A fraction has two parts numerator and denominator which represent the part of a whole object. Here, we will learn about the steps to compare two fractions having the same numerator. Get the solved examples and two simple methods on comparing the fractions with the like numerator in the further section.

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## Comparing Fractions with the Same Numerator

A fraction is a part of the whole. Fractions are represented as numerator/denominator. Compare fractions having the same numerator means checking which fraction has the greatest value and which fraction has the least value.

### How to Compare Fractions with the Same Numerator?

Here are the 2 simple methods to compare fractions with the same numerator value.

**Method 1:**

- If all the fractions having the same numerator, then compare their denominators.
- Write the denominators in ascending order.
- The bigger denominator means the smaller fraction.
- Arrange the fractions in ascending or descending order.

**Method 2:**

- Get various fractions and all fractions must have the same numerator.
- Represent those fractions visually.
- The fraction which has the highest shaded region is the greatest fraction.

### Examples on Comparing Fractions with the Same Numerator

**Question 1:**

Compare the below-provided fractions

(i) \(\frac { 1 }{ 2 } \), \(\frac { 1 }{ 3 } \), \(\frac { 1 }{ 5 } \), \(\frac { 1 }{ 6 } \)

(ii) \(\frac { 6 }{ 2 } \), \(\frac { 6 }{ 4 } \), \(\frac { 6 }{ 5 } \), \(\frac { 6 }{ 8 } \)

**Solution:**

(i) The given fractions are \(\frac { 1 }{ 2 } \), \(\frac { 1 }{ 3 } \), \(\frac { 1 }{ 5 } \), \(\frac { 1 }{ 6 } \)

As all the fractions have the same numerator, compare the denominators

2 < 3 < 5 < 6

The descending order of fractions is \(\frac { 1 }{ 6 } \) < \(\frac { 1 }{ 5 } \) < \(\frac { 1 }{ 3 } \) < \(\frac { 1 }{ 2 } \)

(ii) The given fractions are \(\frac { 6 }{ 2 } \), \(\frac { 6 }{ 4 } \), \(\frac { 6 }{ 5 } \), \(\frac { 6 }{ 8 } \)

As all the fractions have the same numerator, compare the denominators

2 < 4 < 5 < 8

The ascending order of the fractions are \(\frac { 6 }{ 2 } \) > \(\frac { 6 }{ 4 } \) > \(\frac { 6 }{ 5 } \) > \(\frac { 6 }{ 8 } \)

**Question 2:**

Compare the fractions by putting < or > or = symbol

(i) \(\frac { 2 }{ 7 } \), \(\frac { 2 }{ 5 } \), \(\frac { 2 }{ 3 } \)

(ii) \(\frac { 3 }{ 2 } \), \(\frac { 3 }{ 4 } \), \(\frac { 3 }{ 5 } \)

**Solution:**

(i) The given fractions are \(\frac { 2 }{ 7 } \), \(\frac { 2 }{ 5 } \), \(\frac { 2 }{ 3 } \)

As all the fractions have the same numerator, compare the denominators

7 > 5 > 3

The descending order of the fractions are \(\frac { 2 }{ 3 } \) > \(\frac { 2 }{ 5 } \) > \(\frac { 2 }{ 7 } \)

The ascending order of the fractions are \(\frac { 2 }{ 7 } \) < \(\frac { 2 }{ 5 } \) < \(\frac { 2 }{ 3 } \)

(ii) The given fractions are \(\frac { 3 }{ 2 } \), \(\frac { 3 }{ 4 } \), \(\frac { 3 }{ 5 } \)

As all the fractions have the same numerator, compare the denominators

2 < 4 < 5

The descending order of the fractions are \(\frac { 3 }{ 2 } \) > \(\frac { 3 }{ 4 } \) > \(\frac { 3 }{ 5 } \)

The ascending order of the fractions are \(\frac { 3 }{ 5 } \) < \(\frac { 3 }{ 4 } \) < \(\frac { 3 }{ 2 } \)

**Question 3:**

Compare the following fractions using the visualization method.

(a) \(\frac { 5 }{ 7 } \), \(\frac { 5 }{ 6 } \),

(b) \(\frac { 4 }{ 5 } \), \(\frac { 4 }{ 7 } \), \(\frac { 4 }{ 9 } \)

**Solution:**

(a) The given fractions are \(\frac { 5 }{ 7 } \), , \(\frac { 5 }{ 8 } \)

Represent all fractions visually

\(\frac { 5 }{ 7 } \) is

\(\frac { 5 }{ 6 } \) is

\(\frac { 5 }{ 8 } \) is

From the images, the fraction which has highest shaded region is \(\frac { 5 }{ 6 } \) > \(\frac { 5 }{ 7 } \) > \(\frac { 5 }{ 8 } \)

(b) The given fractions are \(\frac { 4 }{ 5 } \), \(\frac { 4 }{ 7 } \), \(\frac { 4 }{ 9 } \)

\(\frac { 4 }{ 5 } \) is

\(\frac { 4 }{ 9 } \) is

\(\frac { 4 }{ 7 } \) is

From the images, the fraction which has the highest shaded region is \(\frac { 4 }{ 5 } \) > \(\frac { 4 }{ 7 } \) > \(\frac { 4 }{ 9 } \)