Let's carefully analyze and simplify each part of the given expressions step by step to reach the final results.
### Expression 1: [tex]\(3 + \frac{4}{2}\)[/tex] and [tex]\(3 + \frac{2}{4}\)[/tex]
#### Step-by-Step Simplification:
1. Simplify the fractions:
- [tex]\(\frac{4}{2} = 2\)[/tex]
- [tex]\(\frac{2}{4} = 0.5\)[/tex]
2. Perform the addition:
- [tex]\(3 + 2 = 5\)[/tex]
- [tex]\(3 + 0.5 = 3.5\)[/tex]
3. Multiply the results:
- [tex]\(5 \times 3.5 = 17.5\)[/tex]
#### Result for Expression 1:
- [tex]\(3 + \frac{4}{2} \times 3 + \frac{2}{4} = 17.5\)[/tex]
### Expression 2: [tex]\(\frac{10}{2} + \frac{14}{4}\)[/tex]
#### Step-by-Step Simplification:
1. Simplify the fractions:
- [tex]\(\frac{10}{2} = 5\)[/tex]
- [tex]\(\frac{14}{4} = 3.5\)[/tex]
2. Perform the addition:
- [tex]\(5 + 3.5 = 8.5\)[/tex]
#### Result for Expression 2:
- [tex]\(\frac{10}{2} + \frac{14}{4} = 8.5\)[/tex]
### Mixed Fraction Calculation:
1. Addition involving numerators:
- Top: [tex]\(40 + 38 = 78\)[/tex]
2. Divide by the denominator:
- [tex]\(\frac{78}{4} = 19.5\)[/tex]
#### Result for Final Evaluation:
- [tex]\(24 + \frac{1}{4} = 24.25\)[/tex]
### Summary of the Results:
1. First Part: [tex]\(17.5\)[/tex]
2. Second Part: [tex]\(8.5\)[/tex]
3. Total in Numerator Form: [tex]\(78\)[/tex]
4. Fractional Form: [tex]\(\frac{78}{4} = 19.5\)[/tex]
5. Mixed Number: [tex]\(24 \frac{1}{4} = 24.25\)[/tex]
These detailed steps illustrate how to arrive at the results for each part of the given mathematical expressions.
