Multiply 2-digit numbers by larger numbers

Key notes :

🔹 Key Idea:

When we multiply a 2-digit number by a larger number (3-digit or more), we use the long multiplication method step by step.

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🔹 Steps to Multiply:

• Write the numbers in columns (larger number on top, 2-digit number below).
• Multiply the bottom number’s ones place with each digit of the top number.
• Multiply the bottom number’s tens place with each digit of the top number (shift one place to the left).
• Add the partial products to get the final answer.

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🔹 Example 1:

Multiply 34 × 256

👉 Step 1: Arrange in columns

     256
   ×  34
  _______

👉 Step 2: Multiply by ones (4 × 256 = 1024)

     256
   ×  34
  _______
    1024   (this is 256 × 4)

👉 Step 3: Multiply by tens (3 × 256 = 768 → shift one place left)

     256
   ×  34
  _______
    1024
   7680   (this is 256 × 30)

👉 Step 4: Add partial products

     1024
   + 7680
   _______
     8704

✅ Final Answer: 34 × 256 = 8,704

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🔹 Example 2:

Multiply 78 × 432

👉 Work out:

• 78 × 2 = 156
• 78 × 3 = 234 → shift one place left = 2340
• 78 × 4 = 312 → shift two places left = 31,200

Now add:

   156
 +2340
+31200
______
 33696

✅ Final Answer: 78 × 432 = 33,696

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🔹 Tips for Students:

• Always align digits carefully in columns.
• Remember to add a zero when shifting left (for tens, hundreds, etc.).
• Double-check your addition at the end.

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🔹 Practice Problems:

• 46 × 325 = ?
• 72 × 418 = ?
• 89 × 637 = ?
• 65 × 504 = ?

Learn with an example

Let’s practice!