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.