To determine which expression is NOT equivalent to [tex]\(1\frac{1}{4}\)[/tex], let’s analyze each option carefully and convert them into a common form if necessary.
Firstly, let's convert [tex]\(1\frac{1}{4}\)[/tex] to an improper fraction:
[tex]\[ 1\frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \][/tex]
Now, let's examine each option:
Option (A): [tex]\(1+\frac{1}{4}\)[/tex]
[tex]\[ 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \][/tex]
Option (3): [tex]\(\frac{1}{4}+\frac{1}{4}+\frac{3}{4}\)[/tex]
[tex]\[ \frac{1}{4} + \frac{1}{4} + \frac{3}{4} = \frac{1+1+3}{4} = \frac{5}{4} \][/tex]
Option (C): [tex]\(\frac{4}{4}+\frac{1}{4}\)[/tex]
[tex]\[ \frac{4}{4} + \frac{1}{4} = \frac{4+1}{4} = \frac{5}{4} \][/tex]
Option (D): [tex]\(\frac{5}{4}+\frac{1}{4}\)[/tex]
[tex]\[ \frac{5}{4} + \frac{1}{4} = \frac{5+1}{4} = \frac{6}{4} = 1\frac{1}{2} \][/tex]
Comparing all the results:
- Option (A): [tex]\(\frac{5}{4}\)[/tex]
- Option (3): [tex]\(\frac{5}{4}\)[/tex]
- Option (C): [tex]\(\frac{5}{4}\)[/tex]
- Option (D): [tex]\( \frac{6}{4} = 1\frac{1}{2} \)[/tex]
The only option that is not equivalent to [tex]\(1\frac{1}{4}\)[/tex] or [tex]\(\frac{5}{4}\)[/tex] is:
Option (D): [tex]\(\frac{5}{4}+\frac{1}{4}\)[/tex], which simplifies to [tex]\(\frac{6}{4} = 1\frac{1}{2}\)[/tex].
Therefore, the answer is:
[tex]\[ \boxed{4} \][/tex]
