Translate Word Equations

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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.

For example, Cyana and Larissa go to the shops and they each have fifty dollars.

Cyana spends 24 dollars and Larissa spends twice as much as Cyana.

How much money do they each have left after their shopping spree ?

We know that spending money is going to reduce or subtract from the original total of 50 dollars.

We also know that “twice” means two times, and thus refers to multiplication.

Cyana = (50 – 24) = $26

Larissa = (50 – 2×24) = (50 – 48) = $2

“Spend” means subtraction, and “twice” means multiply by two.

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Sometimes word problems have missing information that we call “variables” and we use an Algebra letter instead of a number to represent these values.

For example, our previous word problem can be written as follows, for a situation where we do not know exactly how much money the girls spent.

Cyana and Larissa go to the shops and they each have fifty dollars.
Cyana spends “M” dollars and Larissa spends twice as much as Cyana.

(“M” is the unknown amount of money that Cyana spent).

How much money do they each have left after their shopping spree ?

Cyana = 50 – M

Larissa = (50 – 2 x M) = 50 – 2M

This time the answer cannot be worked out to an exact numeric dollar amount, and we have to leave the answer with the unknown value of “M” in it.

“M” is a variable that represents how much money Cyana spent. (“M” = money spent).

If we are later told that “M” = 18 dollars then we can use “substitution” to work out exact answers.

Cyana = 50 – M (but M = 18)
Cyana = 50 – 18 = $32

Larissa = 50 – 2 x 18
Larissa = 50 – 36 = $14

 
 

Translation Tips for Word Problems

The following translation tables help convert word problems into Algebra expressions and equations.

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.

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

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

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

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

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.

 
 

Video Lessons

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

[youtube http://www.youtube.com/watch?v=ubaBrD-NQ_w?rel=0]

 

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.

[youtube http://www.youtube.com/watch?v=m72bUX3bi_c?rel=0]

 

This next video takes things a step further, and shows how we can make “Function Equations” for word problems.

[youtube http://www.youtube.com/watch?v=7OFL3uHvvlQ?rel=0]

 
 

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.

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.

[youtube http://www.youtube.com/watch?v=29uM12GMLA8?rel=0]
Translating Equations Slideshare Presentation

Here is a Slideshare Presentation all about writing equations for word problems.

[slideshare id=610434&doc=c2ch0108-1222031873020264-9]

 
 

Translating Words into Algebra Lessons

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

Click the link below to do this lesson.

http://www.mathgoodies.com/lessons/vol7/equations.html

They also have a similar lesson on translating algebra expressions from words.

http://www.mathgoodies.com/lessons/vol7/expressions.html

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

http://www.homeschoolmath.net/teaching/teach-solve-word-problems.php

 
 

Translating Words Into Equations Worksheets

There are several Number Problems PDF worksheets on the following web page.
Write equation then work out the answer, and then page down to the Answers page to check your work.

http://www.algebra4children.com/printables.html

There are eight mix and match problems on this page, but no checking of the answers is provided.

http://www.math.com/school/subject2/practice/S2U1L3/S2U1L3Pract.html

That’s about it for translating world problems into Algebra and Mathematics.

 
 

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