# Choosing and reading letters
Any letter can work. People often pick:
- `x`, `y` — general unknowns
- `n` — “how many”
- `t` — time
- `p` — price
- `l`, `b` — length, breadth
## How we write multiply
In algebra we usually **hide** the × sign:
- `3 × x` → `3x`
- `x × y` → `xy`
We write numbers **before** letters: `3x` not `x3`.
## Read it aloud
`3x + 2` → “three x plus two”
`2(x + 1)` → “two times the bracket x plus one”
## The hidden multiply is not optional decoration
In arithmetic you write 3 × 4.
In algebra, 3 × x looks noisy, so we write **3x**.
Rules of the house:
1. Number before letter: `5y` not `y5`
2. Letters in alphabetical order when you can: `ab` not `ba` (same value, tidier)
3. Keep brackets if they change the meaning: `2(x + 1)` is not `2x + 1`
### A sentence you should memorise
“A number next to a letter, or a number next to a bracket, means multiply.”
`3x`
`2(x + 1)`
`xy`
All multiply.
Why write 3x instead of 3 × x?
By the end of this lesson
Read 3x, xy and 2(x + 1) aloud, and write multiplication the algebra way (number first, no ×).
Remember
- Any letter can work. Pick one and stick to it in that problem.
- 3 × x is written 3x (number before letter).
- x × y is written xy.
- 2(x + 1) means 2 times the whole bracket.
- Read 3x + 2 as “three x plus two”.
Worked examples
Cover the answer. Try the steps on paper, then open them.
Example 1 — Hide the ×
Rewrite 4 × n, a × b, and 5 × (n + 2) in algebra style.
- 4n
- ab
- 5(n + 2)
Answer: 4n, ab, 5(n+2)
Check: Number first; brackets stay if they are needed.
Example 2 — Read it
Say 2(x + 3) in words, then expand later in the course as 2x + 6.
- “Two times the bracket x plus three.”
- The 2 belongs to the whole (x + 3), not only to x.
Answer: two times (x + 3)
Check: If x = 1: 2(4) = 8, not 2+3=5.
Example 3 — Choose a letter
“A car travels for t hours.” Why t, not q?
- t reminds us of time
- Any letter is legal, but a helpful letter reduces mix-ups
- Once chosen, do not switch mid-problem
Answer: t for time
Check: p for price, n for how many, l and b for length and breadth.
Common mistakes
Slip Writing x3 instead of 3x.
Fix Write the number first: 3x.
This is the worldwide school habit.
Slip Reading 2(x + 1) as 2 + x + 1.
Fix The 2 multiplies the bracket.
Say “two times” every time you see a number glued to a bracket.
Slip Changing letters halfway: start with n, then switch to x.
Fix Pick one letter and define it.
“Let n be the number of tickets.”
Try on paper first
Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.
1. Write 6 × y the short way.
Answer: 6y
2. Write x times y the short way.
Answer: xy
3. Read 5n − 1 aloud.
Answer: five n minus one
4. Write “three times (a number plus 4)”.
Answer: 3(x + 4)
Touch practice
8 tap / typeTap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.
Optional picture lab
After practiceReal world
Shorthand is everywhere — like km and ₹.
Connect
Code also hides multiply: 3 * x.
⭐ Star quiz
9 questionsFinish the touch practice first if you can. Then answer without peeking. Read every “why”.