Math · Algebra & word problems
Expressions and Order of Operations
Estimated time includes reading and one quiz. Take the time you need.
Start here: key ideas
- A variable represents an unknown or changeable number.
- Grouping and exponents come before multiplication and addition.
- Like terms have identical variable parts.
- Distribution multiplies every term inside the grouping.
What you’ll be able to do
- Translate phrases into expressions.
- Evaluate in correct order.
- Combine like terms and distribute.
Build the expression from relationships, then simplify without changing its meaning.
Read an expression
An expression combines numbers, operations, and perhaps a variable, a symbol for a number. In 4x+7, 4 is the coefficient multiplying x. A term is a part separated by addition or subtraction, so 4x and 7 are terms.
Words signal relationships: “five more than n” is n+5, while “five less than n” is n−5. Order reverses after “less than”: “five less than twice n” is 2n−5.
Worked translation: “5 less than three times n” becomes 3n − 5: build three times n first, then subtract 5. “Less than” reverses the order of the two named quantities; it does not change the sign of the variable.
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