What Does Scaling Mixed Numbers Mean?
Scaling means resizing!
When we scale a mixed number by a fraction, we're making it larger or smaller. Think of it like zooming in or out on a picture - we're changing the size but keeping the same shape!
How to Scale Mixed Numbers by Fractions
1️⃣ Convert the mixed number to an improper fraction
2️⃣ Multiply the two fractions together
3️⃣ Simplify your answer (convert back to mixed number if needed)
Let's Practice Together!
Example 1: The Cookie Recipe
Sarah has a recipe that calls for 2½ cups of flour, but she only wants to make ¾ of the recipe. How much flour should she use?
Step 1: Convert 2½ to an improper fraction: \( 2\frac{1}{2} = \frac{5}{2} \)
Step 2: Multiply by ¾: \( \frac{5}{2} \times \frac{3}{4} = \frac{15}{8} \)
Step 3: Convert back to mixed number: \( \frac{15}{8} = 1\frac{7}{8} \) cups
Sarah should use 1⅞ cups of flour.
Great job! You just scaled a mixed number!
Example 2: The Shrinking Playground
A playground is 3⅓ meters long. If we scale it down by \( \frac{2}{5} \), how long will it be?
Try solving this yourself! When you're ready, check your answer.
Solution:
1. Convert 3⅓ to improper fraction: \( \frac{10}{3} \)
2. Multiply by \( \frac{2}{5} \): \( \frac{10}{3} \times \frac{2}{5} = \frac{20}{15} \)
3. Simplify: \( \frac{20}{15} = \frac{4}{3} = 1\frac{1}{3} \) meters
The scaled-down playground will be 1⅓ meters long.
Parent Tips 🌟
- Kitchen Math: Practice scaling recipes together - it's a delicious way to learn!
- Visual Help: Use measuring cups or fraction circles to show what scaling looks like in real life.
- Game Time: Play "Fraction War" with cards where you multiply mixed numbers by fractions to see who gets the larger result.