Algebraic Expression
In short: Algebraic expression is a math phrase that joins numbers, variables and operation signs, like 4n + 9, without an equals sign, so it has a value but is not a sentence.
6th GradeAlgebra6.EE.A.2
What is Algebraic Expression?
An algebraic expression is a math phrase, the way “three more than twice a number” is a phrase in English. It tells you what to compute but never claims that two things are equal.
Precisely, it is a combination of numbers, variables and operation symbols such as \(4n + 9\), \(\frac{x}{3} – 2\) or \(5(t – 1)\). Substituting a number for each variable and following the order of operations produces one numerical value.
How to spot it
- A word phrase like “7 less than a number” or “the product of 6 and a length” must be turned into symbols.
- A rule for a cost, distance or perimeter uses letters and has no equals sign, which makes it an algebraic expression.
- A question says “evaluate” and gives a value for each letter.
- A pattern needs a short formula that works for any position in the list.
The method
- Underline the key words: “more than” means add, “times” or “product” means multiply, “quotient” means divide.
- Pick a letter for the unknown amount and write the operations in the order the words describe.
- To evaluate, replace each letter with its value, using parentheses around negative numbers.
- Compute using the order of operations and write the number with its unit.
Algebraic Expression: solved example
Problem
A parking garage in Boise charges a $6 entry fee plus $3 for each hour. Write an expression for the cost of h hours, then evaluate it for 7 hours.
Solution
The fee is fixed at 6 and the hourly part is 3 times the hours, so the cost is \(6 + 3h\).
For \(h = 7\): \(6 + 3 \cdot 7 = 6 + 21 = 27\). Seven hours cost $27.
Try it
Question 1
Write “5 less than three times a number n” as an expression.
Show the answer
\(3n – 5\). Note that “less than” reverses the order.
Question 2
Evaluate \(2(w + 4) – w\) when \(w = 6\).
Show the answer
\(2(10) – 6 = 20 – 6 = 14\).
Algebraic Expression vs. Equation
An algebraic expression is a phrase such as \(4n + 9\): it can be evaluated or simplified but not solved. An equation has an equals sign, such as \(4n + 9 = 29\), and states that two quantities match, which lets you solve for n.
Keep going
Lessons
Worksheets and quizzes
- Writing and Reading Algebraic Expressions – Worksheet
- Writing and Reading Algebraic Expressions – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Algebra