When we add or subtract two or more fractions with like denominators, we use only one denominator and combine the numerators.
For example,
= 1/3 + 1/3
= (1+1)/3
= 2/3
When we add or subtract two or more fractions with unlike denominators, we can take the Least Common Multiple or use the cross multiplication.
For example,
Using Least Common Multiple :
= 1/4 + 1/5
= (1/4 × 5/5) + (1/5 × 4/4)
= 5/20 + 4/20
= 9/20
Using Cross Multiplication :
= 1/4 + 1/5
= (5 + 4)/20
= 9/20
Find :
Problem 1 :
5/13 + 7/13
Solution :
In the given fraction, the denominators are same. So, we put only one denominator and combine the numerators.
= (5 + 7)/13
= 12/13
Problem 2 :
9/16 + 2/16
Solution :
In the given fraction, the denominators are same. So, we put only one denominator and combine the numerators.
= (9 + 2)/16
= 11/16
Problem 3 :
3/8 + 1/4
Solution :
In the given fraction, the denominators are not the same.
So, we are taking the Least Common Multiple of 8 and 4.
= 3/8 + (1/4 × 2/2)
= 3/8 + 2/8
= 5/8
Problem 4 :
2/5 + 1/6
Solution :
In the given fraction, the denominators are not same.
So, we are taking the Least Common Multiple of 5 and 6.
= (2/5 × 6/6) + (1/6 × 5/5)
= 12/30 + 5/30
= 17/30
Problem 5 :
1 1/3 + 5/6
Solution :
Method 1 :
= 1 1/3 + 5/6
= 1 (1/3 + 5/6)
By taking the least common multiple, we get
= 1 (2 + 5)/6
= 1 7/6
Converting the improper fraction to mixed fraction, we get
= 1 (1 1/6)
= (1 + 1) 1/6
= 2 1/6
Method 2 :
= 1 1/3 + 5/6
Converting the mixed fractions to improper fraction, we get
= 4/3 + 5/6
Here the denominators are not the same. So, we are taking the Least Common Multiple of 3 and 6.
= (4/3 × 2/2) + 5/6 × 1/1)
= [4(2) + 5]/6
= (8 + 5)/6
= 13/6
Converting the improper fraction to mixed fraction, we get
= 2 1/6
Problem 6 :
2 1/3 + 1 1/6
Solution :
Method 1 :
= 2 1/3 + 1 1/6
= (2 + 1) (1/3 + 1/6)
By taking the least common multiple, we get
= 3 (2 + 1)/6
= 3 1/2
Method 2 :
= 2 1/3 + 1 1/6
Converting the mixed fractions to improper fraction, we get
= 7/3 + 7/6
Least common multiple of 3 and 6 is 6.
= [7(2) + 7(1)]/6
= (14 + 7)/6
= 21/6
Converting the improper fraction to mixed fraction, we get
= 3 3/6
= 3 1/2
Problem 7 :
1 1/2 + 4 2/3
Solution :
Method 1 :
= 1 1/2 + 4 2/3
= (1+4) (1/2 + 2/3)
By taking the least common multiple, we get
= 5 (3 + 4)/6
= 5 7/6
Converting the improper fraction to mixed fraction, we get
= 5 (1 1/6)
= (5 + 1) 1/6
= 6 1/6
Method 2 :
= 1 1/2 + 4 2/3
Converting the mixed fractions to improper fraction, we get
= 3/2 + 14/3
Least common multiple of 2 and 3 is 6.
= [3(3) + 14(2)]/6
= (9 + 28)/6
= 37/6
Converting the improper fraction to mixed fraction, we get
= 6 1/6
Find :
Problem 8 :
7/11 - 3/11
Solution :
In the given fraction, the denominators are same. So, we put only one denominator and combine the numerators.
= (7 - 3)/11
= 4/11
Problem 9 :
5/6 - 2/3
Solution :
In the given fraction, the denominators are not same.
So, we are taking the Least Common Multiple of 6 and 3.
= 5/6 - (2/3 × 2/2)
= 5/6 - 4/6
= 1/6
Problem 10 :
4/9 - 1/3
Solution :
In the given fraction, the denominators are not same.
So, we are taking the Least Common Multiple of 9 and 3.
= 4/9 - (1/3 × 3/3)
= 4/9 - 3/9
= 1/9
Problem 11 :
2 3/5 - 1 1/2
Solution :
Method 1 :
= 2 3/5 - 1 1/2
= (2 - 1) (3/5 - 1/2)
By taking the least common multiple, we get
= 1 (6 - 5)/10
= 1 1/10
Method 2 :
= 2 3/5 - 1 1/2
Converting the mixed fractions to improper fraction, we get
= 13/5 - 3/2
Least common multiple of 5 and 2 is 10.
= [13(2) - 3(5)]/10
= (26 - 15)/10
= 11/10
Converting the improper fraction to mixed fraction, we get
= 1 1/10
Problem 12 :
3 1/3 - 1 1/2
Solution :
Method 1 :
= 3 1/3 - 1 1/2
= (3 - 1) (1/3 - 1/2)
By taking the least common multiple, we get
= 2 (2 - 3)/6
= 2 (-1)/6
= 11/6
Converting the improper fraction to mixed fraction, we get
= 1 5/6
Method 2 :
= 3 1/3 - 1 1/2
Converting the mixed fractions to improper fraction, we get
= 10/3 - 3/2
Least common multiple of 3 and 2 is 6.
= [10(2) - 3(3)]/6
= (20 - 9)/6
= 11/6
Converting the improper fraction to mixed fraction, we get
= 1 5/6
Problem 13 :
4 3/7 - 2 1/3
Solution :
Method 1 :
= 4 3/7 - 2 1/3
= (4 - 2) (3/7 - 1/3)
By taking the least common multiple, we get
= 2 (9 - 7)/21
= 2 2/21
Method 2 :
= 4 3/7 - 2 1/3
Converting the mixed fractions to improper fraction, we get
= 31/7 - 7/3
Least common multiple of 7 and 3 is 21.
= [31(3) - 7(7)]/21
= (93 - 49)/21
= 44/21
Converting the improper fraction to mixed fraction, we get
= 2 2/21
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