To find the product of \( \frac{34}{9} \times 15 \), we can follow these steps:
### Step 1: Write the expression
We start with the expression:
\[
\frac{34}{9} \times 15
\]
### Step 2: Convert 15 to a fraction
We can write 15 as a fraction:
\[
15 = \frac{15}{1}
\]
Now, our expression looks like this:
\[
\frac{34}{9} \times \frac{15}{1}
\]
### Step 3: Multiply the fractions
To multiply two fractions, we multiply the numerators together and the denominators together:
\[
\frac{34 \times 15}{9 \times 1} = \frac{34 \times 15}{9}
\]
### Step 4: Calculate the numerator
Now, we calculate \( 34 \times 15 \):
\[
34 \times 15 = 510
\]
So, we have:
\[
\frac{510}{9}
\]
### Step 5: Simplify the fraction
Next, we simplify \( \frac{510}{9} \). We can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 510 and 9 is 3.
Dividing both by 3:
\[
\frac{510 \div 3}{9 \div 3} = \frac{170}{3}
\]
### Final Answer
Thus, the product of \( \frac{34}{9} \times 15 \) is:
\[
\frac{170}{3}
\]
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