In Grade 3 you used a letter for an unknown number in an equation. Letters, called variables, can also stand for a number that changes from one situation to the next.
Key idea
A variable is a letter that stands for a number. Writing a number next to a letter means multiply: $3a$ means $3 \times a$.
Why it works
If pencils cost \$2 each, then 1 pencil costs \$2, 5 pencils cost \$10, and $n$ pencils cost $2n$ dollars. The one expression $2n$ describes every case at once, because $n$ can be any number of pencils. That is the power of a variable: it lets us write a rule instead of a long list.
| Expression | Means |
|---|---|
| $3a$ | 3 times $a$ |
| $a + 3$ | 3 more than $a$ |
| $\frac{a}{3}$ | $a$ divided by 3 |
| $a^2$ | $a$ times $a$ |
Worked example: What does it stand for?
A pen costs $p$ dollars. What does $4p$ stand for?
- $4p$ means 4 times the price of one pen.
- That is the cost of 4 pens.
Answer: The cost of 4 pens, in dollars.
Worked example: Write it with a variable
Movie tickets cost \$9 each. Write an expression for the cost of $t$ tickets.
- Try a number first: 2 tickets cost $9 \times 2$ dollars.
- Put $t$ where the 2 was: $9 \times t$.
Answer: $9t$ dollars
Worked example: Find the value
If $a = 5$, what is $3a$?
- $3a$ means $3 \times a$.
- $3 \times 5 = 15$.
Answer: $15$ (not 35)
Common mistake
Treating a letter as a label: reading $3a$ as "3 apples". In math, $a$ stands for a number, like the number of apples or the price of one apple, and $3a$ is 3 times that number. Quick check: put a number in for the letter and see if the expression still makes sense.