What are mixed numbers and how do you multiply them?

📚 What is a Mixed Number?

A mixed number is a number that combines a whole number and a proper fraction. For example, $2\frac{1}{2}$ is a mixed number. The '2' is the whole number part, and the '\frac{1}{2}' is the fractional part.

• 🔢 Definition: A mixed number represents a quantity greater than one that's expressed as a whole number plus a fraction.
• 📜 History: The concept of mixed numbers dates back to ancient civilizations, where they were used for practical measurements and calculations.
• 💡 Key Principle: To work with mixed numbers in multiplication (or division), you first need to convert them into improper fractions.

➕ Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator of the fraction.
2. Add the numerator of the fraction to the result.
3. Keep the same denominator.

For example, let's convert $2\frac{1}{2}$ to an improper fraction:

1. $2 \times 2 = 4$
2. $4 + 1 = 5$
3. The improper fraction is $\frac{5}{2}$

• 🧮 Formula: Convert $a\frac{b}{c}$ to $\frac{(a \times c) + b}{c}$
• ✍️ Example: $3\frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{17}{5}$
• 🧠 Tip: Always double-check your calculations to ensure accuracy!

✖️ Multiplying Mixed Numbers

To multiply mixed numbers, follow these steps:

1. Convert each mixed number to an improper fraction.
2. Multiply the numerators together.
3. Multiply the denominators together.
4. Simplify the resulting fraction if possible.

Example: Multiply $2\frac{1}{2} \times 1\frac{1}{3}$

1. Convert $2\frac{1}{2}$ to $\frac{5}{2}$
2. Convert $1\frac{1}{3}$ to $\frac{4}{3}$
3. Multiply: $\frac{5}{2} \times \frac{4}{3} = \frac{5 \times 4}{2 \times 3} = \frac{20}{6}$
4. Simplify: $\frac{20}{6} = \frac{10}{3} = 3\frac{1}{3}$

• ✔️ Step 1: Convert mixed numbers to improper fractions.
• ➕ Step 2: Multiply the numerators.
• ➗ Step 3: Multiply the denominators.
• ✨ Step 4: Simplify the resulting fraction (if possible).

➕ Real-World Examples

Mixed numbers are commonly used in everyday situations:

• 🍰 Baking: A recipe might call for $2\frac{1}{4}$ cups of flour.
• 🔨 Construction: A piece of wood might be $5\frac{1}{2}$ inches long.
• 🧵 Sewing: You might need $1\frac{3}{4}$ yards of fabric.

📝 Conclusion

Understanding mixed numbers and how to multiply them is a fundamental skill in mathematics. By converting mixed numbers to improper fractions, you can easily perform multiplication and solve real-world problems. Keep practicing, and you'll master this concept in no time!

• ✅ Key Takeaway: Mixed numbers simplify practical calculations.
• 🚀 Next Steps: Practice converting and multiplying mixed numbers regularly.
• ❓ Further Learning: Explore more complex fraction operations.