Key takeaway: An algebraic expression strings together numbers, letters and operation signs, like 3n + 4, with no equal sign, and turns into a single number once each letter is given a value.
Grade 66.EE.A.2Expressions and Equations
Definition of Algebraic Expression
An algebraic expression is a short piece of math written with numbers, letters and operations. It describes a calculation but makes no claim, so it has no equal sign and cannot be true or false.
Words convert directly into one. “Three notebooks at \$n each plus a \$4 pen” becomes \(3n + 4\). If the letter has a known value, the phrase becomes a single number. If not, it stays as a recipe that works for every value of \(n\). Every algebraic expression is a building block of equations, formulas and functions, so reading and writing them fluently pays off for years.
Formula and notation
Typical forms use addition, subtraction, multiplication, division and exponents:
\[3n + 4 \qquad \frac{m}{5} – 2 \qquad 2(w + 9) \qquad x^2\]
Multiplication is written by placing a number beside a letter. Division is written as a fraction. Parentheses group part of the phrase.
Key facts
- Putting an equal sign between two such phrases turns them into an equation.
- Evaluating means substituting numbers for the letters and following the order of operations.
- Key words signal operations: sum, plus, more than for addition; product, times for multiplication.
- Different-looking expressions can have the same value for every substitution.
Algebraic Expression example
At the school store Cara picks up three notebooks priced \(n\) dollars apiece and a single \$4 pen. Write a phrase for her total, then find the total when \(n = 2.75\).
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Three notebooks cost \(3n\); adding the pen gives \(3n + 4\).
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Substitute \(n = 2.75\): \(3 \times 2.75 + 4\).
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Multiply, then add: \(8.25 + 4 = 12.25\).
The algebraic expression is \(3n + 4\), and the total is \$12.25.
Common mistake
Watch out
Omar simplifies \(3n + 4\) to \(7n\).
Why it is wrong
He added the 3 and the 4, but only one of them goes with \(n\). The 3 counts how many \(n\)’s there are; the 4 is a separate amount. Test with \(n = 2\): \(3(2) + 4 = 10\), yet \(7(2) = 14\). The phrase cannot be shortened.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Expressions and Equations