Solved Examples: Area Models for Multiplying 2-Digit Numbers

📚 Quick Study Guide

• 🧱 The area model breaks down multiplication into smaller, more manageable parts.
• ➗ It leverages the distributive property: $a(b+c) = ab + ac$.
• ✏️ For 2-digit numbers, expand each number into its tens and ones place (e.g., $23 = 20 + 3$).
• ➕ Multiply each part and then add all the partial products to get the final answer.
• 📐 Visualize each multiplication as the area of a rectangle.
• 💡 Area = Length x Width

Practice Quiz

1. What is the first step in using the area model to multiply 23 x 14?
1. A. Multiply 2 x 1.
2. B. Expand 23 into 20 + 3 and 14 into 10 + 4.
3. C. Add 23 and 14.
4. D. Draw a square.
2. Using the area model, what partial product do you get when multiplying the tens digits of 35 and 12?
1. A. 300
2. B. 30
3. C. 50
4. D. 60
3. What is the area of the section representing 46 x 20 in an area model?
1. A. 820
2. B. 920
3. C. 800
4. D. 900
4. If you're multiplying 19 x 11 using an area model, what four multiplications will you perform?
1. A. 1x1, 9x1, 1x1, 9x1
2. B. 10x10, 10x1, 9x10, 9x1
3. C. 1x9, 1x1, 1x1, 1x9
4. D. 10x11, 9x11, 0x0, 0x0
5. After finding all the partial products in an area model, what is the next step?
1. A. Subtract them.
2. B. Multiply them.
3. C. Add them.
4. D. Divide them.
6. Which expression represents the area model for 27 x 15?
1. A. (20x10) + (7x5)
2. B. (20x15) + (7x15)
3. C. (20x5) + (7x10)
4. D. (20+7) + (10+5)
7. What is the final product of 42 x 13 using the area model?
1. A. 546
2. B. 456
3. C. 646
4. D. 406