Writing and reading expressions
Translate words into algebra and identify terms, factors and coefficients.
Before you begin
- Order of operations
- Understanding an unknown quantity
Define a variable and preserve the order
A variable represents a number whose value may be unknown or allowed to change. Define it before writing a model: let n be the number of notebooks. At $3 each plus a fixed $2 delivery fee, cost is 3n + 2. Subtraction is sensitive to word order: five less than n is n − 5, while n less than five is 5 − n.
Name the parts of an expression
Terms are separated by addition or subtraction at the outermost level. In 4x + 7 there are two terms; 4 is the coefficient of x and 7 is a constant term. In 3(x + 2), the whole expression is a product of the factors 3 and (x + 2). The bracket contains a sum, but that entire sum is treated as one factor when multiplied by three.
Worked example
A club charges $8 to join and $4 for each visit. Write the total cost for v visits.
Show the worked solution
- Define v as the number of visits and C as the cost in dollars.
- The visit charge is 4v; the joining fee is paid only once.
- Add the fixed fee: C = 8 + 4v. At zero visits, the cost is still $8.
C = 8 + 4v.
Try it yourself
Which expression means three times the sum of x and five?
Common mistakes
- Multiplication can be written next to a letter, but addition needs a plus sign.
- Use brackets when a phrase groups several terms together.
What can you explain now?
Write an expression for seven less than twice n. Identify its variable term and constant term.
Compare with the explanation
2n − 7; variable term 2n and constant term −7.
Twice n is 2n. Subtract seven from that quantity. The minus sign belongs to the constant term when the expression is viewed as a sum.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗