To solve the problem [tex]$\frac{16}{17} \times 3 \frac{1}{2}$[/tex], follow these steps:
1. Convert the mixed number to an improper fraction:
- The mixed number given is [tex]\(3 \frac{1}{2}\)[/tex].
- To convert this to an improper fraction, use the formula:
[tex]\[
\text{Improper Fraction} = \text{Whole Number} + \frac{\text{Numerator}}{\text{Denominator}}
\][/tex]
- So,
[tex]\[
3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\][/tex]
2. Multiply the fractions:
- We now need to multiply the fractions [tex]\(\frac{16}{17}\)[/tex] and [tex]\(\frac{7}{2}\)[/tex].
- The multiplication of two fractions [tex]\(\frac{a}{b} \times \frac{c}{d}\)[/tex] is given by:
[tex]\[
\frac{a \times c}{b \times d}
\][/tex]
- So,
[tex]\[
\frac{16}{17} \times \frac{7}{2} = \frac{16 \times 7}{17 \times 2}
\][/tex]
3. Calculate the new numerator and denominator:
- Numerator:
[tex]\[
16 \times 7 = 112
\][/tex]
- Denominator:
[tex]\[
17 \times 2 = 34
\][/tex]
4. Simplify the fraction if possible:
- The fraction obtained is [tex]\(\frac{112}{34}\)[/tex].
- When we divide the numerator by the denominator:
[tex]\[
\frac{112}{34} \approx 3.2941176470588234
\][/tex]
Therefore, the product of [tex]\(\frac{16}{17} \times 3 \frac{1}{2}\)[/tex] is approximately 3.2941176470588234.
