Compute $\frac{49}{24}$ of $\frac{15}{14}$. Give your answer as a fraction in simplest form (not a mixed number).

To solve $\frac{49}{24}$ of $\frac{15}{14}$, we multiply the two fractions:

\[
\frac{49}{24} \times \frac{15}{14}
\]

First, multiply the numerators:

\[
49 \times 15 = 735
\]

Next, multiply the denominators:

\[
24 \times 14 = 336
\]

So, we have:

\[
\frac{735}{336}
\]

Now, simplify this fraction by finding the greatest common divisor (GCD) of 735 and 336.

The prime factorization of 735 is:

\[
735 = 3 \times 5 \times 7^2
\]

The prime factorization of 336 is:

\[
336 = 2^4 \times 3 \times 7
\]

The common factors are $3$ and $7$, so the GCD is:

\[
3 \times 7 = 21
\]

Now, divide both the numerator and denominator by 21:

\[
\frac{735 \div 21}{336 \div 21} = \frac{35}{16}
\]

Therefore, the simplified form of $\frac{49}{24} \times \frac{15}{14}$ is $\boxed{\frac{35}{16}}$.

Would you like more details on any of the steps, or have any questions?

Here are 5 related questions to further explore this topic:
1. How would you convert $\frac{35}{16}$ to a mixed number?
2. What is the decimal equivalent of $\frac{35}{16}$?
3. If you multiplied $\frac{49}{24}$ by $\frac{14}{15}$ instead, what would the result be?
4. How do you find the GCD of two large numbers quickly?
5. What is the least common multiple (LCM) of 24 and 14?

**Tip:** When multiplying fractions, simplify before multiplying to reduce the size of the numbers involved.

Learn how to compute 49/24 of 15/14 by multiplying fractions and simplifying the result. This problem involves fractions, multiplication of fractions, and simplification. Suitable for students in Grades 6-8.

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