Questions: Multiply. Write your answer as a mixed number in simplest form. 4 1/6 × 9

Solution Steps

The mixed number \(4 \frac{1}{6}\) can be converted to an improper fraction. To do this, multiply the whole number by the denominator and add the numerator:

\[ 4 \times 6 + 1 = 24 + 1 = 25 \]

So, \(4 \frac{1}{6}\) becomes \(\frac{25}{6}\).

Now, multiply the improper fraction by 9. Since 9 can be written as \(\frac{9}{1}\), the multiplication is:

\[ \frac{25}{6} \times \frac{9}{1} = \frac{25 \times 9}{6 \times 1} = \frac{225}{6} \]

To simplify \(\frac{225}{6}\), find the greatest common divisor (GCD) of 225 and 6, which is 3. Divide both the numerator and the denominator by 3:

\[ \frac{225 \div 3}{6 \div 3} = \frac{75}{2} \]

Convert \(\frac{75}{2}\) to a mixed number by dividing 75 by 2:

\[ 75 \div 2 = 37 \text{ remainder } 1 \]

So, \(\frac{75}{2}\) is equivalent to the mixed number \(37 \frac{1}{2}\).

Final Answer