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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.

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TRANSLATING ENGLISH TO MATH

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  1. TRANSLATING ENGLISH TO MATH SJC ~ San Jacinto Campus Math Center Workshop Series Janice Levasseur

  2. 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.

  3. 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)

  4. Subtraction • Subtracted from • (the differencebetween) • Less • Decreased by • Minus • Less than Note: The difference is the answer to a subtraction. “The difference between x and y” (x – y)

  5. 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)

  6. 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

  7. Power • The square of exponent 2 • The cube of exponent 3 Equals • Equals • Is/Are/Was/Were • Amounts to Note: These lists are not complete.

  8. 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

  9. Ex: the sum of b and eight What is the operation? Addition What is being added? b and 8 Write the expression: (b + 8)

  10. Ex: the total of four and m What is the operation? Addition What is being added? 4 and m Write the expression: (4 + m)

  11. Ex: w increased by fifty-five What is the operation? Addition What is being added? w and 55 Write the expression: w + 55

  12. Ex: g plus twenty What is the operation? Addition What is being added? g and 20 Write the expression: g + 20

  13. Ex: nineteen more than K What is the operation? Addition What is being added? 19 and K Write the expression: K + 19 Can also by written as: 19 + K

  14. Ex: n subtracted from two What is the operation? Subtraction What is being subtracted? n and 2 Write the expression (careful!): 2 – n Subtraction does not possess the commutative property so order is important. There is a difference between what goes in front of the subtraction sign (the minuend) and what goes after (the subtrahend).

  15. Ex: the difference of q and three What is the operation? Subtraction What is being subtracted? q and 3 Write the expression (careful!): (q – 3)

  16. Ex: r less twelve What is the operation? Subtraction What is being subtracted? r and 12 Write the expression (careful!): r – 12

  17. Ex: seventeen decreased by m What is the operation? Subtraction What is being subtracted? 17 and m Write the expression (careful!): 17 – m

  18. Ex: w minus 3 What is the operation? Subtraction What is being subtracted? w and 3 Write the expression (careful!): w – 3

  19. What is the operation? Subtraction Ex: nineteen less than d What is being subtracted? 19 and d Write the expression (careful!): d – 19 Subtraction does not possess the commutative property so order is important. There is a difference between what goes in front of the subtraction sign (the minuend) and what goes after (the subtrahend).

  20. What is the operation? Multiplication Ex: nine times c What is being multiplied? 9 and c Write the expression: 9c

  21. Ex: the product of negative six and b What is the operation? Multiplication What is being multiplied? -6 and b Write the expression: -6b

  22. Ex: five multiplied by a number What is the operation? Multiplication What is being multiplied? 5 and n Write the expression: 5n

  23. Ex: fifteen precent of the selling price What is the operation? Multiplication What is being multiplied? 15% and p Write the expression: .15p

  24. Ex: twice a number What is the operation? Multiplication What is being multiplied? 2 and n Write the expression: 2n

  25. Ex: the square of a number What is the operation? Multiplication What is being multiplied? n and n Write the expression: n2

  26. Ex: the cube of a number What is the operation? Multiplication What is being multiplied? n and n and n Write the expression: n3

  27. What is the operation? Division Ex: four divided by y What is being divided? 4 and y Write the expression (careful!): 4y

  28. Ex: the quotient of the opposite of n and nine What is the operation? Division What is being divided? -n and 9 Write the expression (careful!): -n 9

  29. Ex: the ratio of eleven and p What is the operation? Division 11 and p What is being divided? 11 p Write the expression (careful!): Division does not possess the commutative property so order is important. There is a difference between what goes in front of the division sign/on top (the dividend) and what goes after the division sign /on the bottom (the divisor).

  30. Ex: nine increased by the quotient of t and five What operation(s)? Addition andDivision Take it word for word to translate: nine increased by the quotient of t and five 9 + t 5

  31. Ex: the product of a and the sum of a and thirteen What operation(s)? Multiplicationand Addition Take it word for word to translate: The product of a and the sum of a and thirteen ( )( ) a a + 13

  32. Ex: the quotient of nine less than x and twice x Division & Subtraction &Multiplication What operation(s)? Take it word for word to translate: the quotient of 9 less than x and twice x x - 9 2 x

  33. Translate into a variable expression and then simplify. Identify any variables used. Ex: a number added to the product of five and the number “a number”, “the number”  let n = a number What operation(s)? Addition and Multiplication a number added to the product of 5 and the number n + ( )( ) 5 n = 6n when simplified (combine like terms)

  34. Ex: a number minus the sum of the number and fourteen let n = a number “a number”, “the number”  What operation(s)? Subtraction and Addition a number minus the sum of the number and 14 ( + ) n 14 n _ = n – n – 14 (removing parentheses) = – 14 (combining like terms)

  35. Ex: Twice the quotient of four times a number and eight “a number”  let n = a number What operation(s)? Multiplicationand Division twice the quotient of 4 times a number and 8 2 4 n 8 (Simplifying) = n (Simplifying)

  36. Equals • Equals • Is/Are/Was/Were • Amounts to • The results is • To obtain Note: These lists are not complete.

  37. 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 9 and the first number is 5, what is the second? 4 How did you get that? Subtract: 9 – 5 = 4 * If the sum of two numbers is 17 and the first number is 12, what is the second? 5 How did you get that? Subtract: 17 – 12 = 5

  38. 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

  39. 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 a number is 3 5 and = 3 (__ + __) 5 n Now solve 5 + n = 3 by subtracting 5 from both sides -5 -5 n = - 2

  40. What are we looking for? The number = n Ex: The difference between five and twice a number is one. Find the number. Translate word-for-word: The difference between 5 and twice a number is 1 (______ – ______) 5 2 n = 1 Now solve 5 – 2n = 1 Subtract 5 from both sides – 2n = - 4 Divide both sides by - 2 n = 2

  41. What are we looking for? The number = n Ex: Four times a number is three times the difference between thirty-five and the number. Find the number. Translate word-for-word: Four times a number is three times the difference between 35 and the number n 35 ( _____ - _____) 4n = 3 Solve 4n = 3(35 – n) Simplify – distribute 3 4n = 105 – 3n Collect like terms (add 3n to both sides) 7n = 105 Divide both sides by 7 n = 15

  42. 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 2 – s = larger number. The difference between 8 and twice the smaller is two less than four times the larger 8 2 s 4 (2 – s) ( ______ - ______ ) = _________ - 2

  43. Simplify 8 – 2s = 8 – 4s – 2 Combine like terms Solve 8 – 2s = 4(2 – s) – 2 Collect like terms(add 4s to both sides) 8 – 2s = 6 – 4s Collect like terms(subtract 8 from both sides) 8 + 2s = 6 2s = - 2 Divide both sides by 2 s = - 1  smaller number is -1 Therefore, 2 – s = 2 – ( - 1) = 3 the larger number is 3

  44. 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

  45. There are three times as many TAs as RAs So are there more TAs or RAs? TAs 600 – r How many TAs? The number of TAs is 3 times the number of RAs 600 - r = r 3 Solve 600 – r = 3r (add r to both sides) (divide both sides by 4) 600 = 4r 150 = r 150 RAs and 3r = 3(150) = 450 TAs

  46. 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.

  47. What are we looking for? The perimeter of the larger square What do we know? We will form 2 squares using 2 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.

  48. 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 = 2 s

  49. Solve 12 – s = 2s Add s to both sides Divide both sides by 3 12 = 3s 4 = s Therefore the shorter piece is 4 ft  the smaller square has perimeter 4 ft. Have we answered the question asked? No. We want to find the perimeter of the larger square. So, 12 – s = 12 – 4 = 8 8 ft is the perimeter of the larger square.

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