Expressions using Letter-Numbers

Letters stand for numbers in expressions and formulas. Combine like terms, simplify, and find the value of an expression for given numbers.

Key ideas

A letter-number such as n can stand for any number; an expression such as 3n + 2 gives a rule.
Like terms have the same letter part (4a and 7a); only like terms can be added into one term.
To find the value of an expression, replace each letter with its number, then calculate.
3n means 3 × n; n² means n × n.
Patterns of sticks or dots give rules: 3 sticks for the first triangle and 2 for each new one gives 2n + 1.

Remember

Perimeter	square 4s; rectangle 2(l + b)
Area	square s²; rectangle l × b
Simplifying	5a + 3b − 2a + b = 3a + 4b

Watch out

Adding unlike terms: 3a + 2b is not 5ab.
Reading 3n with n = 4 as 34 (it is 12).
Dropping a sign when collecting terms.

Worked example

A row of triangles, each sharing a side with the next, is made with matchsticks. Write an expression for the sticks needed for n triangles, then use it for n = 13.

Working: 3 for the first, then 2 for each new one: 3 + 2(n − 1) = 2n + 1

Answer: 2n + 1; 27 sticks