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The expression provided is:

\[
\left(1 \frac{4}{5}\right) \left(\frac{10}{27}\right)
\]

To solve this, let's first convert the mixed number \( 1 \frac{4}{5} \) into an improper fraction.

1. Convert \( 1 \frac{4}{5} \) to an improper fraction:
   \[
   1 \frac{4}{5} = \frac{5 \times 1 + 4}{5} = \frac{9}{5}
   \]

2. Now, the expression becomes:
   \[
   \left(\frac{9}{5}\right) \times \left(\frac{10}{27}\right)
   \]

3. Multiply the fractions:
   \[
   \frac{9 \times 10}{5 \times 27} = \frac{90}{135}
   \]

4. Simplify \( \frac{90}{135} \):
   - The greatest common divisor (GCD) of 90 and 135 is 45.
   \[
   \frac{90}{135} = \frac{90 \div 45}{135 \div 45} = \frac{2}{3}
   \]

So, the simplified answer is:

\[
\frac{2}{3}
\]

Would you like any further details or explanation?

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Here are 5 related questions:
1. How do you convert a mixed number into an improper fraction?
2. What are the steps to multiply two fractions?
3. How can you simplify a fraction after multiplying?
4. What is the greatest common divisor (GCD) and how do you calculate it?
5. How do you convert an improper fraction back into a mixed number?

**Tip:** When multiplying fractions, simplify them as early as possible to make calculations easier.

Learn how to multiply the fractions (1 4/5) and (10/27) with a step-by-step explanation. This problem involves converting a mixed number into an improper fraction and simplifying the result. Suitable for students in Grades 5-7.

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