Multi-Digit Multiplication • Topic 2 of 3

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
Area Model: 34 x 2630 x 2060030 x 61804 x 20804 x 624Total = 600 + 180 + 80 + 24 = 88434 x 26 = 884
Solved Examples
1
Worked Example
Multiply 34 x 26.
SolutionStep 1 (ones): 34 x 6 = 204. Step 2 (tens): 34 x 20 = 680. Add: 204 + 680 = 884. Answer: 884.
2
Worked Example
Multiply 67 x 58.
SolutionStep 1: 67 x 8 = 536. Step 2: 67 x 50 = 3,350. Add: 536 + 3,350 = 3,886. Answer: 3,886.
3
Worked Example
A box has 24 packets. Each packet has 75 pencils. How many pencils are there in total?
SolutionMultiply 24 x 75. 24 x 5 = 120. 24 x 70 = 1,680. Total = 120 + 1,680 = 1,800. Answer: 1,800 pencils.

Key Points

  • Split the multiplier into tens and ones for easier calculation
  • Multiply by ones digit first, then by tens digit (add a zero placeholder)
  • Add both partial products to get the final answer
  • The Area Model shows visually why the multiplication works
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The area model splits each number into:
Explanation: Tens and ones.
Q2.$23\times12=$
Explanation: $276$.
Q3.The partial products are ___ to get the answer.
Explanation: Added.
Q4.One partial product of $23\times12$ is $20\times10=$
Explanation: $200$.
Practice more MCQs → 📝 Assignment · 35 marks