.
To solve these problems, we need to perform basic arithmetic operations with fractions. Let’s go through them step by step:
Addition of Fractions:
\[ \frac{3}{5} + \frac{4}{7} \]
To add these, find a common denominator (35):
\[ \frac{3 \times 7}{5 \times 7} + \frac{4 \times 5}{7 \times 5} = \frac{21}{35} + \frac{20}{35} = \frac{41}{35} \]
The result is an improper fraction, \(\frac{41}{35}\).
Multiplication of Fractions:
\[ \frac{3}{5} \times \frac{4}{7} \]
Multiply the numerators and the denominators:
\[ \frac{3 \times 4}{5 \times 7} = \frac{12}{35} \]
This simplifies to \(\frac{12}{35}\).
Multiplication of Fractions (Different Pair):
\[ \frac{3}{5} \times \frac{7}{4} \]
Again, multiply the numerators and the denominators:
\[ \frac{3 \times 7}{5 \times 4} = \frac{21}{20} \]
The result is an improper fraction \(\frac{21}{20}\).
These operations are required to fill in the blanks with the resulting fractions.
