Questions: Multiply. (Enter a reduced fraction. If an answer is undefined, enter UNDEFINED.) 4 1/5 * 7 6/7

Solution Steps

To multiply mixed numbers, first convert them to improper fractions. Then, multiply the numerators together and the denominators together. Finally, simplify the resulting fraction to its lowest terms.

The mixed number \( 4 \frac{1}{5} \) can be converted to an improper fraction as follows: \[ 4 \frac{1}{5} = 4 + \frac{1}{5} = \frac{20}{5} + \frac{1}{5} = \frac{21}{5} \] Similarly, the mixed number \( 7 \frac{6}{7} \) is converted as follows: \[ 7 \frac{6}{7} = 7 + \frac{6}{7} = \frac{49}{7} + \frac{6}{7} = \frac{55}{7} \]

Now, we multiply the two improper fractions: \[ \frac{21}{5} \cdot \frac{55}{7} = \frac{21 \cdot 55}{5 \cdot 7} = \frac{1155}{35} \]

Next, we simplify the fraction \( \frac{1155}{35} \). The greatest common divisor (GCD) of 1155 and 35 is 35, so we divide both the numerator and the denominator by 35: \[ \frac{1155 \div 35}{35 \div 35} = \frac{33}{1} = 33 \]

Final Answer