Algebraic Expressions and Equations: Applications I: Translating Words to Mathematical Symbols

Transcription

1 OpenSta-CNX module: m Algebraic Epressions and Equations: Applications I: Translating Words to Mathematical Symbols Wade Ellis Denny Burzynski This work is produced by OpenSta-CNX and licensed under the Creative Commons Attribution License 3.0 Abstract 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 epressions and equations. 1 Section Overview Translating Words to Symbols 2 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 epressions 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 epressions and if we follow the ve-step method of solving applied problems. To help us translate from words to symbols, we can use the following Mathematics Dictionary. Version 1.2: Aug 18, :14 pm

2 OpenSta-CNX module: m MATHEMATICS DICTIONARY Word or Phrase Mathematical Operation Sum, sum of, added to, increased by, more than, and, plus + Dierence, 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 (or any symbol) Table Sample Set A Translate each phrase or sentence into a mathematical epression or equation. Eample 1 Nine more {{ than some number. {{ 9 + Translation: 9 +. Eample 2 Eighteen minus a number. {{ 18 Translation: 18. Eample 3 A quantity less ve. y 5 Translation: y 5. Eample 4 Four times a number {{ is siteen. 4 Translation: 4 = 16. Eample 5 One {{ fth of a number {{ is thirty. 1 n = Translation: 5 n = 30, or n 5 = 30. = 16 Eample 6 Five {{ times {{ a number {{ is two {{ more {{ than twice {{ the number. {{ 5 = Translation: 5 =

3 OpenSta-CNX module: m Practice Set A Translate each phrase or sentence into a mathematical epression or equation. Eercise 1 (Solution on p. 7.) Twelve more than a number. Eercise 2 (Solution on p. 7.) Eight minus a number. Eercise 3 (Solution on p. 7.) An unknown quantity less fourteen. Eercise 4 (Solution on p. 7.) Si times a number is fty-four. Eercise 5 (Solution on p. 7.) Two ninths of a number is eleven. Eercise 6 (Solution on p. 7.) Three more than seven times a number is nine more than ve times the number. Eercise 7 (Solution on p. 7.) Twice a number less eight is equal to one more than three times the number. 2.3 Sample Set B Eample 7 Sometimes the structure of the sentence indicates the use of grouping symbols. We'll be alert for commas. They set o terms. 0 A number divided by four, 4 minus si, 6 1 C A Translation: 4 6 = 12. is twelve = 12 Eample 8 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. Translation: 20. The word from indicated the motion (subtraction) is to begin at the point of some number. Eample 9 Ten less than some number. Notice that less than can be replaced by from. Ten from some number. Translation: 10.

4 OpenSta-CNX module: m Practice Set B Translate each phrase or sentence into a mathematical epression or equation. Eercise 8 (Solution on p. 7.) A number divided by eight, plus seven, is fty. Eercise 9 (Solution on p. 7.) A number divided by three, minus the same number multiplied by si, is one more than the number. Eercise 10 (Solution on p. 7.) Nine from some number is four. Eercise 11 (Solution on p. 7.) Five less than some quantity is eight. 3 Eercises Translate each phrase or sentence to a mathematical epression or equation. Eercise 12 (Solution on p. 7.) A quantity less twelve. Eercise 13 Si more than an unknown number. Eercise 14 (Solution on p. 7.) A number minus four. Eercise 15 A number plus seven. Eercise 16 (Solution on p. 7.) A number increased by one. Eercise 17 A number decreased by ten. Eercise 18 (Solution on p. 7.) Negative seven added to some number. Eercise 19 Negative nine added to a number. Eercise 20 (Solution on p. 7.) A number plus the opposite of si. Eercise 21 A number minus the opposite of ve. Eercise 22 (Solution on p. 7.) A number minus the opposite of negative one. Eercise 23 A number minus the opposite of negative twelve. Eercise 24 (Solution on p. 7.) Eleven added to three times a number. Eercise 25 Si plus ve times an unknown number. Eercise 26 (Solution on p. 7.) Twice a number minus seven equals four.

5 OpenSta-CNX module: m Eercise 27 Ten times a quantity increased by two is nine. Eercise 28 (Solution on p. 7.) When fourteen is added to two times a number the result is si. Eercise 29 Four times a number minus twenty-nine is eleven. Eercise 30 (Solution on p. 7.) Three fths of a number plus eight is fty. Eercise 31 Two ninths of a number plus one fth is forty-one. Eercise 32 (Solution on p. 7.) When four thirds of a number is increased by twelve, the result is ve. Eercise 33 When seven times a number is decreased by two times the number, the result is negative one. Eercise 34 (Solution on p. 7.) When eight times a number is increased by ve, the result is equal to the original number plus twenty-si. Eercise 35 Five more than some number is three more than four times the number. Eercise 36 (Solution on p. 7.) When a number divided by si is increased by nine, the result is one. Eercise 37 A number is equal to itself minus three times itself. Eercise 38 (Solution on p. 7.) A number divided by seven, plus two, is seventeen. Eercise 39 A number divided by nine, minus ve times the number, is equal to one more than the number. Eercise 40 (Solution on p. 8.) When two is subtracted from some number, the result is ten. Eercise 41 When four is subtracted from some number, the result is thirty-one. Eercise 42 (Solution on p. 8.) Three less than some number is equal to twice the number minus si. Eercise 43 Thirteen less than some number is equal to three times the number added to eight. Eercise 44 (Solution on p. 8.) When twelve is subtracted from ve times some number, the result is two less than the original number. Eercise 45 When one is subtracted from three times a number, the result is eight less than si times the original number. Eercise 46 (Solution on p. 8.) When a number is subtracted from si, the result is four more than the original number. Eercise 47 When a number is subtracted from twenty-four, the result is si less than twice the number.

6 OpenSta-CNX module: m Eercise 48 (Solution on p. 8.) A number is subtracted from nine. This result is then increased by one. The result is eight more than three times the number. Eercise 49 Five times a number is increased by two. This result is then decreased by three times the number. The result is three more than three times the number. Eercise 50 (Solution on p. 8.) Twice a number is decreased by seven. This result is decreased by four times the number. The result is negative the original number, minus si. Eercise 51 Fifteen times a number is decreased by fteen. This result is then increased by two times the number. The result is negative ve times the original number minus the opposite of ten. 3.1 Eercises for Review Eercise 52 (Solution on p. 8.) ( here 1 ) 8 9 of what number is 2 3? Eercise 53 ( here 2 ) Find the value of Eercise 54 (Solution on p. 8.) ( here 3 ) Find the value of Eercise 55 ( here 4 ) Convert to a fraction. Eercise 56 (Solution on p. 8.) ( here 5 ) Solve the equation = 5. 1 "Introduction to Fractions and Multiplication and Division of Fractions: Applications Involving Fractions" < 2 "Addition and Subtraction of Fractions, Comparing Fractions, and Comple Fractions: Addition and Subtraction of Fractions with Unlike Denominators" < 3 "Addition and Subtraction of Fractions, Comparing Fractions, and Comple Fractions: Addition and Subtraction of Mied Numbers" < 4 "Decimals: Converting a Decimal to a Fraction" < 5 "Algebraic Epressions and Equations: Solving Equations of the Form a=b and /a=b" <

7 OpenSta-CNX module: m Solutions to Eercises in this Module Solution to Eercise (p. 3) 12 + Solution to Eercise (p. 3) 8 Solution to Eercise (p. 3) 14 Solution to Eercise (p. 3) 6 = 54 Solution to Eercise (p. 3) 2 9 = 11 Solution to Eercise (p. 3) = Solution to Eercise (p. 3) 2 8 = or 2 8 = = = = 4 5 = ( 6) [ ( 1)] = = = = = = 1

8 OpenSta-CNX module: m = 17 2 = 10 3 = = 2 6 = + 4 Solution to Eercise (p. 6) = Solution to Eercise (p. 6) = 6 Solution to Eercise (p. 6) 3 4 Solution to Eercise (p. 6) Solution to Eercise (p. 6) = 8