To add the mixed numbers [tex]\( 1 \frac{2}{4} \)[/tex] and [tex]\( 1 \frac{1}{4} \)[/tex], we can follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- The first mixed number [tex]\( 1 \frac{2}{4} \)[/tex]:
[tex]\[
1 \frac{2}{4} = 1 + \frac{2}{4} = 1 + \frac{1}{2}
= 1.5
\][/tex]
- The second mixed number [tex]\( 1 \frac{1}{4} \)[/tex]:
[tex]\[
1 \frac{1}{4} = 1 + \frac{1}{4} = 1.25
\][/tex]
2. Add the Improper Fractions:
Adding these values together:
[tex]\[
1.5 + 1.25 = 2.75
\][/tex]
3. Separate the Whole Number and Fractional Part:
The sum [tex]\( 2.75 \)[/tex] consists of:
- Whole number part: [tex]\( 2 \)[/tex]
- Fractional part: [tex]\( 0.75 \)[/tex]
We know that [tex]\( 0.75 \)[/tex] is the same as [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
0.75 = \frac{3}{4}
\][/tex]
4. Combine into Mixed Number Form:
Putting the whole number and fraction together, we get:
[tex]\[
2 \frac{3}{4}
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{2 \frac{3}{4}}
\][/tex]
