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Adding improper fractions with different denominators

How to add improper fractions with different denominators?

Rule for adding improper fractions with different denominators:

1. Add these improper fractions;
2. Convert the result to a mixed fraction.

Examples of adding improper fractions with different denominators

Problem: Add improper fractions with different denominators

11 + 15
87

Solution.

1. Add the improper fractions

11 + 15 = 
87
11 * 7 + 15 * 8 = 
8 * 77 * 8
77 + 120 = 
5656
77 + 120 = 197
5656

2. Convert the improper fraction into a mixed fraction

197 = 329
5656

Answer

11 + 15 = 329
8756

Problem: Add improper fractions with different denominators

37 + 29
317

Solution.

1. Add the improper fractions

37 + 29 = 
317
37 * 17 + 29 * 3 = 
3 * 1717 * 3
629 + 87 = 
5151
629 + 87 = 716
5151

2. Convert the improper fraction into a mixed fraction

716 = 142
5151

Answer

37 + 29 = 142
31751