Sure, let's work through the problem step-by-step:
First, we have the expression [tex]\(5 \times 2 \frac{4}{15}\)[/tex].
1. Convert the mixed number to an improper fraction:
The mixed number [tex]\(2 \frac{4}{15}\)[/tex] can be converted to an improper fraction as follows:
[tex]\[
2 \frac{4}{15} = 2 + \frac{4}{15} = \frac{2 \times 15}{15} + \frac{4}{15} = \frac{30}{15} + \frac{4}{15} = \frac{34}{15}
\][/tex]
2. Multiply the fractions:
Now we need to multiply [tex]\(5\)[/tex] by [tex]\(\frac{34}{15}\)[/tex]. We can treat [tex]\(5\)[/tex] as a fraction by writing it as [tex]\(\frac{5}{1}\)[/tex]:
[tex]\[
5 \times \frac{34}{15} = \frac{5}{1} \times \frac{34}{15}
\][/tex]
3. Find the product of the numerators and the denominators:
Multiply the numerators and the denominators:
[tex]\[
\text{Numerator: } 5 \times 34 = 170
\][/tex]
[tex]\[
\text{Denominator: } 1 \times 15 = 15
\][/tex]
So, the resulting fraction is:
[tex]\[
\frac{170}{15}
\][/tex]
4. Simplify the fraction:
To simplify [tex]\(\frac{170}{15}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 170 and 15 is 5. Now, we divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\][/tex]
Therefore, [tex]\(\frac{170}{15}\)[/tex] simplifies to [tex]\(\frac{34}{3}\)[/tex].
Final Answer:
[tex]\[
5 \times 2 \frac{4}{15} = \frac{34}{3}
\][/tex]
