Algebra
Expressions
Writing algebraic expressions
20 practice questions
2 video lessons
Theory + worked examples
Theory
An algebraic expression combines numbers, variables, and operations. Translate keywords into symbols:
- Sum / more than \(\to +\)
- Difference / less than \(\to -\)
- Product / times \(\to \times\)
- Quotient / per \(\to \div\)
“Less than” reverses the order: “\(5\) less than \(n\)” is \(n-5\), not \(5-n\).
Keywords translate to operations.
Worked translations.
Common translations:
\[\text{sum }a+b,\quad \text{product }ab,\quad \text{quotient }\dfrac{a}{b}\]
A variable stands for an unknown number.
How to write an expression
- Identify the unknown and assign a variable.
- Find the operation keywords.
- Write the operations in the correct order.
- Check “less than” and “divided by” for reversal.
Example 1 — A sum
Write “\(7\) more than a number \(n\)” as an expression.
Solution
“More than” means addition.
| \(n+7\) |
Example 2 — A product
Write “the product of \(4\) and \(x\)”.
Solution
“Product” means multiply.
| \(4x\) |
Example 3 — Two operations
Write “\(5\) less than twice a number \(n\)”.
Solution
Twice \(n\) is \(2n\); “\(5\) less” subtracts \(5\).
| \(2n-5\) |
Example 4 — A quotient
Write “a number \(x\) divided by \(3\)”.
Solution
Division becomes a fraction.
| \(\dfrac{x}{3}\) |
Common pitfalls
“Less than” reverses: \(5\) less than \(n\) is \(n-5\).
“Twice a number” is \(2n\), not \(n+2\).
Use one variable for the same unknown.
Frequently asked questions
What is an algebraic expression?
A combination of numbers, variables, and operations with no equals sign.
How do you write “5 less than n”?
\(n-5\) — “less than” reverses the order.
What is a variable?
A letter standing for an unknown number.
How do you write “twice a number”?
\(2n\).
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