Class 4 Fractions Addition
Introduction to Fractions Addition
Introduction to Fractions Addition
There are mainly 3 types of fraction addition, they are given below.
1. Addition of like fraction
2. Addition of unlike fraction
3. Addition of mixed fraction
Addition of Like Fractions
To add like fractions, we first add the numerators of both the fractions. Then, we place the sum over the common denominator. Let's have a look at some examples.
Example 1. Add 2⁄9 and 52⁄9.
Solution.
Example 2. Add 1⁄12 and 5⁄12.
Solution.
If we simplify 6⁄12 further, then it will become 1⁄2.
Example 3. Add 1⁄7, 2⁄7 and 3⁄7.
Solution.
Example 4. Add 4⁄15 and 6⁄15.
Solution.
If we simplify 10⁄15 further, then it will become 2⁄3.
Addition of Unlike Fractions
Method 1
To add fractions with different denominators, we have to change the fractions into like fractions, or we have to change the fractions to fractions having same denominators. Let's see some examples.
Example 1. Add 2⁄3 and 1⁄4.
Solution.
2⁄3 + 1⁄4
First, we have to convert 2⁄3 and 1⁄4 into like fractions.
Denominator of the first fraction should be multiplied to numerator and denominator of second fraction. In this case, 3 is the denominator of first fraction and it should be multiplied both
numerator and denominator of second fraction 1⁄4.
similarly
Now, add 8⁄12 and 3⁄12.
Example 2. Add 2⁄3 and 5⁄6.
Solution.
Method 2
Example 1. Add 2⁄3 and 3⁄4
Solution.
Find the LCM of the denominators. It is 12 in this case. Divide 12 by the denominator of the first fraction. 12 ÷ 3 = 4. Multiply the quotient (4) by the numerator of the first fraction. 4 x 2 = 8. Now divide 12 by the denominator of the second fraction 12 ÷ 4 = 3. Multiply the quotient by the numerator of the second fraction 3 x 3 = 9. So, the resultant fraction numerator will be 8 + 9 = 17 and denominator will be 12. Let’s see the mathematical operation.
Example 2. Add 3⁄5 and 4⁄15.
Solution.
3⁄5 + 4⁄15
LCM of 5 and 15 is equal to 15.
Example 3. Add 3⁄4, 5⁄8 and 7⁄12.
Solution.
3⁄4 + 5⁄8 + 7⁄12
LCM of 4, 8 and 12 is equal to 24.
Addition of Mixed Fraction
Method 1
Convert the mixed fractions to improper fractions and then add the fractions. Let's see some examples.
Example 1. Add 32⁄5 and 21⁄5
Solution.
First convert 32⁄5 and 21⁄5 into improper fraction.
Improper fraction of 32⁄5 is equal to 17⁄5.
Improper fraction of 21⁄5is equal 11⁄5.
Now add both the improper fraction.
Method 2
In this method, we first add the whole numbers and keep the sum aside. Then, we add the fractions. To write the answer, we first write the whole number and on it's right, we write the sum of the fractions.
Example 1. Add 21⁄5 and 33⁄5
Solution.
First add the whole numbers, that is 2 + 3 = 5. Keep it aside on the left.
Then, add the fractions 1⁄5 and 3⁄5
5(1⁄5 + 3⁄5) = 54⁄5
Example 2. Add 22⁄5 and 33⁄10
Solution.
22⁄5 + 33⁄10
First, add the whole numbers, that is, 2 + 3 = 5
Then, add the fractions.
So, the answer is 57⁄10.
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