Arithmetic Operations
Multiplication as Repeated Addition
The cleanest way to understand multiplication is to see it as a shortcut for repeated addition. Every multiplication fact you learn was originally an addition problem.
Side-by-Side Comparison
| Addition | Multiplication | Answer |
|---|---|---|
| 2 + 2 + 2 | 3 × 2 | 6 |
| 5 + 5 + 5 + 5 | 4 × 5 | 20 |
| 10 + 10 + 10 + 10 + 10 | 5 × 10 | 50 |
| 7 + 7 | 2 × 7 | 14 |
Number Line Jumps
On a number line, multiplication appears as equal jumps from zero.
The Limitation of Repeated Addition
Imagine calculating 247 × 358 using repeated addition. You would add 247 to itself 358 times — thousands of steps. Multiplication handles this in seconds. This is why we develop multiplication as a separate operation.
Worked Examples
6 × 3 = 3 + 3 + 3 + 3 + 3 + 3 = 18
8 × 7 = 7 repeated 8 times = 7+7+7+7+7+7+7+7 = 56
Each shelf holds 12 books. There are 5 shelves. Total = 12 × 5 = 12+12+12+12+12 = 60 books
Key Takeaways
- a × b means add a to itself b times (or add b to itself a times).
- Multiplication gives the same result as repeated addition but far more efficiently.
- Number line jumps visualise multiplication as equal steps.
Practice: Fill in the Gap
A repeated addition sum is shown below. Work out how many times the number is being added. If you get it wrong (or leave it blank), we'll count the groups together.