Expressions using Letter-Numbers
Dropping the multiplication sign
Learn why we can drop the multiplication sign when we write letter-numbers.
Look at 4, 8, 12, 16, 20, 24, 28, ...: the 4 times table. The 3rd term is 4 × 3, the 29th is 4 × 29, so the nth term (n is the position) is 4 × n.
We usually write 4 × n as 4n: the multiplication sign is dropped, the number comes first, then the letter. The × is still there; it's just hidden.
Working out values is the same as before:
- 7k when k = 4: 7 × 4 = 28
- 5m + 3 when m = 2: 5 × 2 + 3 = 13 (multiply first, because 5m is one term)
This is where beginners slip. Spot the mistakes:
| Wrong | Why | Right |
|---|---|---|
| d = 6, so 3d = 36 | 3d is 3 × 6, not the digits side by side | 18 |
| r = 8, so 2r + 1 = 29 | 2r is 2 × 8 = 16 | 17 |
| a = −4, so 10 − a = 6 | taking away −4 means adding 4 | 14 |
| s = 7, so 3s − 2 = 15 | that's 3 × (7 − 2); but 3s − 2 is 3 × 7 − 2 | 19 |
4 × n is written 4n, number first and letter after — and 3d with d = 6 is 18, never 36.
Practise this lesson
Questions that get harder as you improve, a Tutor that helps without giving the answer away, and progress you can see. Free for every learner.
No account, no email address. Opens the real product.