Algebraic Translations - MathBitsNotebook(A1) (2024)

Algebraic Translations - MathBitsNotebook(A1) (1)

Translating to Algebraic Expressions
MathBitsNotebook.com

Topical Outline | Algebra 1 Outline | MathBits' Teacher ResourcesTerms of Use Contact Person: Donna Roberts

Mathematics is often referred to as being another language. With this idea in mind, let's take a look at how to translate words from English into mathematics, in this case algebra.

Algebraic Translations:

Whentranslatingmathematical expressions written in word form (verbal expressions), you need to know how to represent the unknown quantities and the operations assigned to the expressions. This skill of translating expressions is dependent upon the language that is being used in thedescriptionof the expression.

For example, consider the expression which is read "exceedsnby four".
The unknown quantity in this expression is given to be "n". But, what"mathematical operation"is represented by the wordexceeds?

If you guessed that "exceeds" impliesaddition, you are correct.
This expression is mathematically written asn+ 4.

Below are some of the most common words and phrases used in translating expressions,
together with the operations they represent.
This is not an exhaustive list. You may also find other words that apply.

A sampling of words used to represent mathematical operations:

ADD	SUBTRACT	MULTIPLY	DIVIDE
add sum increased by more than exceeds total plus in all gain deposit	subtract difference decreased by fewer less than * diminished by minus take away withdraw reduced by	multiplied by product of times double triple twice	divide quotient per divided equally split into fraction ratio of

*be careful using"less than"- it reverses the order of things.
It is not written in the order it is read.
"5 less than 8"is written8 - 5andnot 5 - 8
"3 less thann"is writtenn- 3andnot 3 -n

Also, be careful of the placement ofcommasin statements.

Consider:Is there a difference between these two statements?

• the sum ofaandb,divided by 3

• the sum ofaandbdivided by 3

The answer is "yes". (No comma in the second statement.)
But there is also a mathematical difference between these statements.

In the first statement,"the sum ofaandb, divided by 3",
the comma indicates the completion of the concept presented before the comma.
Theaandbwill be addedBEFOREconsidering the division by 3.
Think of the statement as"find the sum ofaandb", pause (the comma), then"divide by 3".
Mathematically it looks like:

In the second statement,"the sum ofaandbdivided by 3",
there is no comma after theb, so there is no "pause" in the statement.
The statement is interpreted as the adding of (a) and (bdivided by 3).
You are simply "adding" what comes before the word "and" to what comes after the word "and".
Mathematically it looks like:.

Algebraic Translations - MathBitsNotebook(A1) (9)

In these examples, we will be using "n" to represent "a number".
Actually, any letter can be used, such asx, a, b,etc.

	Verbal Statement	Algebraic Expression
1.	Five increased by four times a number.	5 + 4n
2.	Eight less than twice a number.	2n - 8
3.	Three times a number, increased by 9.	3n + 9
4.	The product of 4, and a number decreased by 7	4 (n - 7)
5.	The number of feet in x yards.	3x
6.	Express the width of a rectangle which is seven less than its length, l.	l - 7
7.	A number repeated as a factor 3 times.	n • n • n = n³
8.	The quotient of fourteen and triple a number.	14 / (3n)
9.	Twelve times, a number increased by 6.	12 (n + 6)

In a problem like Example #8, remember that 14/3nis not the same as 14/(3n).

It may be necessary to reverse this situation.
Given the algebraic expression, create a possible verbal statement.

10.

Given 3n - 2, write a verbal expression that matches this mathematical expression.

Here are five possible answers:
• three times a number decreased by two
• triple a number minus two
• two less than three times a number
• three times a number diminished by two
• the product of three and a number, reduced by two

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Topical Outline | Algebra 1 Outline | MathBitsNotebook.com | MathBits' Teacher Resources Terms of Use Contact Person: Donna Roberts