The expression in the image can be written as:

$2.7 \cdot 2 - \frac{1}{12} + \left(3.4 - 1 \frac{2}{3}\right) : 1 \frac{4}{9}$

Let's break it down step by step:

1. First part: $2.7 \cdot 2 - \frac{1}{12}$

   • Multiply $2.7 \cdot 2 = 5.4$
   • Now subtract $\frac{1}{12}$ from $5.4$: $5.4 - \frac{1}{12} = 5.4 - 0.0833 \approx 5.3167$

2. Second part: $\left( 3.4 - 1 \frac{2}{3} \right) : 1 \frac{4}{9}$

   • Convert $1 \frac{2}{3}$ to improper fraction: $1 \frac{2}{3} = \frac{5}{3}$

   • Subtract $\frac{5}{3}$ from $3.4$ (which is 34/10): $3.4 = \frac{34}{10} = \frac{51}{15}, \quad \frac{5}{3} = \frac{25}{15}$ So, $\frac{51}{15} - \frac{25}{15} = \frac{26}{15}$.

   • Now, for the division part $\frac{26}{15} : 1 \frac{4}{9}$, first convert $1 \frac{4}{9}$ into improper fraction: $1 \frac{4}{9} = \frac{13}{9}$ Division of fractions: $\frac{26}{15} \div \frac{13}{9} = \frac{26}{15} \cdot \frac{9}{13} = \frac{234}{195} = \frac{78}{65} \approx 1.2$

3. Final step: Add the results from the two parts: $5.3167 + 1.2 = 6.5167$

Thus, the final result is approximately:

$\boxed{6.52}$

Would you like more details or have any questions?

Here are 5 related questions to further explore:

1. How do you convert mixed numbers to improper fractions?
2. What are the steps for dividing fractions?
3. Can you explain the significance of decimals and fractions in calculations?
4. How would you calculate if you were given only fractions?
5. How can rounding affect the final result in calculations?

Tip: Always keep track of decimals and fractions during calculations to maintain accuracy.