To solve multiplication problems involving mixed number fractions, you can follow these steps:

Step 1: Convert Mixed Numbers to Improper Fractions

A mixed number consists of a whole number and a fraction. To convert a mixed number to an improper fraction:

• Multiply the whole number by the denominator of the fraction.
• Add this result to the numerator of the fraction.
• The sum becomes the numerator of the improper fraction, and the denominator remains the same.

For example, for the mixed number $2 \frac{3}{4}$: $2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$

Step 2: Multiply the Improper Fractions

Once you've converted all mixed numbers to improper fractions, multiply the fractions by:

• Multiplying the numerators together to get the new numerator.
• Multiplying the denominators together to get the new denominator.

For example, multiplying $\frac{11}{4}$ by $\frac{5}{2}$: $\frac{11}{4} \times \frac{5}{2} = \frac{11 \times 5}{4 \times 2} = \frac{55}{8}$

Step 3: Simplify the Result (If Necessary)

If the fraction can be simplified, do so by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Step 4: Convert Back to a Mixed Number (If Necessary)

If the result is an improper fraction and you need to present it as a mixed number:

• Divide the numerator by the denominator to get the whole number part.
• The remainder becomes the numerator of the fractional part.

For example, converting $\frac{55}{8}$ back to a mixed number: $\frac{55}{8} = 6 \frac{7}{8}$ Where 6 is the whole number (since $55 \div 8 = 6$ remainder 7), and $\frac{7}{8}$ is the fraction part.

Example Problem

Multiply $3 \frac{1}{2}$ by $2 \frac{2}{3}$:

1. Convert to improper fractions: $3 \frac{1}{2} = \frac{7}{2}, \quad 2 \frac{2}{3} = \frac{8}{3}$

2. Multiply the improper fractions: $\frac{7}{2} \times \frac{8}{3} = \frac{7 \times 8}{2 \times 3} = \frac{56}{6}$

3. Simplify the fraction (if possible): $\frac{56}{6} = \frac{28}{3}$

4. Convert back to a mixed number: $\frac{28}{3} = 9 \frac{1}{3}$

So, $3 \frac{1}{2} \times 2 \frac{2}{3} = 9 \frac{1}{3}$.

Would you like to explore this topic further or solve a specific problem?

Here are 5 related questions:

1. How do you add mixed numbers with unlike denominators?
2. How would you solve division problems involving mixed numbers?
3. Can you explain how to simplify fractions after multiplication?
4. What are some common mistakes to avoid when working with mixed numbers?
5. How do you multiply mixed numbers by whole numbers?

Tip: Always simplify fractions at the end of your calculations to ensure your answer is in its simplest form.