To multiply the fractions \(\dfrac{6}{7}\) and \(\dfrac{5}{8}\), you simply multiply the numerators together and the denominators together:

\[
\dfrac{6}{7} \times \dfrac{5}{8} = \dfrac{6 \times 5}{7 \times 8} = \dfrac{30}{56}
\]

Now, simplify the fraction \(\dfrac{30}{56}\) by finding the greatest common divisor (GCD) of 30 and 56. The GCD of 30 and 56 is 2.

Divide both the numerator and the denominator by 2:

\[
\dfrac{30 \div 2}{56 \div 2} = \dfrac{15}{28}
\]

So, the answer in its simplest form is:

\[
\dfrac{15}{28}
\]

Would you like details or have any questions?

Here are some related questions:
1. How do you determine the greatest common divisor of two numbers?
2. Can you multiply fractions by cross-multiplying? Why or why not?
3. What is the general rule for multiplying fractions?
4. How would you simplify the fraction \(\dfrac{15}{28}\) if it could be reduced further?
5. What are some real-life applications of multiplying fractions?

**Tip:** Always check if the fraction can be simplified by finding common factors between the numerator and denominator before finalizing your answer.

Learn how to multiply fractions \(\frac{6}{7}\) and \(\frac{5}{8}\) with a detailed step-by-step solution. Simplify the resulting fraction \(\frac{30}{56}\) to \(\frac{15}{28}\) using the greatest common divisor (GCD). Suitable for students in Grades 6-8.

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