To find out how far Alberto ran on Tuesday, we need to calculate \( \frac{9}{10} \) of the distance he ran on Monday, which was \( \frac{4}{5} \) kilometer.
We can find this by multiplying the two fractions:
\[ \text{Distance on Tuesday} = \frac{9}{10} \times \frac{4}{5} \]
To multiply the fractions, we multiply the numerators together and the denominators together:
\[ \text{Distance on Tuesday} = \frac{9 \times 4}{10 \times 5} = \frac{36}{50} \]
Now, we need to simplify \( \frac{36}{50} \). To do that, we find the greatest common divisor (GCD) of 36 and 50.
The factors of 36 are \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \) and the factors of 50 are \( 1, 2, 5, 10, 25, 50 \). The GCD is 2.
Now we simplify the fraction:
\[ \frac{36 \div 2}{50 \div 2} = \frac{18}{25} \]
Thus, the distance that Alberto ran on Tuesday, in simplest form, is
\[ \boxed{\frac{18}{25}} \] kilometers.
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