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
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