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Writing algebraic expressions worksheets

“7 less than a number n” is n − 7, and almost every mark lost on this topic is the other one. These free printable worksheets give a phrase or a situation and four expressions, and the wrong ones are the reversals a real student writes.

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Writing algebraic expressions
Writing algebraic expressions worksheet — One or two operations, one letter, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Evaluating an expression and writing one are different skills, and only the second is any use in a word problem. This page is the writing half: read the words, decide what is being done and to which number, and put it down in algebra. Every option on the page is built from the same two numbers as the question, so nothing can be crossed off without reading it.

Why this sheet works

Word order is the whole topic. “7 less than n” is n − 7 and never 7 − n; “n divided by 4” is n ÷ 4 and never 4 ÷ n. The two-step phrases come in matched pairs for the same reason — “5 times a number, then add 3” is 5n + 3 while “add 3 to a number, then multiply by 5” is 5(n + 3), the same two numbers and the same two operations with the bracket deciding everything.

How this one works

Read it in order, then say which way round

m= a number
adding
m + 9
  1. The phrase is "9 more than a number m". The letter m is the number nobody has told us; everything else in the phrase says what to do to it.
  2. The words say we are adding.
  3. "more than" makes 9 bigger, so 9 is what is added to.

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