**Can you give the mathematical expressions for these words?**

- Seventy three minus forty -two
- Twelve less two
- Six times fifteen
- Thirty plus eleven take away nine

Sometimes, in a mathematical expression, we use letters to represent numbers we do not know.

If we say that there were some people at a party and 7 people left, we can show this as an expression, n-7, where n represents the number of people in the party.

If there were 12 people at the party, then n would represent 12. If there were 20 people at the party, then n would represent 20.

**These letters are called variable because they can represent any number.**

**CHECKPOINT:** When we write an expression using variables, words and/or operations, it is called an algebraic expression.

Let *p* be the number of pencils in your pencil box. Study the algebraic expressions for each:

12 pencils more than the number of pencils in your box → *p* + 12 or 12 + *p*

4 pencils less than the number of pencils in your box → *p* – 4

Three times the number of pencils in your box. → 3 × *p* also written as 3*p*

The number of pencils in your box divided by 4 → *p* ÷ 4 also written as p/4

**Here, the expressions have been put into words. The unknown number or the variable is ***w.*

18 + *w *→ *w* added to 18

10 – *w *→ *w* subtracted from 10

7*w *→ The product of *w* and 7

6 ÷ *w *→ 6 divided by *w*

If we know that *w* = 3, Then expressions above can be simplified and a value can be obtained for each expression.

If we substitute 3 in place of *w*, we get

18 + *w* = 18 + 3 = 21

10 – *w = *10 – 3 = 7

7*w* = 7 × 3 = 21

6 ÷ *w = *6 ÷ 3 = 2