R1 · Lesson 3: Multiply Multi-Digit Numbers

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Why this matters for Grade 6: Standard 6.NS.2 calls for fluent multi-digit multiplication as part of the standard algorithm for division. 6.NS.3 extends this to decimal multiplication — if you can multiply whole numbers confidently, decimals are just one extra step.

Learn It

Multiplying Multi-Digit Numbers

One-digit multiplier: Multiply each digit by the one-digit number, right to left. Regroup (carry) when needed.

Example 1: 213 × 7

213
× 7
─────
1,491

Ones: 3×7=21, write 1 carry 2 · Tens: 1×7+2=9 · Hundreds: 2×7=14 → 1,491

Two-digit multiplier (standard algorithm): Multiply by the ones digit, then by the tens digit (shifting one place left), then add the partial products.

Example 2: 34 × 26

34
× 26
────
204 ← 34×6
+ 680 ← 34×20
────
884

34 × 6 = 204 | 34 × 20 = 680 | 204 + 680 = 884

Multiplying by multiples of 10: Multiply the non-zero parts, then attach the zeros.

Example 3 (Area context): A rectangular hall is 125 ft long and 40 ft wide. What is its area?

125 × 40 = 125 × 4 × 10 = 500 × 10 = 5,000 sq ft

Area model:

	100	20	5
40	4,000	800	200

4,000 + 800 + 200 = 5,000 ✓

Try It · Guided

Work These Together

1. What is 312 × 4?

Hint

Ones: 2×4=8 · Tens: 1×4=4 · Hundreds: 3×4=12 → 1,248.

2. Which partial product is correct for 45 × 30?

Hint

45 × 30 = 45 × 3 × 10 = 135 × 10 = 1,350.

Practice · On Your Own

You Try

3. Compute: 417 × 6

Hint

Ones: 7×6=42, write 2 carry 4 · Tens: 1×6+4=10, write 0 carry 1 · Hundreds: 4×6+1=25 → 2,502.

4. Compute: 34 × 26

Hint

34 × 6 = 204. 34 × 20 = 680. Add: 204 + 680 = 884.

5. A classroom has 24 rows of tiles, each row is 15 tiles wide. How many tiles are there in all?

Hint

24 × 15: 24×5=120, 24×10=240. 120+240=360 tiles.

★

Exit Ticket

Show What You Know

6. Compute: 125 × 40

Hint

125 × 4 = 500. Attach one zero: 500 × 10 = 5,000.

7. What is 53 × 18?

Hint

53 × 8 = 424. 53 × 10 = 530. 424 + 530 = 954.

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