How to Multiply Mixed Numbers and Whole Numbers: Step-by-Step Math Guide

Converting Mixed Numbers to Improper Fractions

• 💡 To begin multiplying a mixed number by a whole number, first convert the mixed number into an improper fraction.
• 📌 Rewrite the denominator, then multiply the whole number part of the mixed number by the denominator and add the numerator.
• ✅ For example, to convert 3 and 2/5, rewrite the denominator as 5. Then, (3 * 5) + 2 = 17, resulting in the improper fraction 17/5.

Multiplying Fractions

• 🚀 The whole number should also be converted into a fraction, typically by writing it over 1 (e.g., 4 becomes 4/1).
• ✖️ Multiply the numerators together and the denominators together to find the product of the two fractions.
• 📊 For instance, multiplying 17/5 by 4/1 involves calculating (17 * 4) / (5 * 1), which equals 68/5.

Converting Improper Fractions Back to Mixed Numbers

• 🔍 To convert the resulting improper fraction (e.g., 68/5) back into a mixed number, use long division or an alternative method.
• 🔑 Find the highest multiple of the denominator (5) that is less than or equal to the numerator (68), which is 65.
• ➕ Separate the improper fraction into two parts: the multiple of the denominator and the remainder (65/5 + 3/5).
• 💯 Simplify the first part (65/5 = 13) and combine it with the remainder fraction (3/5) to get the final mixed number: 13 and 3/5.

Alternative Method: Distributive Property

• 🧠 An alternative approach is to view multiplication by a whole number as repeated addition.
• ➕ Add the whole number part of the mixed number the specified number of times (e.g., 3 * 4 = 12).
• ➕ Then, multiply the fractional part of the mixed number by the whole number (e.g., 2/5 * 4 = 8/5).
• ⚖️ Convert the resulting fractional part (8/5) into a mixed number (1 and 3/5) and add it to the sum of the whole number parts (12 + 1 and 3/5 = 13 and 3/5).

Example: 4 and 3/8 multiplied by 7

• 🎯 Using the improper fraction method: Convert 4 and 3/8 to 35/8. Multiply by 7/1 to get 245/8. Convert back to a mixed number: 30 and 5/8.
• 🎯 Using the distributive property: (4 * 7) + (3/8 * 7) = 28 + 21/8. Convert 21/8 to 2 and 5/8. Add to 28: 28 + 2 and 5/8 = 30 and 5/8.