To subtract the mixed numbers [tex]\( 5 \frac{1}{2} \)[/tex] and [tex]\( 4 \frac{5}{8} \)[/tex], let's break the problem down into a detailed, step-by-step process.
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\( 5 \frac{1}{2} \)[/tex]:
- The whole number part is [tex]\(5\)[/tex].
- The fractional part is [tex]\(\frac{1}{2}\)[/tex].
- Convert [tex]\( 5 \frac{1}{2} \)[/tex] to an improper fraction:
[tex]\[
5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2}
\][/tex]
- For [tex]\( 4 \frac{5}{8} \)[/tex]:
- The whole number part is [tex]\(4\)[/tex].
- The fractional part is [tex]\(\frac{5}{8}\)[/tex].
- Convert [tex]\( 4 \frac{5}{8} \)[/tex] to an improper fraction:
[tex]\[
4 \frac{5}{8} = 4 + \frac{5}{8} = \frac{32}{8} + \frac{5}{8} = \frac{37}{8}
\][/tex]
2. Find a Common Denominator:
- The denominators for the fractions are [tex]\(2\)[/tex] and [tex]\(8\)[/tex]. Convert [tex]\(\frac{11}{2}\)[/tex] to have a common denominator of [tex]\(8\)[/tex].
- [tex]\(\frac{11}{2} = \frac{11 \times 4}{2 \times 4} = \frac{44}{8}\)[/tex]
3. Subtract the Improper Fractions:
- Now subtract [tex]\(\frac{37}{8}\)[/tex] from [tex]\(\frac{44}{8}\)[/tex].
[tex]\[
\frac{44}{8} - \frac{37}{8} = \frac{44 - 37}{8} = \frac{7}{8}
\][/tex]
4. Verify the Results:
- Upon completing the calculations, the result is [tex]\(\frac{7}{8}\)[/tex].
- Thus, the subtraction of [tex]\( 5 \frac{1}{2} \)[/tex] and [tex]\( 4 \frac{5}{8} \)[/tex] results in [tex]\( \frac{7}{8} \)[/tex].
In conclusion, the answer to the subtraction problem
[tex]\[
\begin{array}{r}
5 \frac{1}{2} \\
-4 \frac{5}{8} \\
\hline
\end{array}
\][/tex]
is [tex]\( \frac{7}{8} \)[/tex].
