Unlike fractions are fractions with different denominators. The denominators of fractions have different values in this case. 2/3, 9/13, 6/7, and 8/9, for example, are unlike fractions.
Example: 5/16 + 4/8
When need to find the LCM of 16 and 8. The LCM is 16 itself. We know that, 8 x 2 = 16. Therefore, we multiply the second fractions by 2 to get 8/16.
Conversion of Unlike Fraction to Like Fraction
In order to convert an unlike fraction to like fraction, we must find out the LCM of the denominators for the entire group.
Here are the steps to convert unlike fractions to like fractions.
Step 1: Find the LCM of the denominators of the given fractions.
Step 2: Find the quotient by dividing the LCM by the denominator of the given fractions.
Step 3: Multiply the numerator by the corresponding quotient.
Example: Convert 2/9 and 5/6 to like fractions.
Step 1: Find the LCM of the denominators of the given fractions.
Here the denominators are 9 and 6. Their LCM is 18.
Step 2: Find the quotient by dividing the LCM by the denominator of the given fractions.
For 18/9 = 2 and 18/6 = 3. Thus, the quotients are 2 and 3 respectively.
Step 3: Multiply the numerator by the corresponding quotient.
We multiply both the numerator and denominator by their respective quotients.
We get 4/18 and 15/18. Now, these are like fractions.
Now we have two like fractions. Now we can easily perform the addition as (5 + 4)/16 = 9/16.
Operations on Unlike fractions:
(i) Addition of Unlike Fractions:
In the case of unlike fractions, the addition operation is performed by finding the LCM, multiplying by the quotient and conversion into Like Fractions.
Example: 2/9 + 4/3 LCM is 9. We multiply the second fraction by quotient 3, to get, 12/9 = 2/9 + 12/9 = 14/9
(ii) Subtraction of Unlike Fractions:
In the case of unlike fractions, the subtraction operation is performed by finding the LCM, multiplying by the quotient and converting it into Like Fractions.
Example: 4/3 – 2/9 LCM is 9. We multiply the second fraction by quotient 3, to get, 12/9 = 12/9 – 2/9 = 10/9
(iii) Multiplication of Unlike Fractions:
In the case of unlike fractions, the multiplication operation is performed by multiplying numerator with numerator and denominator with denominator.
Example: 4/3 x 2/9 = 8/27
(iv) Division of Unlike Fractions:
In the case of unlike fractions, the multiplication operation is performed by multiplying numerator with numerator and denominator with denominator.
Example: \(\frac{4}{3} \times \frac{2}{9} = \frac{8}{27}\)
\(\frac{4}{3} \div \frac{2}{9}= \frac{4}{3} \times \frac{9}{2} = \frac{4\times9}{2\times3} = \frac{36}{6} = 6\)
