Find [tex]\( \frac{5}{7} + \frac{-6}{11} + \frac{-8}{21} + \frac{22}{77} \)[/tex]
Answer (2)
To sum the fractions 7 5 + 11 − 6 + 21 − 8 + 77 22 , we first find the least common denominator, which is 231. After converting each fraction to this common denominator and combining them, the result is 231 17 .
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To solve the expression 7 5 + 11 − 6 + 21 − 8 + 77 22 , we need to find a common denominator so that we can add all the fractions together.
Find the Least Common Denominator (LCD):
The denominators are 7 , 11 , 21 , and 77 .
The LCD is the smallest number that is a multiple of these numbers. In this case, it is 231 .
Convert each fraction to have the LCD as the denominator:
7 5 = 7 × 33 5 × 33 = 231 165
11 − 6 = 11 × 21 − 6 × 21 = 231 − 126
21 − 8 = 21 × 11 − 8 × 11 = 231 − 88
77 22 = 77 × 3 22 × 3 = 231 66
Add the fractions:
Combine all the fractions using the common denominator: 231 165 + 231 − 126 + 231 − 88 + 231 66
Adding the numerators: 165 − 126 − 88 + 66 = 17
The result is: 231 17
Therefore, the sum of 7 5 + 11 − 6 + 21 − 8 + 77 22 is 231 17 . This fraction is already in its simplest form as 17 and 231 have no common factors other than 1.
