To add the mixed number [tex]\(5 \frac{1}{4}\)[/tex] and the decimal [tex]\(15.5\)[/tex], let's follow a detailed step-by-step solution:
1. Convert the mixed number to an improper fraction:
- [tex]\(5 \frac{1}{4}\)[/tex] means we have 5 whole parts plus a fraction [tex]\(\frac{1}{4}\)[/tex].
- Convert 5 to a fraction with denominator 4: [tex]\(5 = \frac{5 \times 4}{4} = \frac{20}{4}\)[/tex].
- Now add this to the fraction part: [tex]\(\frac{20}{4} + \frac{1}{4} = \frac{21}{4}\)[/tex].
2. Convert the decimal [tex]\(15.5\)[/tex] to a fraction:
- [tex]\(15.5\)[/tex] can be written as [tex]\(15 \frac{1}{2}\)[/tex].
- Convert [tex]\(15 \frac{1}{2}\)[/tex] to an improper fraction: [tex]\(15 \times 2 = 30\)[/tex] and [tex]\(\frac{30}{2} + \frac{1}{2} = \frac{31}{2}\)[/tex].
3. Find a common denominator for the fractions:
- The denominators we have are 4 and 2. The least common multiple of 4 and 2 is 8.
- Convert [tex]\(\frac{21}{4}\)[/tex] to a fraction with denominator 8: [tex]\(\frac{21}{4} \times \frac{2}{2} = \frac{42}{8}\)[/tex].
- Convert [tex]\(\frac{31}{2}\)[/tex] to a fraction with denominator 8: [tex]\(\frac{31}{2} \times \frac{4}{4} = \frac{124}{8}\)[/tex].
4. Add the two fractions:
- We now add [tex]\(\frac{42}{8} + \frac{124}{8}\)[/tex].
- Since they have the same denominator, we can add the numerators: [tex]\(42 + 124 = 166\)[/tex].
- Therefore, [tex]\(\frac{42}{8} + \frac{124}{8} = \frac{166}{8}\)[/tex].
5. Expressing the sum as a fraction:
- The sum of [tex]\(5 \frac{1}{4}\)[/tex] and [tex]\(15.5\)[/tex] is [tex]\(\frac{166}{8}\)[/tex].
So, the answer is:
[tex]\[
\boxed{166/8}
\][/tex]
