IMOClass 2 › Multiplication

Multiplication

Multiplication as Repeated Addition

Multiplication is a fast way to add equal groups. 3 groups of 4 = 4 + 4 + 4 = 12, which we write as 3 × 4 = 12. The sign × means times.

The order does not change the answer: 3 × 4 = 4 × 3 = 12.

Example 1: Write 5 + 5 + 5 as multiplication.
3 groups of 5 = 3 × 5 = 15.
Example 2: What is 2 × 6?
2 groups of 6 = 6 + 6 = 12.
Quick recap
  • Multiplication adds equal groups quickly.
  • × means times; 3 × 4 = 4 + 4 + 4 = 12.
  • Order does not matter: a × b = b × a.
✓ Quick check
4 + 4 + 4 = ___ × 4 ?
Three 4s means 3 × 4.
What is 2 × 7?
7 + 7 = 14.

Tables of 2, 5 and 10

The table of 2 counts in twos: 2, 4, 6, 8, 10… The table of 5 counts in fives: 5, 10, 15, 20… The table of 10 counts in tens: 10, 20, 30… Knowing these tables makes multiplication quick.

Example 1: What is 5 × 4?
Count by 5 four times: 5, 10, 15, 20. So 5 × 4 = 20.
Example 2: What is 10 × 3?
10, 20, 30. So 10 × 3 = 30.
Quick recap
  • Table of 2: 2, 4, 6, 8, 10…
  • Table of 5: 5, 10, 15, 20…
  • Table of 10: 10, 20, 30…
✓ Quick check
What is 5 × 6?
5, 10, 15, 20, 25, 30 — so 30.
What is 10 × 7?
10 × 7 = 70.

Equal Groups & Word Problems

Many real situations use equal groups: rows of chairs, packets of biscuits, wheels on cars. Find how many groups and how many in each group, then multiply.

Example 1: A car has 4 wheels. How many wheels on 3 cars?
3 × 4 = 12 wheels.
Example 2: 5 packets have 2 pens each. How many pens?
5 × 2 = 10 pens.
Quick recap
  • Look for equal groups in the problem.
  • Multiply groups × items in each group.
✓ Quick check
There are 6 boxes with 5 balls each. How many balls in all?
6 × 5 = 30 balls.
A hand has 5 fingers. How many fingers on 2 hands?
2 × 5 = 10 fingers.
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