Multi-Digit Multiplication

The Standard Algorithm

To multiply large numbers, use partial products or the standard algorithm.

Example: $346 \times 28$

Step 1: Multiply 346 by 8 (ones digit): $346 \times 8 = 2,768$

Step 2: Multiply 346 by 20 (tens digit): $346 \times 20 = 6,920$

Step 3: Add the partial products: $2,768 + 6,920 = 9,688$

So $346 \times 28 = 9,688$ ✅

Estimating Products

Round factors to estimate: $346 \times 28 \approx 350 \times 30 = 10,500$ (close to 9,688 ✓)

Properties of Multiplication

• Commutative: $a \times b = b \times a$
• Associative: $(a \times b) \times c = a \times (b \times c)$
• Distributive: $a \times (b + c) = a \times b + a \times c$

Using the distributive property: $7 \times 98 = 7 \times (100 - 2) = 700 - 14 = 686$

Powers of 10

• $10^1 = 10$ (one zero)
• $10^2 = 100$ (two zeros)
• $10^3 = 1,000$ (three zeros)

To multiply by a power of 10, add zeros: $45 \times 1,000 = 45,000$

Check: Your product should have approximately as many digits as the sum of digits in both factors.