Let's evaluate the given expression step-by-step:

Expression:  
\[
\frac{45}{56} \cdot 78 + 910 \cdot \frac{512}{1}
\]

1. **Division**: 
   \[
   \frac{45}{56}
   \]

2. **Multiplication** (next to the division result): 
   \[
   \frac{45}{56} \cdot 78
   \]

3. **Multiplication** (separate expression):
   \[
   910 \cdot \frac{512}{1} = 910 \cdot 5
   \]

4. **Addition**:
   Add the two results from above.

Simplifying this gives:

1. First, calculate \(\frac{45}{56} \times 78\).
2. Then, multiply \(910 \times \frac{512}{1}\).
3. Finally, add the results of the multiplications.

Now let's solve this:

1. \(\frac{45}{56} \times 78 = \frac{45 \times 78}{56}\)
2. \(910 \times 512\)
3. Add the results from steps 1 and 2.

Let me do the calculations for you:Here's the step-by-step solution:

1. Calculation of \(\frac{45}{56} \times 78\):
   \[
   \frac{45 \times 78}{56} = \frac{1755}{28}
   \]

2. Calculation of \(910 \times 5\):
   \[
   910 \times 5 = 4550
   \]

3. Adding the two results:
   \[
   \frac{1755}{28} + 4550 = \frac{129155}{28} \approx 4619.82
   \]

The final result is approximately **4619.82**.

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How do you simplify fractions step-by-step?
2. What are

Learn how to evaluate the arithmetic expression 4 ÷ 5 ∙ 6 + 7 ∙ 8 + 9 ∙ 10 ∙ 5 ∙ 12 step-by-step with a detailed solution. This problem involves basic arithmetic operations and the order of operations rule. Suitable for students in Grades 7-9.

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