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Sagot :

Answer:

[tex] \frac{233}{120} [/tex]

Step-by-step explanation:

1. Find the Least Common Denominator (LCD):

  • The denominators are 5, 3, and 8.
  • The least common multiple of 5, 3, and 8 is 120.

2. Convert each fraction to have a denominator:

  • [tex] \frac{2}{5} \: becomes \: \frac{2 \times 24}{5 \times 24} = \frac{48}{120} [/tex]
  • [tex] \frac{2}{3} \: becomes \: \frac{2 \times 40}{3 \times 40} = \: \frac{80}{120} [/tex]
  • [tex] \frac{7}{8} \: becomes \: \frac{7 \times 15}{8 \times 15} = \frac{105}{120} [/tex]

3. Add the fraction

  • [tex] \frac{48}{120} + \frac{80}{120} + \frac{105}{120} [/tex]

4. Perform the addition:

  • [tex] \frac{48 + 80 + 105}{120} = \frac{233}{120} [/tex]

5. Therefore,

[tex] \frac{2}{5} + \frac{2}{3} + \frac{7}{8} = \frac{233}{120} [/tex]