To solve the problem of adding the mixed fraction [tex]\(5 \frac{1}{4}\)[/tex] and the decimal [tex]\(15.5\)[/tex], follow these steps:
1. Convert the mixed fraction to an improper fraction:
A mixed fraction like [tex]\(5 \frac{1}{4}\)[/tex] can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator.
- Whole number part: [tex]\(5\)[/tex]
- Fractional part: [tex]\(\frac{1}{4}\)[/tex]
Conversion steps:
[tex]\(5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}\)[/tex].
Thus, [tex]\(5 \frac{1}{4} = \frac{21}{4}\)[/tex].
2. Convert the decimal to a fraction:
The decimal [tex]\(15.5\)[/tex] can be written as a fraction by recognizing that [tex]\(0.5\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
Conversion steps:
[tex]\(15.5 = 15 + 0.5 = 15 + \frac{1}{2} = \frac{2 \times 15 + 1}{2} = \frac{30 + 1}{2} = \frac{31}{2}\)[/tex].
Thus, [tex]\(15.5 = \frac{31}{2}\)[/tex].
3. Make sure the fractions have a common denominator:
The two fractions we have are [tex]\(\frac{21}{4}\)[/tex] and [tex]\(\frac{31}{2}\)[/tex]. The common denominator for these fractions is [tex]\(4\)[/tex].
Convert [tex]\(\frac{31}{2}\)[/tex] to a fraction with a denominator of [tex]\(4\)[/tex]:
[tex]\(\frac{31}{2} = \frac{31 \times 2}{2 \times 2} = \frac{62}{4}\)[/tex].
4. Add the fractions:
With both fractions having the same denominator, we can simply add the numerators:
[tex]\[\frac{21}{4} + \frac{62}{4} = \frac{21 + 62}{4} = \frac{83}{4}.\][/tex]
5. Express the answer:
The sum of [tex]\(5 \frac{1}{4}\)[/tex] and [tex]\(15.5\)[/tex] is [tex]\(\frac{83}{4}\)[/tex].
Thus, the result is:
[tex]\(\boxed{\frac{83}{4}}\)[/tex]
