Answer :
To calculate the sum of the fractions [tex]\frac{-7}{10} + \frac{13}{15} + \frac{27}{20}[/tex], we need to find a common denominator so that we can add them together.
Determine the Least Common Denominator (LCD):
- The denominators are 10, 15, and 20.
- The least common multiple (LCM) of these numbers is 60.
Convert each fraction to have the LCD as the denominator:
- [tex]\frac{-7}{10}[/tex] becomes [tex]\frac{-7 \times 6}{10 \times 6} = \frac{-42}{60}[/tex].
- [tex]\frac{13}{15}[/tex] becomes [tex]\frac{13 \times 4}{15 \times 4} = \frac{52}{60}[/tex].
- [tex]\frac{27}{20}[/tex] becomes [tex]\frac{27 \times 3}{20 \times 3} = \frac{81}{60}[/tex].
Add the fractions:
- Now, add the numerators of the fractions since they have the same denominator:
[tex]\frac{-42}{60} + \frac{52}{60} + \frac{81}{60} = \frac{-42 + 52 + 81}{60}[/tex] - Calculate the sum of the numerators:
[tex]-42 + 52 + 81 = 91[/tex] - Therefore, the resulting fraction is:
[tex]\frac{91}{60}[/tex]
- Now, add the numerators of the fractions since they have the same denominator:
Simplify if necessary:
- The fraction [tex]\frac{91}{60}[/tex] is already in its simplest form.
Therefore, the sum of the fractions is [tex]\frac{91}{60}[/tex].
