Like Fractions and Unlike Fractions
Like fractions and unlike fractions are two common types of fractions based on the denominators. If two or more fractions share the same denominator we call them like fractions, while on the other hand, if the denominators of two or more fractions are different, those are known as unlike fractions. For example, 1/2 and 3/2 are like fractions and 1/2 and 3/4 are unlike fractions.
What are Like Fractions and Unlike Fractions?
As explained above, like fractions and unlike fractions are the two basic types of fractions that we need to know before learning about the comparison of fractions and arithmetic operations on fractions. We should always have at least two fractions to categorize them into like fractions and unlike fractions. Let us understand their definitions in detail.
Like Fractions
The fractions which have the same denominator are called like fractions. i.e. their denominators are equal. For example, if we have a group of fractions such as 1/5, 2/5, 3/5, 4/5. Since the denominators of each of the fractions are the same i.e. 5, they are like fractions. In like fractions, the whole is always the same which is represented by the common denominators.
Note: There are fractions such as 1/3, 2/6, and 3/9. These are also called like fractions even though their denominators are different since we can simplify all of them to 1/3 where we get the same denominator 3. Whole numbers such as 1,2 and 3 are considered like fractions since their denominators though not explicitly stated, are considered 1.
Unlike Fractions
Unlike fractions are the fractions where the denominator of each fraction is different. For example, if we have a group of fractions such as 3/8, 2/3, 3/5, and 2/7, they are unlike fractions since the denominators 8, 3, 5, and 7 are different. In unlike fractions, we take parts of the different whole.
Comparing Like Fractions and Unlike Fractions
There are different ways to compare like fractions and unlike fractions which are explained below. It is easy to compare like fractions just by looking at their numerators, but we have to convert unlike fractions to like fractions in order to compare them.
To compare like fractions, we only need to compare the numerators since the denominators are equal. For example, let us compare two fractions 7/8 and 5/8 which have the same denominator 8. Since 7 shaded parts of 8 are bigger than the 5 shaded parts of 8 therefore 7/8 > 5/8. The comparison of like fractions is shown in the image below.
There are two cases that come up while comparing two or more unlike fractions. First is when the numerators of unlike fractions are the same and denominators are different. In this case, the fraction having a smaller denominator is the largest and the fraction having the largest denominator is the smallest. Let us compare two fractions 8/9 and 8/11 which have the same numerator. Since 8 shaded parts of 9 are bigger than the 8 shaded parts of 11 therefore 8/9 > 8/11. The second case is when both numerators and denominators are different. Here, we have to first convert unlike fractions to like fractions by taking LCM of their denominators. For example, let us compare 2/3 and 4/5. The LCM of the denominators 3 and 5 is 15. Now, multiply the numerator and denominator of the first fraction by 5 to get 15 as the denominator, 2/3 × 5/5 = 10/15. Now, multiply the numerator and denominator of the second fraction by 3 to get 15 as the denominator, 4/5 × 3/3 = 12/15. Now we have to compare these two like fractions obtained, 10/15 and 12/15. Here, 10/15<12/15, therefore, 2/3<4/5.
This is how comparison of like and unlike fractions are done.
Arithmetic Operations on Like Fractions and Unlike Fractions
They are 4 basic arithmetic operations on like fractions and unlike fractions. They are as follows: addition, subtraction, multiplication, and division. Let us understand how to perform each of these operations on like fractions and unlike fractions in detail.
Addition of Like and Unlike Fractions
To add like fractions i.e. fractions having the same denominators, simply add the numerators and consider the denominators only once. For example, to add 3/5 and 7/5, we add the numerators 3 and 7, which is 10. Now, use the common denominator as the denominator of the sum. So the final answer is 10/5, which can be simplified to 2.
To add unlike fractions, we first convert them to like fractions and then add them. To know more about adding like and unlike fractions, click here.
Subtraction of Like Fractions and Unlike Fractions
To subtract one like fraction from the other, simply subtract one numerator from the other and consider the denominators only once. For example, to subtract 1/4 from 3/4, we subtract their numerators, as 3-1 =2. Now, use the common denominator as the denominator of the answer. So, 3/4 - 1/4 = 2/4. We can further simplify 2/4 by dividing both the numerator by 2, so 2/4 = 1/2. Therefore, 3/4 - 1/4 = 1/2.
To subtract one unlike fraction from the other, there are two methods. They are the cross-multiplication method and the LCM method.
Let us consider the subtraction of fractions 4/15 from 7/12. The denominators are 12 and 15. The common divisor between 12 and 15 are 1 and 3. Since 1 is not the only common divisor between 12 and 15, we can apply the LCM method as shown below:
7/12 - 4/15
The LCM of the denominators 12 and 15 is 60
7/12 - 4/15 = ((7 x 5)/(12 x 5)) - ((4 x 4)/(15 x 4))
(35/60) - (16/60)
(35 - 16)/60
=19/60
To know more about the subtraction of fractions, click here.
Multiplication of Like and Unlike Fractions
To multiply like and unlike fractions, we need to multiply the numerators, multiply the denominators, and then simplify the result if needed.
- Example of like fractions multiplication: 1/3 x 2/3 = (1 x 2)/(3 x 3) = 2/9
- Example of unlike fractions multiplication: 1/5 x 3/8 = (1 x 3)/(5 x 8) = 3/40
To know more about multiplication of fractions, click here.
Division of Like Fractions and Unlike Fractions:
To divide like fractions and unlike fractions, we need to replace the division sign with multiplication and take the reciprocal of the second fraction or flip/change its numerator and denominator and then follow the same steps as multiplication.
- Example for division of like fractions: 3/5 ÷ 4/5 = 3/5 × 5/4 = (3 × 5)/(5 × 4) = 15/20. This can be simplified to 3/4 by dividing both the numerator and the denominator by 5. Therefore, 3/5 ÷ 4/5 = 3/4
- Example of unlike fractions division: 2/5 ÷ 3/7 = 2/5 × 7/3 =(2 × 7)/(5 × 3) = 14/15. Observe that 3/7 has been flipped/changed to 7/3 and the sign changed from division to multiplication.
To know more about the division of fractions, click here.
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FAQs on Like Fractions and Unlike Fractions
What are Like Fractions and Unlike Fractions?
Like fractions have the same denominators. For example, for a group of fractions 3/5, 4/5, and 7/5, all the denominators are the same i.e 5. Therefore, they are like fractions. Unlike fractions have different denominators. For example, for a group of fractions 2/3, 3/5, and 4/7, the denominators are 3, 5, and 7. We can see that each of the denominators is different from the others. Therefore, they are unlike fractions.
Do Like Fractions and Unlike Fractions have the Same Numerator?
Like fractions are fractions having the same denominators; the numerators can be the same or different. Unlike fractions are fractions having different denominators. The numerators in unlike fractions also can be the same or different. For example, 1/2 and 1/3 are unlike fractions having the same numerator, while 3/4 and 5/6 are unlike fractions having different numerators.
How to Convert Unlike Fractions to Like Fractions?
Unlike fractions can be converted to like fractions by finding the lowest common multiple (LCM) of the denominators first and then calculating their equivalent fractions with the same denominator. For example, 2/5 and 3/7 are unlike fractions. They can be converted to like fractions by following the steps given below.
- Calculate the LCM of the denominators. The denominators are 5 and 7. The LCM of 5 and 7 is 35.
- Calculate the equivalent fractions: 2/5 = (2 × 7)/(5 × 7) = 14/35 and 3/7 = (3 × 5)/(7 × 5) = 15/35
Therefore, 2/5 = 14/35 and 3/7 = 15/35, and 14/35 and 15/35 are like fractions since the denominator is the same i.e. 35.
How to Compare Like Fractions and Unlike Fractions?
For like fractions, the denominators are the same, therefore to compare like fractions, we compare the numerators. The fraction is greater if the numerator is greater and is smaller if the numerator is smaller. For example, to compare 3/7 and 5/7, we check if they are like fractions and since they are, we compare the numerators 3 and 5. Since 5 > 3, therefore, 5/7 > 3/7.
For unlike fractions, the denominators of each of the fractions are different from the others, therefore to compare unlike fractions, we need to first convert them to like fractions and then compare the numerators. The fraction is greater if the numerator is greater and is smaller if the numerator is smaller. For example, to compare 3/5 and 4/7, we check if they are like fractions and since they are not, we need to convert them to like fractions.
3/5 and 4/7
The LCM of 5 and 7 is 35
(3 × 7)/35 and (4 × 5)/35
= 21/35 and 20/35
21/35 > 20/35 since the numerator 21> 20.
Therefore, 3/5 > 4/7
What are the 5 Examples of Unlike Fractions and Like Fractions?
Like fractions and unlike fractions are always considered in pairs or in groups. The five examples of like fractions are given below:
- 1/2, 3/2, 4/2
- 2/3, 5/3, 1/3
- 6/7, 4/7
- 3/4, 1/4, 2/4, 5/4
- 1/6, 4/6
Five examples of unlike fractions are given below:
- 1/2, 5/8
- 6/7, 6/11, 6/5
- 1/3, 4/3, 5/7
- 3/4, 8/23, 7/24
- 4/5, 8/9