How to Multiply Mixed Numbers: Step-by-Step Math Tutorial

Converting Mixed Numbers to Improper Fractions

• 💡 To multiply mixed numbers, the first step is to convert each mixed number into an improper fraction.
• 🎯 For a mixed number like 2 and 1/3, the denominator (3) stays the same. The new numerator is calculated by multiplying the whole number by the denominator and adding the original numerator: (2 * 3) + 1 = 7. So, 2 and 1/3 becomes 7/3.
• 🔑 Similarly, for 4 and 2/5, the denominator (5) remains. The numerator is (4 * 5) + 2 = 22. Thus, 4 and 2/5 converts to 22/5.

Multiplying Improper Fractions

• 🚀 Once converted, multiply the improper fractions by multiplying the numerators together and the denominators together.
• 📊 For example, multiplying 7/3 by 22/5 involves calculating 7 * 22 for the new numerator and 3 * 5 for the new denominator.
• 📈 7 * 22 equals 154, and 3 * 5 equals 15, resulting in the improper fraction 154/15.

Converting Back to Mixed Numbers

• 🧩 The final step is to convert the resulting improper fraction back into a mixed number.
• 🔍 To convert 154/15, find the highest multiple of the denominator (15) that is less than the numerator (154). This is 150 (15 * 10).
• 💡 The remainder is 154 - 150 = 4. So, 154/15 can be expressed as 10 and 4/15.

Second Example Walkthrough

• 🎯 The process is repeated for another example, such as 3 and 1/4 multiplied by 2 and 5/6.
• 🔑 Convert 3 and 1/4 to 13/4 and 2 and 5/6 to 17/6.
• 🚀 Multiply these improper fractions: 13 * 17 = 221 (numerator) and 4 * 6 = 24 (denominator), yielding 221/24.
• 📈 Convert 221/24 to a mixed number by finding the highest multiple of 24 under 221, which is 216 (24 * 9). The remainder is 221 - 216 = 5.
• 💡 The final mixed number is 9 and 5/24.