How do you multiply two mixed numbers?

To multiply two mixed numbers, convert them to improper fractions, multiply, then simplify the result.

First, let's understand what mixed numbers and improper fractions are. A mixed number consists of a whole number and a fraction, like \(2 \frac{1}{3}\). An improper fraction has a numerator larger than its denominator, like \(\frac{7}{3}\).

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. For example, to convert \(2 \frac{1}{3}\) to an improper fraction:
\[ 2 \times 3 + 1 = 6 + 1 = 7 \]
So, \(2 \frac{1}{3}\) becomes \(\frac{7}{3}\).

Do this for both mixed numbers you want to multiply. Suppose we have \(2 \frac{1}{3}\) and \(1 \frac{2}{5}\). Converting \(1 \frac{2}{5}\):
\[ 1 \times 5 + 2 = 5 + 2 = 7 \]
So, \(1 \frac{2}{5}\) becomes \(\frac{7}{5}\).

Next, multiply the improper fractions:
\[ \frac{7}{3} \times \frac{7}{5} = \frac{7 \times 7}{3 \times 5} = \frac{49}{15} \]

Finally, simplify the result if possible. In this case, \(\frac{49}{15}\) is already in its simplest form. If needed, you can convert it back to a mixed number by dividing the numerator by the denominator:
\[ 49 \div 15 = 3 \text{ remainder } 4 \]
So, \(\frac{49}{15}\) is \(3 \frac{4}{15}\).

By following these steps, you can multiply any two mixed numbers accurately.