded that 5/6> 4/6. Note also that one-sixth can be viewed as the new unit. 5/6 means 5 one-sixth and 4/6 means 4 one-sixth. From the description above, it is clear that 5 is greater than 4, so 5/6> 4/6.

So, to compare several fractions with the same denominator, it is enough to compare the numerators. If the numerator is larger, the fraction is also larger. This kind of fraction is indeed much simpler than similar fractions.

Then, let’s start by comparing 1/2 and 1/3. We know that 1/2 is equal to 3/6 and 1/3 is equal to 2/6. The four fractions can be modeled as shown below. You can see that, 1/2> 1/3 and 3/6> 2/6, because 1/2 = 3/6 and 1/3 = 2/6. Attached figure 10.2 and Attached figure 10.3

So, the way to compare it is to express the fractions as like fractions and then compare the numerators. To make a dissimilar fraction into a like fraction, the least common multiple of the denominators of the fraction can be used.

**Several Examples of Comparing Fractions**

Example problem I:

Use the <, = or> sign to compare the fractions 1/3 and 2/7.

Stage I: Determine the KPK from the denominator, namely the KPK from 3 and 7.

Multiples of 3 = 3, 4, 9, 12, 15, 18, 21, 24,…

Multiples of 7 = 7, 14, 21, 28,…

Thus, the LCM of 3 and 7 is 21, because 21 is the smallest number that can be divisible by 3 and divided by 7.

Stage II: Determine the fraction equal to 1/3 and the fraction equal to 2/7 using the KPK in Stage I as the denominator.

1 × 7 | = | 7 | Then | 1 | = | 7 |

3 × 7 | 21 | 3 | 21 |

2 × 3 | = | 6 | Then | 2 | = | 6 |

7 × 3 | 21 | 7 | 21 |

Stage III: Comparing similar fractions, namely 7/21 and 6/21. Look at the numerators for the two fractions of a kind. Because the numbers 7> 6 then:

7/21> 6/21

So that:

1/3> 2/7

Thus, the answer to the problem in the election of Student Council Chair above was that Candidate I had more voters than Candidate II.

After learning both similar and dissimilar fractions, you will learn the comparison between them easily. There are so many things in our life is needed this concept of fraction comparison. Thus, the knowledge of **comparing fractions** is necessary.