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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to translate word to mathematical symbols. By the end of the module students should be able to translate phrases and statements to mathematical expressions and equations.

Section overview

  • Translating Words to Symbols

Translating words to symbols

Practical problems seldom, if ever, come in equation form. The job of the problem solver is to translate the problem from phrases and statements into mathematical expressions and equations, and then to solve the equations.

As problem solvers, our job is made simpler if we are able to translate verbal phrases to mathematical expressions and if we follow the five-step method of solving applied problems. To help us translate from words to symbols, we can use the following Mathematics Dictionary.

MATHEMATICS DICTIONARY
Word or Phrase Mathematical Operation
Sum, sum of, added to, increased by, more than, and, plus +
Difference, minus, subtracted from, decreased by, less, less than -
Product, the product of, of, multiplied by, times, per
Quotient, divided by, ratio, per ÷
Equals, is equal to, is, the result is, becomes =
A number, an unknown quantity, an unknown, a quantity x size 12{x} {} (or any symbol)

Sample set a

Translate each phrase or sentence into a mathematical expression or equation.

Nine 9 more than + some number. x

Translation: 9 + x size 12{9+x} {} .

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Eighteen 18 minus - a number. x

Translation: 18 x size 12{"18" - x} {} .

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A quantity y less - five. 5

Translation: y 5 size 12{y - 5} {} .

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Four 4 times a number x is = sixteen. 16

Translation: 4 x = 16 size 12{4x="16"} {} .

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One fifth 1 5  of  a number n  is =  thirty. 30

Translation: 1 5 n = 30 size 12{ { {1} over {5} } n="30"} {} , or n 5 = 30 size 12{ { {n} over {5} } ="30"} {} .

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 Five 5  times  a number x  is =  two 2  more than +  twice 2  the number. x

Translation: 5 x = 2 + 2 x size 12{5x=2+2x} {} .

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Practice set a

Translate each phrase or sentence into a mathematical expression or equation.

Twelve more than a number.

12 + x size 12{"12"+x} {}

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Eight minus a number.

8 x size 12{8 - x} {}

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An unknown quantity less fourteen.

x 14 size 12{x - "14"} {}

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Six times a number is fifty-four.

6 x = 54 size 12{6x="54"} {}

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Two ninths of a number is eleven.

2 9 x = 11 size 12{ { {2} over {9} } x="11"} {}

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Three more than seven times a number is nine more than five times the number.

3 + 7 x = 9 + 5 x size 12{3+7x=9+5x} {}

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Twice a number less eight is equal to one more than three times the number.

2 x 8 = 3 x + 1 size 12{2x - 8=3x+1} {} or 2 x 8 = 1 + 3 x size 12{2x - 8=1+3x} {}

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Sample set b

Sometimes the structure of the sentence indicates the use of grouping symbols. We’ll be alert for commas . They set off terms.

A number ( x divided by ÷ four, 4 ) minus - six, 6 is = twelve 12

Translation: x 4 6 = 12 size 12{ { {x} over {4} } - 6="12"} {} .

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Some phrases and sentences do not translate directly. We must be careful to read them properly. The word from often appears in such phrases and sentences. The word from means “a point of departure for motion.” The following translation will illustrate this use.

The statement twenty is subtracted from some number can be broken into three parts and converted into a mathematical expression. Some number becomes x, the phrase, is subtracted from, becomes a minus symbol, and twenty becomes the number 20. This translates to the expression x - 20.

Translation: x 20 size 12{x - "20"} {} .

The word from indicated the motion (subtraction) is to begin at the point of “some number.”

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Ten less than some number. Notice that less than can be replaced by from .

Ten from some number.

Translation: x 10 size 12{x - "10"} {} .

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Practice set b

Translate each phrase or sentence into a mathematical expression or equation.

A number divided by eight, plus seven, is fifty.

x 8 + 7 = 50 size 12{ { {x} over {8} } +7="50"} {}

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A number divided by three, minus the same number multiplied by six, is one more than the number.

2 3 6 x = x + 1 size 12{ { {2} over {3} } - 6x=x+1} {}

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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