 Comparison of Like Fractions – Definition, Methods, Examples | How do you Compare Like Fractions?

In maths, the fraction is a numerical value that can be defined as a part of a whole. A fraction can be formed by cutting an apple into two equal parts. Comparing fractions means, you need to identify which is the larger fraction and which is a smaller fraction. Students can learn the different methods to compare two like fractions and example questions in the below-mentioned sections of this page.

What is meant by Comparing Like Fractions?

Fraction is nothing but a part of the whole thing. If you divide or break down an object into pieces, each piece of that particular object represents a fraction. The simple and important rule for a fraction is each part has to be equal.

The two parts of the fraction are the numerator and the denominator. Like fractions are the fractions which are having the same number in the denominator. Comparing like fractions means checking whether those fractions are equal or which one is greater or which is lesser.

Example:
The comparing sales of a particular product.

Also, Check

How to Compare Like Fractions?

It is very easy to compare the like fractions. The following are the simple steps that help you to solve the questions on comparison of like fractions.

• Take the fractions which are having the same denominator.
• Compare the numerators of the fractions.
• The fraction which is having the highest numerator is the largest fraction and the fraction with the smallest numerator is the smallest fraction.

Comparing Like Fractions Examples with Answers

Question 1:
Compare the following like fractions.
(i) (ii) (iii) (iv) Solution:
(i) The shaded region in the question represents $$\frac { 3 }{ 10 }$$
(ii) The shaded region in the question represents $$\frac { 4 }{ 10 }$$
(iii) The shaded region in the question represents $$\frac { 6 }{ 10 }$$
(iv) The shaded region in the question represents $$\frac { 7 }{ 10 }$$
All the denominators having the same numbers, so compare the numerators
3 < 4 and 4 < 6 and 6 < 7
So, $$\frac { 3 }{ 10 }$$ < $$\frac { 4 }{ 10 }$$ < $$\frac { 6 }{ 10 }$$ < $$\frac { 7 }{ 10 }$$ or
We can write it as $$\frac { 7 }{ 10 }$$ > $$\frac { 6 }{ 10 }$$ > $$\frac { 4 }{ 10 }$$ > $$\frac { 3 }{ 10 }$$

Question 2:
Arrange the following like fractions in ascending order and descending order.
(i) $$\frac { 1 }{ 7 }$$, $$\frac { 5 }{ 7 }$$, $$\frac { 3 }{ 7 }$$, $$\frac { 2 }{ 7 }$$, 1
(ii) $$\frac { 2 }{ 3 }$$, 1, $$\frac { 1 }{ 3 }$$, $$\frac { 5 }{ 3 }$$, 2
(iii) $$\frac { 1 }{ 3 }$$, $$\frac { 1 }{ 6 }$$, $$\frac { 2 }{ 3 }$$, 1, $$\frac { 5 }{ 6 }$$
(iv) $$\frac { 1 }{ 2 }$$, $$\frac { 3 }{ 4 }$$, $$\frac { 1 }{ 4 }$$, $$\frac { 7 }{ 4 }$$, $$\frac { 5 }{ 2 }$$
Solution:
(i) Given fractions are
$$\frac { 1 }{ 7 }$$, $$\frac { 5 }{ 7 }$$, $$\frac { 3 }{ 7 }$$, $$\frac { 2 }{ 7 }$$, 1
All the fractions are not having the same denominator.
So make the above fractions as like fractions by multiplying both numerator and denominator by the same number.
1 x $$\frac { 7 }{ 7 }$$ = $$\frac { 7 }{ 7 }$$
Now, all fractions have same denominator. So, compare the numerators
1 < 2 < 3 < 5 < 7
The comparison of frcations is $$\frac { 1 }{ 7 }$$ < $$\frac { 2 }{ 7 }$$ < $$\frac { 3 }{ 7 }$$ < $$\frac { 5 }{ 7 }$$ < $$\frac { 7 }{ 7 }$$
The ascending order is $$\frac { 1 }{ 7 }$$, $$\frac { 2 }{ 7 }$$, $$\frac { 3 }{ 7 }$$, $$\frac { 5 }{ 7 }$$, 1
The descending order is 1, $$\frac { 5 }{ 7 }$$, $$\frac { 3 }{ 7 }$$, $$\frac { 2 }{ 7 }$$, $$\frac { 1 }{ 7 }$$
(ii) Given fractions are
$$\frac { 2 }{ 3 }$$, 1, $$\frac { 1 }{ 3 }$$, $$\frac { 5 }{ 3 }$$, 2
All the fractions are not having the same denominator.
So make the above fractions as like fractions by multiplying both numerator and denominator by the same number.
1 x $$\frac { 3 }{ 3 }$$ = $$\frac { 3 }{ 3 }$$
2 x $$\frac { 3 }{ 3 }$$ = $$\frac { 6 }{ 3 }$$
Now, all fractions have same denominator. So, compare the numerators
1 < 2 < 3 < 5 < 6
The comparison of fractions is $$\frac { 1 }{ 3 }$$ < $$\frac { 2 }{ 3 }$$ < $$\frac { 3 }{ 3 }$$ < $$\frac { 5 }{ 3 }$$ < $$\frac { 6 }{ 3 }$$
The ascending order is $$\frac { 1 }{ 3 }$$, $$\frac { 2 }{ 3 }$$, 1, $$\frac { 5 }{ 3 }$$, 2
The descending order is 2, $$\frac { 5 }{ 3 }$$, 1, $$\frac { 2 }{ 3 }$$, $$\frac { 1 }{ 3 }$$
(iii) Given fractions are
$$\frac { 1 }{ 3 }$$, $$\frac { 1 }{ 6 }$$, $$\frac { 2 }{ 3 }$$, 1, $$\frac { 5 }{ 6 }$$
All the fractions are not having the same denominator.
So make the above fractions as like fractions by multiplying both numerator and denominator by the same number.
$$\frac { 1 }{ 3 }$$ x $$\frac { 2 }{ 2 }$$ = $$\frac { 2 }{ 6 }$$
$$\frac { 2 }{ 3 }$$ x $$\frac { 2 }{ 2 }$$ = $$\frac { 4 }{ 6 }$$
1 x $$\frac { 6 }{ 6 }$$ = $$\frac { 6 }{ 6 }$$
Now, all fractions have same denominator. So, compare the numerators
1 < 2 < 4 < 5 < 6
The comparison of fractions is $$\frac { 1 }{ 6 }$$ < $$\frac { 2 }{ 6 }$$ < $$\frac { 4 }{ 6 }$$ < $$\frac { 5 }{ 6 }$$ < $$\frac { 6 }{ 6 }$$
The ascending order is $$\frac { 1 }{ 6 }$$, $$\frac { 1 }{ 3 }$$, $$\frac { 2 }{ 3 }$$, $$\frac { 5 }{ 6 }$$, 1
The descending order is 1, $$\frac { 5 }{ 6 }$$, $$\frac { 2 }{ 3 }$$, $$\frac { 1 }{ 3 }$$, $$\frac { 1 }{ 6 }$$
(iv) Given fractions are
$$\frac { 1 }{ 2 }$$, $$\frac { 3 }{ 4 }$$, $$\frac { 1 }{ 4 }$$, $$\frac { 7 }{ 4 }$$, $$\frac { 5 }{ 2 }$$
All the fractions are not having the same denominator.
So make the above fractions as like fractions by multiplying both numerator and denominator by the same number.
$$\frac { 1 }{ 2 }$$ x $$\frac { 2 }{ 2 }$$ = $$\frac { 2 }{ 4 }$$
$$\frac { 5 }{ 2 }$$ x $$\frac { 2 }{ 2 }$$ = $$\frac { 10 }{ 4 }$$
Now, all fractions have the same denominator. So, compare the numerators
1 < 2 < 3 < 7 < 10
The comparison of fractions is $$\frac { 1 }{ 4 }$$ < $$\frac { 1 }{ 2 }$$ < $$\frac { 3 }{ 4 }$$ < $$\frac { 7 }{ 4 }$$ < $$\frac { 5 }{ 2 }$$
The ascending order is $$\frac { 1 }{ 4 }$$, $$\frac { 1 }{ 2 }$$, $$\frac { 3 }{ 4 }$$, $$\frac { 7 }{ 4 }$$, $$\frac { 5 }{ 2 }$$
The descending order is $$\frac { 5 }{ 2 }$$, $$\frac { 7 }{ 4 }$$, $$\frac { 3 }{ 4 }$$, $$\frac { 1 }{ 2 }$$, $$\frac { 1 }{ 4 }$$

Question 3:
Compare the following like fractions and put = or < or > symbols.
(i) $$\frac { 8 }{ 10 }$$, $$\frac { 15 }{ 10 }$$
(ii) $$\frac { 6 }{ 5 }$$, $$\frac { 10 }{ 5 }$$
(iii) $$\frac { 2 }{ 8 }$$, $$\frac { 1 }{ 4 }$$
Solution:
(i) Given fractions are
$$\frac { 8 }{ 10 }$$, $$\frac { 15 }{ 10 }$$
Both fractions having the same denominator. So, compare the numerators.
8 < 15
So, $$\frac { 8 }{ 10 }$$ < $$\frac { 15 }{ 10 }$$
(ii) Given fractions are
$$\frac { 6 }{ 5 }$$, $$\frac { 10 }{ 5 }$$
Both fractions having the same denominator. So, compare the numerators.
10 > 6
So, $$\frac { 10 }{ 5 }$$ > $$\frac { 6 }{ 5 }$$
(iii) Given fractions are
$$\frac { 2 }{ 8 }$$, $$\frac { 1 }{ 4 }$$
To make like fractions multiply the same number by both numerator and denominator of the fraction.
$$\frac { 1 }{ 4 }$$ x $$\frac { 2 }{ 2 }$$ = $$\frac { 2 }{ 8 }$$
Now, both fractions having the same denominator. So, compare the numerators.
2 = 2
So, $$\frac { 2 }{ 8 }$$ = $$\frac { 1 }{ 4 }$$

Question 4:
Arrange the below mentioned like fractions in ascending and descending order.
(i) $$\frac { 1 }{ 10 }$$,  . . . $$\frac { 8 }{ 10 }$$
(ii) $$\frac { 11 }{ 9 }$$, . . . $$\frac { 18 }{ 9 }$$
Solution:
(i) Given fractions are $$\frac { 1 }{ 10 }$$, $$\frac { 2 }{ 10 }$$, $$\frac { 3 }{ 10 }$$, $$\frac { 4 }{ 10 }$$, $$\frac { 5 }{ 10 }$$, $$\frac { 6 }{ 10 }$$, $$\frac { 7 }{ 10 }$$, $$\frac { 8 }{ 10 }$$
As all the fractions are like fractions, compare the numerators
1 < 2 < 3 < 4 < 5 < 6 < 7 < 8
Comparing like fractions is $$\frac { 1 }{ 10 }$$ < $$\frac { 2 }{ 10 }$$ < $$\frac { 3 }{ 10 }$$ < $$\frac { 4 }{ 10 }$$ < $$\frac { 5 }{ 10 }$$ < $$\frac { 6 }{ 10 }$$ < $$\frac { 7 }{ 10 }$$ < $$\frac { 8 }{ 10 }$$
The ascending order is $$\frac { 1 }{ 10 }$$, $$\frac { 2 }{ 10 }$$, $$\frac { 3 }{ 10 }$$, $$\frac { 4 }{ 10 }$$, $$\frac { 5 }{ 10 }$$, $$\frac { 6 }{ 10 }$$, $$\frac { 7 }{ 10 }$$, $$\frac { 8 }{ 10 }$$
The descending order is $$\frac { 8 }{ 10 }$$, $$\frac { 7 }{ 10 }$$, $$\frac { 6 }{ 10 }$$, $$\frac { 5 }{ 10 }$$, $$\frac { 4 }{ 10 }$$, $$\frac { 3 }{ 10 }$$, $$\frac { 2 }{ 10 }$$, $$\frac { 1 }{ 10 }$$
(ii) Given fractions are $$\frac { 11 }{ 9 }$$, $$\frac { 12 }{ 9 }$$, $$\frac { 13 }{ 9 }$$, $$\frac { 14 }{ 9 }$$, $$\frac { 15 }{ 9 }$$, $$\frac { 16 }{ 9 }$$, $$\frac { 17 }{ 9 }$$, $$\frac { 18 }{ 9 }$$
As all the fractions are like fractions, compare the numerators
18 > 17 > 16 > 15 > 14 > 13 > 12
Comparing like fractions is
$$\frac { 18 }{ 9 }$$ > $$\frac { 17 }{ 9 }$$ > $$\frac { 16 }{ 9 }$$ > $$\frac { 15 }{ 9 }$$ > $$\frac { 14 }{ 9 }$$ > $$\frac { 13 }{ 9 }$$ > $$\frac { 12 }{ 9 }$$ > $$\frac { 11 }{ 9 }$$
The ascending order is $$\frac { 11 }{ 9 }$$, $$\frac { 12 }{ 9 }$$, $$\frac { 13 }{ 9 }$$, $$\frac { 14 }{ 9 }$$, $$\frac { 15 }{ 9 }$$, $$\frac { 16 }{ 9 }$$, $$\frac { 17 }{ 9 }$$, $$\frac { 18 }{ 9 }$$
The descending order is $$\frac { 18 }{ 9 }$$, $$\frac { 17 }{ 9 }$$, $$\frac { 16 }{ 9 }$$, $$\frac { 15 }{ 9 }$$, $$\frac { 14 }{ 9 }$$, $$\frac { 13 }{ 9 }$$, $$\frac { 12 }{ 9 }$$, $$\frac { 11 }{ 9 }$$

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