Sure, I'll provide a detailed, step-by-step solution for the expression [tex]\(5 \frac{5}{8} - 1 \frac{1}{4}\)[/tex].
Step 1: Convert the mixed numbers to improper fractions.
- For [tex]\(5 \frac{5}{8}\)[/tex]:
- Convert [tex]\(5\)[/tex] into a fraction with a common denominator of 8: [tex]\(5 = \frac{40}{8}\)[/tex]
- Add the fractional part: [tex]\(\frac{40}{8} + \frac{5}{8} = \frac{45}{8}\)[/tex]
- For [tex]\(1 \frac{1}{4}\)[/tex]:
- Convert [tex]\(1\)[/tex] into a fraction with a common denominator of 4: [tex]\(1 = \frac{4}{4}\)[/tex]
- Add the fractional part: [tex]\(\frac{4}{4} + \frac{1}{4} = \frac{5}{4}\)[/tex]
Step 2: Convert these improper fractions to decimal form for simplicity.
- [tex]\(\frac{45}{8}\)[/tex] converts to [tex]\(5.625\)[/tex]
- [tex]\(\frac{5}{4}\)[/tex] converts to [tex]\(1.25\)[/tex]
Step 3: Subtract the decimal equivalents.
[tex]\[ 5.625 - 1.25 = 4.375 \][/tex]
So, the result of the expression [tex]\(5 \frac{5}{8} - 1 \frac{1}{4}\)[/tex] is [tex]\(4.375\)[/tex].
