TRANSLATING ENGLISH TO MATH

TRANSLATING ENGLISH TO MATH SJC ~ San Jacinto Campus Math Center Workshop Series Janice Levasseur • One of the major skills required in mathematics is the ability to translate a verbal statement into a mathematical (variable) expression or equation • This ability requires recognizing the verbal phrases that translate into mathematical operations Addition • • • • • • Added to (the sum of) (the total of) Increased by Plus More than Note: The sum is the answer to an addition problem “The sum of x and y”  (x + y) Subtraction • • • • • • Subtracted from (the difference between) Less Decreased by Minus Less than Note: The difference is the answer to a subtraction “The difference between x and y”  (x – y) Multiplication • • • • • Times The product of Multiplied by Of Twice Note: The product is the answer to a multiplication problem “The product of x and y”  (x)(y) Division • Divided by • The quotient of • The ratio of Note: The quotient is the answer to a division problem “The quotient of x and y”  x y Power • The square of • The cube of exponent exponent Equals • Equals • Is/Are/Was/Were • Amounts to Note: These lists are not complete Translate the following verbal expressions into variable expressions: Ex: y added to sixteen What is the operation? Addition What is being added? y and 16 Write the expression: y + 16 Ex: the sum of b and eight What is the operation? Addition What is being added? b and Write the expression: (b + 8) Ex: the total of four and m What is the operation? Addition What is being added? and m Write the expression: (4 + m) Equals • • • • • Equals Is/Are/Was/Were Amounts to The results is To obtain Note: These lists are not complete Write a variable expression Identify any variables used Ex: The sum of two numbers is 18 Express the numbers in terms of the same variable * If the sum of two numbers is and the first number is 5, what is the second? How did you get that? Subtract: – = * If the sum of two numbers is 17 and the first number is 12, what is the second? How did you get that? Subtract: 17 – 12 = Back to the example: Ex: The sum of two numbers is 18 Let n = first number Then the second number is found by subtracting: 18 – n = second number Check: Do n and 18 – n sum to 18? n + (18 – n) = n + 18 – n = 18 Translate the English sentences into equations and solve Identify any variables used Ex: The sum of five and a number is three Find the number What are we looking for? The number = n Translate word-for-word: The sum of and a number is = ( + ) n Now solve + n = by subtracting from both sides -5 -5 n=-2 Ex: The difference between five and twice a number is one Find the number What are we looking for? The number = n Translate word-for-word: The difference between and twice a number is ( – ) 2n = Now solve – 2n = Subtract from both sides – 2n = - n=2 Divide both sides by - Ex: Four times a number is three times the difference between thirty-five and the number Find the number What are we looking for? The number = n Translate word-for-word: Four times a number is three times the difference between 35 and the number n 35 ( _ _) 4n = Solve 4n = 3(35 – n) Simplify – distribute 4n = 105 – 3n Collect like terms (add 3n to both sides) 7n = 105 Divide both sides by n = 15 Ex: The sum of two numbers is two The difference between eight and twice the smaller number is two less than four times the larger Find the two numbers What are we looking for? Two numbers: Let s = smaller number Then – s = larger number The difference between and twice the smaller is two less than four times the larger s (2 – s) - = _ Solve – 2s = 4(2 – s) – – 2s = – 4s – Simplify Combine like terms – 2s = – 4s Collect like terms + 2s = Collect like terms 2s = - Divide both sides by (add 4s to both sides) (subtract from both sides) s = -  smaller number is -1 Therefore, – s = – ( - 1) = the larger number is Ex: A college employs a total of 600 teaching assistants (TA) and research assistants (RA) There are three times as many TAs as RAs Find the number of RAs employed by the university What are we looking for? The number of RAs = r The number of TAs = 600 - r There are three times as many TAs as RAs So are there more TAs or RAs? TAs How many TAs? 600 – r The number of TAs is times the number of RAs 600 - r Solve 600 – r = 3r 600 = 4r = 3r (add r to both sides) (divide both sides by 4) 150 = r  150 RAs and 3r = 3(150) = 450 TAs Ex: A wire 12 ft long is cut into two pieces Each piece is bent into the shape of a square The perimeter of the larger square is twice the perimeter of the smaller square Find the perimeter of the larger square What are we looking for? The perimeter of the larger square What we know? We will form squares using pieces of wire The pieces are from cutting a single piece in two: How long is each piece of wire? Let s = length of the shorter piece  Then, 12 – s = length of the longer piece since we start with a 12 ft wire Now, take the smaller wire and bend it into a square What is the perimeter of the smaller square? s since the shorter piece is of length s What is the perimeter of the larger square? 12 – s since the longer piece is of length 12 - s Now what? Use the information, translate into an equation: perimeter of the larger square is twice the perimeter of the smaller square 12 – s = s Solve 12 – s = 2s 12 = 3s Add s to both sides Divide both sides by 4=s Therefore the shorter piece is ft  the smaller square has perimeter ft Have we answered the question asked? No We want to find the perimeter of the larger square So, 12 – s = 12 – = 8 ft is the perimeter of the larger square ... in mathematics is the ability to translate a verbal statement into a mathematical (variable) expression or equation • This ability requires recognizing the verbal phrases that translate into mathematical... mathematical operations Addition • • • • • • Added to (the sum of) (the total of) Increased by Plus More than Note: The sum is the answer to an addition problem “The sum of x and y”  (x + y)... difference is the answer to a subtraction “The difference between x and y”  (x – y) Multiplication • • • • • Times The product of Multiplied by Of Twice Note: The product is the answer to a multiplication