# ADDING AND SUBTRACTING MIXED FRACTIONS WITH UNLIKE DENOMINATORS

Problem 1 :

= 1  2/3 + 3  1/4

Solution :

Converting the mixed fraction to improper fraction, we get

=  5/3 + 13/4

Least common multiple of 3 and 4 is 12.

= [5(4) + 13(3)]/12

= (20 + 39)/12

= 59/12

Converting the improper fraction to mixed fraction, we get

= 4  11/12

Problem 2 :

3  3/4 - 1  1/2

Solution :

= 3  3/4 - 1  1/2

Converting the mixed fraction to improper fraction, we get

= 15/4 - 3/2

Least common multiple of 4 and 2 is 4.

= [15(1) – 3(2)]/4

= (15 – 6)/4

= 9/4

Converting the improper fraction to mixed fraction, we get

= 2  1/4

Problem 3 :

3/4  - 2  1/2

Solution :

= 3/4  - 2  1/2

Converting the mixed fraction to improper fraction, we get

= 3/4 - 5/2

Least common multiple of 4 and 2 is 4.

= [3(1) – 5(2)]/4

= (3 - 10)/4

= -7/4

Converting the improper fraction to mixed fraction, we get

= -1  3/4

Problem 4 :

4  1/3 + 2  1/6

Solution :

=  4  1/3 + 2  1/6

Converting the mixed fraction to improper fraction, we get

= 13/3 + 13/6

Least common multiple of 3 and 6 is 6.

= [13(2) + 13(1)]/6

= (26 + 13)/6

= 39/6

= 13/2

Converting the improper fraction to mixed fraction, we get

= 6  1/2

Problem 5 :

2  2/3  - 5  5/6

Solution :

=  2  2/3  - 5  5/6

Converting the mixed fraction to improper fraction, we get

= 8/3 - 35/6

Least common multiple of 3 and 6 is 6.

= [8(2) – 35(1)]/6

= (16 - 35)/6

= -19/6

Converting the improper fraction to mixed fraction, we get

= - 3 1/6

Problem 5 :

-2  1/4 + 3  1/8

Solution :

= -2  1/4 + 3  1/8

Converting the mixed fraction to improper fraction, we get

= (-9/4) + 25/8

Least common multiple of 4 and 8 is 8.

= [(-9(2) + 25(1)]/8

= (-18 + 25)/8

= 7/8

Problem 7 :

4  1/5  - 2  1/6

Solution :

=  4  1/5 - 2  1/6

Converting the mixed fraction to improper fraction, we get

= 21/5 - 13/6

Least common multiple of 5 and 6 is 30.

= [(21(6) – 13(5)]/30

= (126 - 65)/30

= 61/30

= 13/2

Converting the improper fraction to mixed fraction, we get

= 2  1/30

Problem 8 :

2  1/3 + 1  1/6

Solution :

= 2  1/3 + 1  1/6

Converting the mixed fraction to improper fraction, we get

= 7/3 + 7/6

= [7(2) + 7(1)]/6

Least common multiple of 3 and 6 is 6.

=(14 + 7)/6

= 21/6

Converting the improper fraction to mixed fraction, we get

= 3  1/2

Problem 9 :

1  1/2 + 4  2/3

Solution :

= 1  1/2 + 4  2/3

Converting the mixed fraction to improper fraction, we get

= 3/2 + 14/3

= [3(3) + 14(2)]/6

Least common multiple of 3 and 2 is 6.

= (9 + 28)/6

= 37/6

Converting the improper fraction to mixed fraction, we get

= 6  1/6

Problem 10 :

3  1/3  - 1  1/2

Solution :

=  3  1/3 - 1  1/2

Converting the mixed fraction 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 11 :

4  3/7  - 2  1/3

Solution :

=  4  3/7 - 2  1/3

Converting the mixed fraction 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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