Understanding Mixed Number Multiplication
Mixed numbers are numbers that have both whole numbers and fractions, like
2½ or 3¾.
When we multiply a mixed number by a whole number, we can use two methods: convert to improper fractions
or use the distributive property. Today we'll learn both ways!
How to Multiply Mixed Numbers by Whole Numbers
1️⃣ Method 1: Convert the mixed number to an improper fraction, then multiply
2️⃣ Method 2: Multiply the whole number parts and fraction parts separately
3️⃣ Simplify: Always simplify your final answer
Let's Practice Together!
Example 1: \(2\frac{1}{2} × 4\)
Method 1: Convert \(2\frac{1}{2}\) to improper fraction (\(\frac{5}{2}\)), then multiply by 4
\(\frac{5}{2} × 4 = \frac{20}{} = 10\)
Method 2: (2 × 4) + (\(\frac{1}{2}\) × 4) = 8 + 2 = 10
Answer: 10
Try It Yourself: \(3\frac{3}{4} × 6\)
Can you solve this problem? Try both methods and check your answer!
Method 1: \(3\frac{3}{4} = \frac{15}{4}, \frac{15}{4} × 6 = \frac{90}{4} = 22\frac{1}{2}\)
Method 2: (3 × 6) + (\(\frac{3}{4}\) × 6) = 18 + \(4\frac{1}{2}\) = \(22\frac{1}{2}\)
Answer: \(22\frac{1}{2}\)
Example 2: 1⅓ × 5
Method 1: Convert 1⅓ to improper fraction (4/3), then multiply by 5
4/3 × 5 = 20/3 = 6⅔
Method 2: (1 × 5) + (⅓ × 5) = 5 + 1⅔ = 6⅔
Answer: 6⅔
Challenge Problem: 4⅖ × 3
Ready for a challenge? Solve this problem using your preferred method!
Method 1: 4⅖ = 22/5, 22/5 × 3 = 66/5 = 13⅕
Method 2: (4 × 3) + (⅖ × 3) = 12 + 1⅕ = 13⅕
Answer: 13⅕
Parent Tips 🌟
- Kitchen Math: Practice with cooking measurements - "If we need 2½ cups of flour for one batch, how much for 3 batches?"
- Visual Help: Use fraction circles or bars to show how the multiplication works visually
- Real-world Problems: Create word problems about pizza slices, fabric lengths, or sports distances to make it practical