Algebra Expressions

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Word Problems in Mathematics books always have a problem about colored marbles. We have one for you a bit later in this lesson.

Word Problems need to be turned into Algebra Expressions so that we can do mathematics on them, and work out number answers. (Or write a Computer App that gets the answer).

Translating word problems into Algebra requires us to know how various words translate into mathematical symbols such as + – X and / .

If the word problems only have numbers, then it is easy to translate them, once we have practiced doing a few word problems.


Algebra Expressions

An Algebra Expression is made up of Numbers and Letters (or “Pronumerals”), as well as + – x ÷ symbols.

Algebra Expressions One

Consider the following real life example.

Algebra Expressions Two Football mv

Mathematicians rewrite word situations into Algebra Expressions to make them simpler and more direct to work with.

Algebra Expressions are needed in computer apps which are written to process real world situations.

Computers use letter variables and mathematical symbols in the Algorithms in their programs, rather than full word English sentences.

Algebra Expressions Three


Translation Tips for Word Problems

The following translation tables help convert word problems into Algebra Expressions.

Look for the following key words and phrases when reading through word problems.

Whenever you find one of these words, translate the word or phrase into
+, -, x, / , or = .

This will help form the Algebra equation for the word problem.


The following words in a sentence indicate that Adding is taking place.

Adding Translations


The following words in a sentence indicate that Subtraction is taking place.

Subtracting Translations

We need to be careful when translating Subtraction words.

Algebra Expressions Less Than Money


The following words in a sentence indicate that Dividing is taking place.

Dividing Translations


The following words in a sentence indicate that Multiplying is taking place.

Multiplying Translations


The following words in a sentence need to be translated into an equals sign.

Equals Translations


Whenever we get a word problem to convert into Algebra, we can use these translation tables to help us work out what mathematical symbols we need to use to replace the words.

Here are some simple examples.

Translate Examples


Algebra Expressions Example 1


Algebra Expressions Example Two


Algebra Expressions Example 3


Algebra Expressions Example 4


Video Lessons

This first video shows how to translate word statements into mathematics for Addition and Subtraction.


In this follow up video, Professor Perez includes division and multiplication word problems.

Note that Americans use a Dot to represent a multiply sign, whereas other countries like Australia use an “x” to represent multiplication.


Tips and Traps for Word Problems

Word problems involving subtraction often cause difficulty.

For example “five more than twenty” translates to 5 + 20

But “five less than twenty” does NOT translate to 5 – 20

and “five subtracted from 20″ does NOT translate to 5 – 20

and “five taken away from 20″ does NOT translate to 5 – 20

Think of the following money example to help make sense of this.

Algebra Expressions Less Than Money

Subtraction words like “less than”, “subtracted from”, and “taken away from” all require that we swap the order of the numbers in the sentence.

“Five less than twenty” = 20 – 5

“Five subtracted from 20″ = 20 -5

“Five taken away from 20″ = 20 -5

Note that the Algebra numbers end up in reverse order to what they were in the original word sentence.

Eg. In the original word sentence the five came first and then the 20. But in the Algebra sentence the twenty comes first, and the five comes last.

The following video is a very comprehensive narrated slideshow about how to translate equations. This video includes examples of “Reversing the Order” subtraction phrases in word problems.


Translating Words into Algebra Lessons

Math Goodies has a good lesson on writing expressions for word sentences with a quick five question online quiz at the end of the lesson.

The following web page has some great hints for teachers and students about Solving math word problems and setting up equations


Related Items

Algebra Terms Coefficients Variables and Constants.
Introduction to Powers Indices and Exponents
Algebra Substitution Using Positive Numbers.
Algebra Substitution Using Negative Numbers.
Real World Algebra Formulas
Survivor Algebra – Class Activity


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