How to Write an Algebraic Expression

Translating word problems into algebraic expressions involves identifying key phrases and converting them into mathematical operations.

The following diagram gives some examples of word problems keywords or clue words. Scroll down the page for more examples and solutions of word problems.

Printable & Online Algebra Worksheets

1. Identify the Unknowns:
   Read the problem carefully and determine what quantities are unknown.
   Assign variables (usually letters like x, y, n, etc.) to represent these unknowns.
   Be specific about what each variable represents. For example:
   Let n be the number of apples.
   Let w be the width of the rectangle (in meters).
   Let t be the time taken (in hours).
   

2. Look for Keywords and Phrases:
   Certain words and phrases indicate specific mathematical operations:
   Addition (+): sum, more than, increased by, added to, plus, total
   Subtraction (-): difference, less than, decreased by, subtracted from, minus, reduced by
   Multiplication (× or ·): product, times, multiplied by, of (often indicates multiplication with fractions or percentages)
   Division (÷ or /): quotient, divided by, per, ratio of
   Equals (= or is, was, will be): results in, is equal to, gives, amounts to
   

3. Translate Phrase by Phrase:
   Break down the word problem into smaller phrases and translate each phrase into a mathematical expression.
   

4. Combine the Expressions:
   Use the relationships described in the word problem to combine the individual algebraic expressions into a larger expression.

Tips for Using Keywords:
Context is Key: Don’t just blindly translate word by word. Understand the relationship being described.
Order Matters: Pay close attention to the order of operations, especially with subtraction and division.
Identify the Unknowns: Determine what the variables will represent first.
Break Down Complex Sentences: Translate phrase by phrase.

How to translate words into algebraic expressions?
Examples:
The sum of a number and six.
The difference of a number and two.
The product of a number and five.
The quotient of a number and four.
The ratio of a number and four.
Seven less than a number.
Nine decreased by a number.
Twice a number.
Three times a number subtracted from ten.
Five added to the product of nine and a number.
Six less than the quotient of number and four.

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How to write algebraic expressions when one quantity is more or less than another?
Examples:

1. Juan is 6 inches taller than Niko. If we let N represent Niko’s height in inches, write an algebraic expression for Juan’s height.
   
2. Linda and Joan went shopping. Linda spent $25 less than Joan. If we let J represent how much Joan spent, write an algebraic expression for how much Linda spent.

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How to write algebraic expressions?
Examples:

1. Rita’s score is 13 more than 4 times Milan’s score. If we let s represent Milan’s score, write an algebraic expression for Rita’s score.
   
2. Ted’s debt is 15 less than half of Mike’s debt. If we let x represent Mike’s debt, write an algebraic expression for Ted’s debt.

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How to write an algebraic expression for the distance traveled by two people with the total distance known?
Example:
Ron and Monique were driving to a business meeting 85 miles from their office. Ron drove the first x miles, then Monique drove the rest of the way. Write an algebraic expression for how many miles Monique drove.

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