To convert the mixed number [tex]\(3 \frac{5}{8}\)[/tex] to an improper fraction, follow these steps:
1. Identify the whole number and fractional part:
The mixed number consists of a whole number part [tex]\(3\)[/tex] and a fractional part [tex]\(\frac{5}{8}\)[/tex].
2. Convert the whole number to a fraction:
Convert the whole number [tex]\(3\)[/tex] into a fraction with the same denominator as the fractional part. To do this, multiply the whole number [tex]\(3\)[/tex] by the denominator [tex]\(8\)[/tex]:
[tex]\[
3 = \frac{3 \times 8}{8} = \frac{24}{8}
\][/tex]
3. Add the fractional part:
Now, add the fractional part [tex]\(\frac{5}{8}\)[/tex] to the fraction obtained from the whole number:
[tex]\[
\frac{24}{8} + \frac{5}{8}
\][/tex]
4. Combine the fractions:
Since both fractions have the same denominator, combine the numerators:
[tex]\[
\frac{24 + 5}{8} = \frac{29}{8}
\][/tex]
Thus, the mixed number [tex]\(3 \frac{5}{8}\)[/tex] converted to an improper fraction is [tex]\(\frac{29}{8}\)[/tex].
