Absolutely, let's solve each part of the problem step-by-step.
### 1. [tex]\( 25 \frac{5}{2} + -3 \frac{5}{8} \)[/tex]
1. Convert mixed fractions to improper fractions:
- [tex]\( 25 \frac{5}{2} = 25 + \frac{5}{2} \)[/tex]
- [tex]\( 25 = \frac{50}{2} \)[/tex]
- [tex]\( 25 \frac{5}{2} = \frac{50}{2} + \frac{5}{2} = \frac{55}{2} \)[/tex]
- [tex]\( -3 \frac{5}{8} = -3 - \frac{5}{8} \)[/tex]
- [tex]\( -3 = -\frac{24}{8} \)[/tex]
- [tex]\( -3 \frac{5}{8} = -\frac{24}{8} - \frac{5}{8} = -\frac{29}{8} \)[/tex]
2. Find a common denominator to add the fractions:
- For [tex]\(\frac{55}{2}\)[/tex], convert it to a fraction with denominator 8:
- [tex]\(\frac{55}{2} \times \frac{8}{8} = \frac{440}{16}\)[/tex]
- For [tex]\(-\frac{29}{8}\)[/tex], convert it to a fraction with denominator 16:
- [tex]\(\frac{-29}{8} \times \frac{2}{2} = \frac{-58}{16}\)[/tex]
3. Add the fractions:
- [tex]\(\frac{440}{16} + \frac{-58}{16} = \frac{382}{16}\)[/tex]
4. Simplify the result to a mixed number:
- [tex]\(\frac{382}{16} = 23 \frac{14}{16} = 23 \frac{7}{8}\)[/tex]
Therefore, the result is [tex]\( 23 \frac{7}{8} \)[/tex].
### 2. [tex]\( 134 + 3 + \frac{3}{5} + 5 \frac{1}{2} \)[/tex]
1. Convert mixed fractions to improper fractions:
- [tex]\( 134 + 3 = 137 \)[/tex]
- [tex]\( \frac{3}{5} \)[/tex] stays as is.
- [tex]\( 5 \frac{1}{2} = 5 + \frac{1}{2} \)[/tex]
- [tex]\( 5 = \frac{10}{2} \)[/tex]
- [tex]\( 5 \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \)[/tex]
2. Add the fractions and whole numbers:
- [tex]\( 137 \)[/tex]
- [tex]\( \frac{3}{5} \)[/tex]
- [tex]\(\frac{11}{2} = 5.5\)[/tex]
3. Combine all:
- [tex]\( 137 + \frac{3}{5} + 5.5 \)[/tex]
- [tex]\( = 137 + 0.6 + 5.5 \)[/tex]
- [tex]\( 137 + 0.6 + 5.5 = 143.1 \)[/tex]
Therefore, the result is [tex]\( 143.1 \)[/tex].
### 3. [tex]\( 18 \frac{3}{5} - 10 \frac{5}{9} \)[/tex]
1. Convert mixed fractions to improper fractions:
- [tex]\( 18 \frac{3}{5} = 18 + \frac{3}{5} \)[/tex]
- [tex]\( 18 = \frac{90}{5} \)[/tex]
- [tex]\( 18 \frac{3}{5} = \frac{90}{5} + \frac{3}{5} = \frac{93}{5} \)[/tex]
- [tex]\( 10 \frac{5}{9} = 10 + \frac{5}{9} \)[/tex]
- [tex]\( 10 = \frac{90}{9} \)[/tex]
- [tex]\( 10 \frac{5}{9} = \frac{90}{9} + \frac{5}{9} = \frac{95}{9} \)[/tex]
2. Find a common denominator to subtract the fractions:
- For [tex]\(\frac{93}{5}\)[/tex], convert it to a fraction with denominator 45:
- [tex]\(\frac{93}{5} \times \frac{9}{9} = \frac{837}{45}\)[/tex]
- For [tex]\(\frac{95}{9}\)[/tex], convert it to a fraction with denominator 45:
- [tex]\(\frac{95}{9} \times \frac{5}{5} = \frac{475}{45}\)[/tex]
3. Subtract the fractions:
- [tex]\(\frac{837}{45} - \frac{475}{45} = \frac{362}{45}\)[/tex]
4. Simplify the result to a mixed number:
- [tex]\(\frac{362}{45} \approx 8 \frac{2}{45}\)[/tex]
Therefore, the result is [tex]\( 8 \frac{2}{45} \)[/tex].
