What is multiplication?
Multiplication is a quick way to add equal groups. If you have 4 bags with 6 apples in each, you could add 6 + 6 + 6 + 6. Or you could multiply: 4 × 6 = 24.
| Part | Name |
|---|---|
| 4 and 6 | Factors |
| × | "times" or "multiplied by" |
| 24 | Product |
Ways to picture multiplication
Equal groups: 4 groups of 6.
Repeated addition: 6 + 6 + 6 + 6 = 24.
Array: 4 rows of 6.
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Number line: 4 jumps of 6 → 6, 12, 18, 24.
Order doesn’t matter
4 × 6 = 6 × 4 = 24. Turn the array sideways and you get 6 rows of 4. This is the commutative property. It halves the facts you need to learn!
Strategies for learning facts
| Factor | Strategy |
|---|---|
| × 0 | Always 0 |
| × 1 | The same number |
| × 2 | Double it |
| × 4 | Double, then double again |
| × 5 | Half of × 10; products end in 0 or 5 |
| × 9 | × 10 then subtract the number (9 × 7 = 70 − 7 = 63) |
| × 10 | Put a zero on the end |
| × 3 | Double it, then add one more group |
| × 6 | × 5 plus one more group |
| × 8 | Double three times |
Breaking apart a harder fact
Use facts you know. For 7 × 8:
- 7 × 8 = (5 × 8) + (2 × 8) = 40 + 16 = 56.
The multiplication table
Patterns to notice:
- The table is symmetrical across the diagonal (because of the commutative property).
- The diagonal has the square numbers: 1, 4, 9, 16, 25 …
- Each column is skip counting.
Word clues
"Each", "per", "groups of", "rows of", "times" and "how many in all" (with equal groups) often signal multiplication.
Worked examples
Example 1: 4 × 6 = ?
4 groups of 6: 6, 12, 18, 24 → 24.
Example 2: A carton holds 12 eggs. How many eggs in 3 cartons?
3 × 12 = 36 eggs.
Example 3: Use doubles to find 4 × 7.
2 × 7 = 14, double it: 28.
Common mistakes
- Adding instead of multiplying: 4 × 6 is not 10.
- Mixing up × 0 and × 1: 8 × 0 = 0, but 8 × 1 = 8.
- Losing count of groups when skip counting. Track on your fingers.
Try it yourself
- 3 × 8 =
- 9 × 6 =
- 7 × 7 =
- A theatre has 8 rows of 10 seats. How many seats?
- Use breaking apart to find 6 × 9.
Answers: 1) 24 2) 54 3) 49 4) 80 5) (5 × 9) + (1 × 9) = 45 + 9 = 54
Quick recap
- Multiplication combines equal groups; the answer is the product.
- Picture it as repeated addition, an array or jumps.
- Order of factors doesn’t matter.