Solution:
1. The original equation is: 6.5 \div 6 \cdot X = 0.8.
2. Solve for X by isolating it on one side.
- First, calculate 6.5 \div 6:
6.5 \div 6 = \frac{6.5}{6} = \frac{13}{12}.
3. Substitute the result back into the equation:
\frac{13}{12} \cdot X = 0.8.
4. Solve for X by multiplying both sides by the reciprocal of \frac{13}{12}:
X = 0.8 \cdot \frac{12}{13}.
5. Calculate further:
X = \frac{0.8 \times 12}{13},
X = \frac{9.6}{13}.
6. Simplify the fraction:
- Since 9.6 can be written as 96/10, the equation becomes:
X = \frac{96}{130},
- Simplifying by dividing numerator and denominator by 2:
X = \frac{48}{65}.
7. The value of X is:
X = \frac{48}{65}.