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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Addition and Subtraction of Mixed Fractions

To add or subtract mixed fractions, first convert them into improper fractions.

Then convert unlike improper fractions into like fractions and then add or subtract as the like
fractions as usual.
1 1 1 1
Example 16: (a) Add 1 and 6 . (b) Subtract 1 from 6 .
4 2 3 2
Solution: (a) First convert the mixed fractions into improper fractions.

1 5 1 13
1 = and 6 =
4 4 2 2
The LCM of the denominators 4 and 2 is 4.
×
5 13 51 13 2 5 26 526 31 3 Quick Check
×
+
∴ + = + = + = = = 7
4 2 41 22 4 4 4 4 4 Add and subtract as
×
×
(b) First convert the mixed fractions into improper directed and fill in the
fractions. empty boxes.
+
1 4 1 13
1 = and 6 = 9 8
3 3 2 2 14 16
The LCM of the denominators 3 and 2 is 6. – 1 2
13 − 4 = 13 × 3 − 42 = 39 − 8 = 31 = 5 1 . 4 5
×
×
×
2 3 23 32 6 6 6 6
1 1 1 1
Example 17: Simplify: 2 − 3 + 4 +− .
5
5 10 15 3
Solution: First convert the mixed fractions into improper fractions:
1 11 1 31 1 61
2 = 3 , = 4 , =
5 5 10 10 15 15
LCM of 5, 10, 15 and 3 = 30
×
×
×
11 31 61 1 11 6 31 3 61 2 530 110 66 93 122 150 10
×
×
− + + 5 − = − + + − = − + + −
×
×
0
×
×
5 10 15 3 56 10 3 15 2 130 310 30 30 30 30 30
×
+
−
+
66 93 122 150 10 235
−
= =
30 30
47 5
= = 7 .
6 6
2
1
Example 18: Megha bought two packets of biscuits for ` 13 and a cream roll for `16 . Find the
total money she spent. 2 3
1 27
Solution: Cost of two packets of biscuit = `13 = `
2 2
2
Cost of a cream roll = `16 = ` 50
3 3
+
 27 50  81 100  181
Total cost of both items = `  2 + 3  = `   6  = `   6 




1
Thus, Megha spent total ` 30 on both items.
6
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