Addition and Subtraction of Mixed Fractions

Mixed fractions have a whole and a part

Eg: 1 1/2, 2 2/3, 7 6/11, 8 1/8

Let’s take some examples

Add 1 1/2 & 3 1/2

11/2 = 1 + 1/2 = (1 × 2 + 1)/2 = (2 + 1)/2 = 3/2

31/2 = 3 + 1/2 = (3 × 2 + 1)/2 = (6 + 1)/2 = 7/2

Thus,

  1 1/2 + 3 1/2 = 3/2 + 7/2

            = (3 + 7)/2

           = 10/2

           = 5

Subtract 8   1/3 & 5 2/3

81/3 = 8 + 1/3 = (8 × 3 + 1)/3 = (24 + 1)/3 = 25/3

52/3 = 5 + 2/3 = (5 × 3 + 2)/3 = (15 + 2)/3 = 17/3

Thus,

  8  1/3 – 5 2/3 = 25/3 – 17/3

              = (25 - 17)/3

                         = 8/3

Add 1 1/2 & 7 4/11

1 1/2 = 1 + 1/2 = (1 × 2 + 1)/2 = (2 + 1)/2 = 3/2

74/11 = 7 + 4/11 (7 × 11 +4)/11 = (77 + 4)/11 = 81/11

.

Thus,

  1 1/2 + 74/11 = 3/2 + 81/11

             = (3 × 11 + 81 × 2)/(2 × 11)

             = (33 + 162)/22

             = 195/22

Subtract 9 4/7 & 8   1/3

94/7 = 9 + 4/7 = (9 × 7 + 4)/7 = (63 + 4)/7 = 67/7

81/3 = 8 + 1/3 = (8 × 3 + 1)/3 = (24 + 1)/3 = 25/3

Thus,

  94/7 – 8  1/3 = 67/7 – 25/3

            = (67 × 3 - 25 × 7)/(7 × 3)

            = (201 - 175)/21

 = 26/21