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All courses Math Foundations · MF.EQ.1 28 of 60
Translate verbal phrases and short contexts into algebraic expressions.

Translate simple add-subtract phrases

Problem
Translate this phrase into an algebraic expression: 9 less than n.
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Hint

Start by identifying the variable: the phrase is about n.

In a phrase with “less than,” the subtraction order is reversed from the word order—the amount after “than” comes first.

Solution walkthrough

01

Identify the variable

\[n\]

The phrase already tells us the variable is \(n\), so the expression must be written using \(n\).

02

Interpret the words “less than”

\[9~\text{less}~\text{than}~n\]

The words \(\text{less}~\text{than}\) mean subtract, but the order matters. \(9~\text{less}~\text{than}~n\) means start with \(n\) and subtract \(9\).

03

Write the expression

\[n~-~9\]

Since the phrase means \(n\) minus \(9\), the algebraic expression is \(n~-~9\).

04

State the final result

\[9~\text{less}~\text{than}~n~=~n~-~9\]

So the correct translation of the phrase is \(n~-~9\).

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Another way

  1. Check with a sample value. If \(n~=~15\), then \(9~\text{less}~\text{than}~n\) should be \(6\). The expression \(15~-~9\) gives \(6\), so \(n~-~9\) matches the phrase.

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Common mistake

Writing \(9~-~n\). That keeps the words in left-to-right order, but \(\text{less}~\text{than}\) reverses the subtraction order. \(9~\text{less}~\text{than}~n\) means subtract \(9\) from \(n\), so it is \(n~-~9\).