Expressions & Equations
Writing Algebraic Expressions
Translating a verbal description into an algebraic expression.
From Words to Symbols
Try translating these two phrases into expressions before reading on: 'five more than a number' and 'five less than a number.' If you wrote n + 5 for the first one, good — but did the second one become n − 5, or did something feel different about the order?
'Five more than a number' adds 5 to the number: n + 5. But 'five less than a number' means starting from the number and taking 5 away — the number comes first conceptually, giving n − 5, not 5 − n. Phrases with 'less than' or 'subtracted from' often reverse the order you'd expect from reading left to right, which is exactly why translating carefully matters.
Worked Example — Translating an Addition or Subtraction Phrase
Worked Example — Translating a Multiplication Phrase
Tip
Common Mistakes
Translating 'a number decreased by 8' or '8 less than a number' in reading order, writing 8 − n instead of n − 8.
'Less than' and 'decreased by' phrases describe the number as the starting amount that something is taken from — the number goes first in the expression, regardless of the order the words appear.
Leaving out parentheses when a description like 'the sum of a number and 3' is itself multiplied by something else.
Whenever a full phrase like 'the sum of...' is treated as one quantity for another operation, group it in parentheses — 'twice the sum of a number and 3' is 2(n + 3), not 2n + 3.
Key Takeaways
- Translating a phrase into an algebraic expression means matching each word or phrase to an operation, in the order the description actually means.
- 'Less than' and 'decreased by' reverse the reading order — the number being reduced comes first in the expression.
- A phrase describing a full calculation, like 'the sum of...,' needs parentheses when it's used as one quantity in a larger expression.
Summary
Writing algebraic expressions turns a real description into precise notation, watching carefully for phrases that reverse order. The next lesson simplifies expressions like these using the same properties that made arithmetic strategies work in earlier grades.
Sign in to track your progress and mark this lesson complete.
Track your progress