Rashad created another equivalent expression to

1 

6 

(9x+15) 

8 with a 2 in the denominator. What could be the numerator? 

To solve this problem, we start by simplifying the original expression:

\[
\frac{1}{6} \times \frac{9x + 15}{8}
\]

First, multiply the numerators and the denominators:

\[
\text{Numerator} = 1 \times (9x + 15) = 9x + 15
\]
\[
\text{Denominator} = 6 \times 8 = 48
\]

So, the expression simplifies to:

\[
\frac{9x + 15}{48}
\]

Now, the problem asks for an equivalent expression with a denominator of 2. To achieve this, let's find an equivalent fraction with a denominator of 2.

We need to multiply both the numerator and the denominator by a factor that will convert the denominator from 48 to 2. The factor is:

\[
\frac{48}{2} = 24
\]

So, we multiply the numerator by 24:

\[
\text{New numerator} = (9x + 15) \times 24 = 216x + 360
\]

Thus, the equivalent expression with a denominator of 2 has a numerator of \(216x + 360\).

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you determine if two expressions are equivalent?
2. What are some methods for simplifying fractions?
3. Can you explain the process of cross-multiplication in finding equivalent fractions?
4. How would you find an equivalent expression with a different denominator, such as 4 or 8?
5. What is the importance of maintaining equivalence in algebraic expressions?

**Tip:** Always verify your work by simplifying the equivalent expression back to its original form to ensure accuracy.

Learn how to find an equivalent expression with a denominator of 2 for the fraction 1/6 * (9x + 15) / 8. Detailed step-by-step solution provided, covering fractions and equivalent expressions. Suitable for students in Grades 6-8.

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