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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in modules (<link document="m21980"/>) and (<link document="m21979"/>)). Objectives of this module: be able to translate from verbal to mathematical expressions.

Overview

  • Translating from Verbal to Mathematical Expressions

Translating from verbal to mathematical expressions

To solve a problem using algebra, we must first express the problem algebraically. To express a problem algebraically, we must scrutinize the wording of the problem to determine the variables and constants that are present and the relationships among them. Then we must translate the verbal phrases and statements to algebraic expressions and equations.

To help us translate verbal expressions to mathematics, we can use the following table as a mathematics dictionary.

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

Sample set a

Translate the following phrases or sentences into mathematical expressions or equations.

six 6 more than + a number x 6 + x .

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Fifteen 15 minus - a number x 15 - x .

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A quantity y less - eight 8 y - 8 .

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Twice 2 a number x is = ten . 10 2 x = 10

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One half 1 2 of a number z is = twenty . 20 1 2 z = 20

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Three 3 times a number y is = five 5 more than + twice 2 the same number . y 3 y = 5 + 2 y

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Practice set a

Translate the following phrases or sentences into mathematical expressions or equations.

Eleven more than a number.

11 + x

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Nine minus a number.

9 x

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A quantity less twenty.

x 20

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Four times a number is thirty two.

4 x = 32

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One third of a number is six.

x 3 = 6

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Ten times a number is eight more than five times the same number.

10 x = 8 + 5 x

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Sometimes the structure of the sentence indicates the use of grouping symbols.

Sample set b

Translate the following phrases or sentences into mathematical expressions or equations.

A number divided by five, (  x  ÷ 5 ) minus ten, 10 is = fifteen . 15 x 5 10 = 15

Commas set off terms.

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Eight 8 divided by ÷ five more than a number ( 5 + x ) is = ten 10 The wording indicates this is to be considered as a single quantity.

8 5 + x = 10

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A number x multiplied by ten more than itself ( 10 + x ) is = twenty . 20 x ( 10 + x ) = 20

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A number plus one is divided by three times the number minus twelve and the result is four.
( x + 1 ) ÷ ( 3 x 12 ) = 4 x + 1 3 x 12 = 4
Notice that since the phrase "three times the number minus twelve" does not contain a comma, we get the expression 3 x 12 . If the phrase had appeared as "three times the number, minus twelve," the result would have been
x + 1 3 x 12 = 4

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
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what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Adjanou
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A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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answer
Magreth
progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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