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Door 4 · Grade 4

🔢 Multi-Digit Multiplication

Align numbers so the rightmost digits line up

▶ Play Door 4

Multiply 4-Digit by 1-Digit

Multiplying a 4-digit number by a 1-digit number means repeated addition. We use the column method (standard algorithm) with carrying.
Steps:
• Align numbers by the rightmost digit
• Multiply each digit from right to left
• If the product has two digits, write the units digit and carry the tens digit
• Add the carry to the next multiplication

Example: 4,523 x 4 = 18,092

Worked example

Problem: Multiply 4,523 x 4.

  1. Step 1: 4x3=12, write 2 carry 1.
  2. Step 2: 4x2=8+1=9, write 9.
  3. Step 3: 4x5=20, write 0 carry 2.
  4. Step 4: 4x4=16+2=18, write 18.

Answer: 18,092.

Multiply 2-Digit by 2-Digit (Area Model)

When multiplying by a 2-digit number, we split it into two parts and multiply separately, then add the partial products.
Area Model: Break both numbers into tens and ones, then multiply each part.
Example: 23 x 45 = (20+3) x (40+5) = 800 + 100 + 120 + 15 = 1,035
Column Method:
• Multiply by the ones digit first
• Then multiply by the tens digit (add a placeholder zero)
• Add both partial products

Worked example

Problem: Multiply 34 x 26.

  1. Step 1 (ones): 34 x 6 = 204.
  2. Step 2 (tens): 34 x 20 = 680.
  3. Add: 204 + 680 = 884.

Answer: 884.

Estimate Products Before Calculating

Estimation helps us check if our answer is reasonable. We round numbers to a convenient value before multiplying.
How to Estimate:
• Round each number to the nearest 10, 100, or 1,000
• Multiply the rounded numbers
• Compare with the actual answer — they should be close

Estimation is especially useful to detect calculation errors!

Worked example

Problem: Estimate and then find the actual product of 487 x 32.

  1. Estimate: 487 rounds to 500; 32 rounds to 30.
  2. Estimate = 500 x 30 = 15,000.
  3. Actual: 487 x 32 = 15,584.
  4. The estimate (15,000) is close to the actual (15,584).

Answer: The estimate (15,000) is close to the actual (15,584).