Let's solve these expressions one by one.
### Expression 1: [tex]\( 3 \cdot 3 \frac{1}{2} \times 3 \frac{2}{5} \)[/tex]
1. Convert mixed numbers to improper fractions:
- [tex]\( 3 \frac{1}{2} = \frac{7}{2} \)[/tex]
- [tex]\( 3 \frac{2}{5} = \frac{17}{5} \)[/tex]
2. Substitute the improper fractions into the expression:
- [tex]\( 3 \cdot \frac{7}{2} \times \frac{17}{5} \)[/tex]
3. Simplify the expression:
- [tex]\( 3 \cdot \frac{7}{2} = \frac{21}{2} \)[/tex]
- Then multiply: [tex]\( \frac{21}{2} \times \frac{17}{5} = \frac{357}{10} = 35.7 \)[/tex]
So, the result of [tex]\( 3 \cdot 3 \frac{1}{2} \times 3 \frac{2}{5} \)[/tex] is [tex]\( 35.7 \)[/tex].
### Expression 2: [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} \)[/tex]
1. Convert mixed numbers to improper fractions:
- [tex]\( 4 \frac{3}{5} = \frac{23}{5} \)[/tex]
- [tex]\( 5 \frac{3}{4} = \frac{23}{4} \)[/tex]
2. To add these fractions, find a common denominator:
- The common denominator of 5 and 4 is 20.
3. Convert each fraction to have the common denominator:
- [tex]\( \frac{23}{5} = \frac{23 \times 4}{5 \times 4} = \frac{92}{20} \)[/tex]
- [tex]\( \frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20} \)[/tex]
4. Add the fractions:
- [tex]\( \frac{92}{20} + \frac{115}{20} = \frac{207}{20} = 10.35 \)[/tex]
So, the result of [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} \)[/tex] is [tex]\( 10.35 \)[/tex].
### Expression 3: [tex]\( \frac{4}{2} \times 3 \frac{4}{7} \)[/tex]
1. Convert the mixed number to an improper fraction:
- [tex]\( 3 \frac{4}{7} = \frac{25}{7} \)[/tex]
2. Substitute into the expression:
- [tex]\( \frac{4}{2} \times \frac{25}{7} \)[/tex]
3. Simplify the expression:
- [tex]\( \frac{4}{2} = 2 \)[/tex]
- Then multiply: [tex]\( 2 \times \frac{25}{7} = \frac{50}{7} = 7.142857142857143 \)[/tex]
So, the result of [tex]\( \frac{4}{2} \times 3 \frac{4}{7} \)[/tex] is [tex]\( 7.142857142857143 \)[/tex].
### Summary
- [tex]\( 3 \cdot 3 \frac{1}{2} \times 3 \frac{2}{5} = 35.7 \)[/tex]
- [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} = 10.35 \)[/tex]
- [tex]\( \frac{4}{2} \times 3 \frac{4}{7} = 7.142857142857143 \)[/tex]
These are the results for the given expressions.
