Alright, let's solve the problem \(9 \frac{4}{6} - 3 \frac{5}{8}\) step by step.
1. Convert the mixed fractions to improper fractions:
For \(9 \frac{4}{6}\):
[tex]\[
9 \frac{4}{6} = 9 + \frac{4}{6}
\][/tex]
Since 9 is equivalent to \( \frac{54}{6} \) (because \(9 \times 6 = 54\)), we add \(\frac{4}{6}\) to get:
[tex]\[
9 \frac{4}{6} = \frac{54}{6} + \frac{4}{6} = \frac{58}{6}
\][/tex]
For \(3 \frac{5}{8}\):
[tex]\[
3 \frac{5}{8} = 3 + \frac{5}{8}
\][/tex]
Since 3 is equivalent to \( \frac{24}{8} \) (because \(3 \times 8 = 24\)), we add \(\frac{5}{8}\) to get:
[tex]\[
3 \frac{5}{8} = \frac{24}{8} + \frac{5}{8} = \frac{29}{8}
\][/tex]
2. Find a common denominator to subtract the fractions:
To subtract \(\frac{58}{6}\) and \(\frac{29}{8}\), we need a common denominator. The least common denominator (LCD) of 6 and 8 is 24.
Convert \(\frac{58}{6}\) to a fraction with denominator 24:
[tex]\[
\frac{58}{6} = \frac{58 \times 4}{6 \times 4} = \frac{232}{24}
\][/tex]
Convert \(\frac{29}{8}\) to a fraction with denominator 24:
[tex]\[
\frac{29}{8} = \frac{29 \times 3}{8 \times 3} = \frac{87}{24}
\][/tex]
3. Subtract the fractions with the common denominator:
[tex]\[
\frac{232}{24} - \frac{87}{24} = \frac{232 - 87}{24} = \frac{145}{24}
\][/tex]
Therefore, the result of \(9 \frac{4}{6} - 3 \frac{5}{8}\) is:
[tex]\[
\frac{145}{24}
\][/tex]
In summary, the step-by-step solution shows that
[tex]\[
9 \frac{4}{6} - 3 \frac{5}{8} = \frac{145}{24}
\][/tex]
