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MathidiaMathematics Academy
Algebraic notation and substitution
Lesson 32 of 75
Easy practice

Write algebraic expressions

Objective. Translate verbal rules into concise algebraic expressions.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Writing an algebraic expression means translating a worded description into symbols using a variable to represent the unknown quantity. Phrases like 'add 5' become +5, 'multiply by 3' becomes ×3, and 'subtract from' reverses the order of the terms. For example, 'four more than twice a number' becomes 2x+4, since you double the number first then add four. Careful attention to word order matters: 'five less than a number' is x−5, but 'five less a number' could mean 5−x depending on context.

Worked example

Write an algebraic expression for 'seven more than three times a number, n'.

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Illustrated card showing ?
  1. 1Identify the variable: n represents the unknown number.
  2. 2Translate 'three times a number' as 3n.
  3. 3Translate 'seven more than' as adding 7 to the previous result.
  4. 4Combine to write the expression.

Answer: 3n + 7

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Practice

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Common mistake. Pupils often write 'three less than a number' as 3−x instead of x−3, reversing the subtraction. Read the phrase slowly and identify what is being subtracted from what.

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