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]