We need to simplify the expression:

\[
\frac{5}{3} \div \left(\left(\frac{5}{6}\right)^2\right) - \frac{3}{10}
\]

### Step 1: Square the fraction \(\frac{5}{6}\)

\[
\left(\frac{5}{6}\right)^2 = \frac{25}{36}
\]

### Step 2: Divide \(\frac{5}{3}\) by \(\frac{25}{36}\)

Dividing fractions involves multiplying the first fraction by the reciprocal of the second:

\[
\frac{5}{3} \div \frac{25}{36} = \frac{5}{3} \times \frac{36}{25} = \frac{5 \times 36}{3 \times 25} = \frac{180}{75} = \frac{12}{5}
\]

### Step 3: Subtract \(\frac{3}{10}\) from \(\frac{12}{5}\)

Convert \(\frac{12}{5}\) to have the same denominator as \(\frac{3}{10}\):

\[
\frac{12}{5} = \frac{24}{10}
\]

Now subtract:

\[
\frac{24}{10} - \frac{3}{10} = \frac{21}{10}
\]

### Final Answer:
\[
\frac{21}{10} \text{ or } 2.1
\]

Would you like any details or have any questions?

Here are 5 related questions for practice:
1. Simplify \(\frac{7}{4} \div \left(\frac{3}{5}\right)^2 - \frac{1}{2}\).
2. What is \(\frac{9}{2} \div \left(\frac{7}{3}\right)^2 + \frac{5}{6}\)?
3. How do you multiply and divide mixed fractions?
4. Simplify \(\frac{8}{3} \times \left(\frac{2}{7}\right)^3 - \frac{4}{9}\).
5. Evaluate \(\left(\frac{1}{2}\right)^3 + \frac{5}{12} \div \frac{2}{3}\).

**Tip:** When dividing fractions, always multiply by the reciprocal of the divisor!

Learn how to simplify the expression 1 2/3 divided by (5/6)^2 minus 3/10 with a step-by-step breakdown. This solution involves dividing fractions, exponentiation, and subtraction of fractions. Ideal for students in Grades 6-8.

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