IMOClass 3 › Multiplication

Multiplication

Repeated Addition & Tables

Multiplication is a short way to add equal groups. 4 groups of 6 = 6 + 6 + 6 + 6 = 24, written as 4 × 6 = 24. The order does not matter: 4 × 6 = 6 × 4.

Knowing the tables from 2 to 10 makes multiplication fast. For example, the table of 7 is 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

Example 1: Write 4 + 4 + 4 + 4 + 4 as multiplication.
Five 4s = 5 × 4 = 20.
Example 2: What is 6 × 7?
From the table of 6 (or 7), 6 × 7 = 42.
Quick recap
  • Multiplication adds equal groups quickly.
  • Order does not matter: a × b = b × a.
  • Learn tables 2 to 10 by heart.
✓ Quick check
What is 8 × 7?
8 × 7 = 56.
What is 9 × 6?
9 × 6 = 54.

Multiplying by a 1-digit Number

To multiply a 2- or 3-digit number by a 1-digit number, multiply the Ones first, then the Tens, then the Hundreds, carrying when a product is 10 or more.

For 34 × 3: ones 3 × 4 = 12 (write 2, carry 1), tens 3 × 3 = 9, plus carry 1 = 10, so the answer is 102.

Example 1: Multiply 34 × 3.
3 × 4 = 12 (carry 1); 3 × 3 = 9 + 1 = 10 → 102.
Example 2: Multiply 213 × 4.
4 × 3 = 12 (carry 1); 4 × 1 = 4 + 1 = 5; 4 × 2 = 8 → 852.
Quick recap
  • Multiply Ones, then Tens, then Hundreds.
  • Carry to the next place when a product is 10 or more.
✓ Quick check
Multiply: 45 × 2 = ?
2 × 5 = 10 (carry 1); 2 × 4 = 8 + 1 = 9 → 90.
Multiply: 123 × 3 = ?
3 × 3 = 9, 3 × 2 = 6, 3 × 1 = 3 → 369.

Multiplying 2-digit by 2-digit & Word Problems

To multiply two 2-digit numbers, split the second number into tens and ones, multiply each part, then add. For 23 × 12: 23 × 2 = 46 and 23 × 10 = 230, so 46 + 230 = 276.

In word problems, look for equal groups — rows, packets, dozens — and multiply.

Example 1: Multiply 23 × 12.
23 × 2 = 46, 23 × 10 = 230, total 276.
Example 2: A box has 25 pens. How many pens in 6 boxes?
6 × 25 = 150 pens.
Quick recap
  • Split the second number into tens and ones, multiply, then add.
  • Word problems with equal groups use multiplication.
✓ Quick check
Multiply: 14 × 11 = ?
14 × 1 = 14 and 14 × 10 = 140, so 14 + 140 = 154.
A shelf holds 13 books. How many books on 12 such shelves?
13 × 12 = 156 books.
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