To solve the expression \(\frac{6}{5} \cdot \frac{7}{8} \cdot \frac{24}{21} \cdot 2425\), we need to simplify step-by-step:

1. Simplify the product of the fractions: 
\[
\frac{6}{5} \cdot \frac{7}{8} \cdot \frac{24}{21}
\]

2. Calculate the result of this product.

3. Multiply the result by 2425.

First, let's simplify the fraction multiplication:

\[
\frac{6}{5} \cdot \frac{7}{8} \cdot \frac{24}{21}
\]

We can multiply the numerators and denominators separately:
\[
\frac{6 \cdot 7 \cdot 24}{5 \cdot 8 \cdot 21}
\]

Now calculate the products in the numerator and the denominator:
\[
\frac{6 \cdot 7 \cdot 24}{5 \cdot 8 \cdot 21} = \frac{1008}{840}
\]

Next, simplify the fraction \(\frac{1008}{840}\). We do this by finding the greatest common divisor (GCD) of 1008 and 840. Using the Euclidean algorithm:

\[
1008 \div 840 \approx 1.2 \implies \text{remainder} = 168
\]
\[
840 \div 168 \approx 5 \implies \text{remainder} = 0
\]

So, the GCD is 168.

Now, divide both the numerator and the denominator by the GCD:
\[
\frac{1008 \div 168}{840 \div 168} = \frac{6}{5}
\]

So, the simplified form of the fraction product is \(\frac{6}{5}\).

Now, we multiply this by 2425:

\[
\frac{6}{5} \cdot 2425
\]

First, perform the multiplication:

\[
6 \cdot 2425 = 14550
\]

Then divide by 5:

\[
\frac{14550}{5} = 2910
\]

Thus, the expression simplifies correctly to 2910.

If you have any questions or need further details, let me know!

Here are five additional questions you might want to explore:

1. How do you solve a quadratic equation?
2. What is the integral of \(x^2\) with respect to \(x\)?
3. How do you find the derivative of \(\sin(x)\)?
4. What is the formula for the area of a circle?
5. How do you convert a fraction to a decimal?

**Tip:** When multiplying fractions, always simplify the fractions first if possible to make calculations easier.

Learn how to solve the expression involving fractions and multiplication step-by-step. This problem covers key concepts in fractions, multiplication, and finding the greatest common divisor (GCD). Suitable for students in Grades 6-8.

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