To solve the given problem and express the answer as a fraction, we need to follow these steps:
1. Convert the mixed number [tex]\( 5 \frac{1}{4} \)[/tex] to an improper fraction:
First, multiply the whole number part (5) by the denominator (4) of the fractional part:
[tex]\[
5 \times 4 = 20
\][/tex]
Then, add the numerator (1) of the fractional part to this result:
[tex]\[
20 + 1 = 21
\][/tex]
So, [tex]\( 5 \frac{1}{4} \)[/tex] can be written as the improper fraction [tex]\( \frac{21}{4} \)[/tex].
2. Convert the decimal number [tex]\( 15.5 \)[/tex] to a fraction:
Since [tex]\( 15.5 \)[/tex] is equivalent to [tex]\( 15 \frac{1}{2} \)[/tex], first express [tex]\( 0.5 \)[/tex] as a fraction:
[tex]\[
15.5 = 15 + 0.5 = 15 + \frac{1}{2}
\][/tex]
Convert [tex]\( 15 \frac{1}{2} \)[/tex] to an improper fraction:
[tex]\[
15 \frac{1}{2} = \frac{30 + 1}{2} = \frac{31}{2}
\][/tex]
3. Find a common denominator:
The least common multiple (LCM) of the denominators 4 and 2 is 4.
Convert [tex]\( \frac{31}{2} \)[/tex] to a fraction with a denominator of 4:
[tex]\[
\frac{31}{2} = \frac{31 \times 2}{2 \times 2} = \frac{62}{4}
\][/tex]
4. Add the two fractions:
Now add [tex]\( \frac{21}{4} \)[/tex] and [tex]\( \frac{62}{4} \)[/tex]:
[tex]\[
\frac{21}{4} + \frac{62}{4} = \frac{21 + 62}{4} = \frac{83}{4}
\][/tex]
5. Express the final fraction:
The result of the addition is:
[tex]\[
5 \frac{1}{4} + 15.5 = \frac{83}{4}
\][/tex]
So, the answer is [tex]\(\boxed{\frac{83}{4}}\)[/tex].
