Real-World Examples of the Distributive Property: High School Math Applications

📚 Quick Study Guide

• 🍎 The Distributive Property states that $a(b + c) = ab + ac$. This means you multiply the term outside the parentheses by each term inside.
• ➕ It applies to both addition and subtraction: $a(b - c) = ab - ac$.
• 🔢 Be careful with signs! If $a$ is negative, remember to distribute the negative sign as well.
• 💡 The distributive property simplifies expressions and makes calculations easier.
• 📝 Real-world applications include calculating costs, areas, and proportions.

🎯 Practice Quiz

1. What is the area of a rectangular garden that is 5 feet wide and (x + 3) feet long?
   1. 5x + 3
   2. 5x + 15
   3. x + 15
   4. 5 + x + 3
2. A movie theater charges $8 per ticket and sells (y - 2) tickets. What is the total revenue?
   1. 8y - 2
   2. 8y - 16
   3. y - 16
   4. 8y + 16
3. John buys 3 packs of pencils, each containing (2z + 5) pencils. How many pencils does he have in total?
   1. 6z + 5
   2. 6z + 15
   3. 5z + 15
   4. 3z + 15
4. Sarah is baking cookies. She wants to double a recipe that calls for (w + 4) cups of flour. How much flour does she need?
   1. w + 8
   2. 2w + 4
   3. 2w + 8
   4. 2w + 16
5. A store is offering a 20% discount on all items. If an item costs (p + 10) dollars, what is the discount amount in dollars?
   1. 0.2p + 2
   2. 0.2p + 10
   3. p + 2
   4. 0.2p + 20
6. A farmer has 4 fields, each with (q - 3) rows of crops. How many rows of crops does the farmer have in total?
   1. 4q - 3
   2. 4q - 12
   3. q - 12
   4. 4q + 12
7. A school is ordering t-shirts. Each t-shirt costs $6, and they are ordering (r + 7) t-shirts. What is the total cost?
   1. 6r + 7
   2. 6r + 42
   3. r + 42
   4. 6r - 42