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Chapter 11 – Introduction to Algebra (Part II)

Chapter 11 – Introduction to Algebra (Part II). Week 9 – Math Skills. Outline . Section 11.5 – Translating Verbal Expression to Mathematical Expressions Section 11.6 – Translating Sentences into Equations. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions.

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Chapter 11 – Introduction to Algebra (Part II)

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  1. Chapter 11 – Introduction to Algebra (Part II) Week 9 – Math Skills

  2. Outline • Section 11.5 – Translating Verbal Expression to Mathematical Expressions • Section 11.6 – Translating Sentences into Equations

  3. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • Word problems contain key words that help us solve them. • These keywords translate directly into mathematical expressions. • Keywords for addition Addition “More than” “The sum of” “The total of” “Increased by” • 5 more than x  5 + x • The sum of w and 3  w + 3 • The total of 6 and z is  6 + z • x increased by 7 is  x + 7

  4. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • Keywords for subtraction Subtraction “Less than” “The difference between” “Decreased by” • 5 less than y  y – 5 • The difference between w and 3  w – 3 • 8 decreased by a  8 - a

  5. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • Keywords for multiplication Multiplication “Times” “The product of” “of” “Twice” • 3 times c  3c • The product of 4 and t  4t • 2/3 of v (2/3)v • twice d  2d

  6. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • Keywords for division Division “Divided by” “the quotient of” “the ratio of” • n divided by 3  n/3 • The quotient of z and 4  z/4 • The ratio of s to 6  s/6

  7. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • Examples • Translate “The sum of 5 and the product of 4 and n” into a mathematical expression. • The sum of 5  5 + • The product of 4 and n  4n • Put these together  5 + 4n • Translate “ the product of 3 and the difference between z and 4” into a mathematical expression. • The product of 3 and  3 • • The difference between z and 4  z – 4 • Put these together  3(z – 4)

  8. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • Class Examples • Translate “The difference between 8 and twice t” into a mathematical expression. • The difference between 8 and  8 - • Twice t  2t • Put these together  8 – 2t • Translate “the quotient of 5 and the product of 7 and x” into a mathematical expression. • The quotient of 5 and  5 ÷ • The product of 7 and x  7x • Put these together  5 ÷ 7x

  9. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • In some mathematical phrases, we are not given the name of the variable • Before we were given • Translate “the difference between 8 and twice t” • We are given the variable here (i.e. t) • Now not given the name of the variable. What to do? • Example: Translate “the difference between seven and twice a number” • “a number” could be x, y, z, a, b, c, any variable you choose… • It is just a placeholder • The difference between 7 and  7 – • Twice a number  2n • Put these together  7 – 2n

  10. Section 11.5 – Translating Verbal Expressions into Mathematical Expressions • Example • Translate “the total of a number and the square of the number” • Choose a variable… • The total of a number  n + • The square of the number  n2 • Put these together  n + n2 • Class Example • Translate “the product of a number and one-half of the number” • Choose variable… • The product of a number and  n • • One-half of the number  ½ n • Put these together  n • ½ n

  11. Section 11.6 – Translating Sentences into Equations and Solving • An equation states that two mathematical expressions are equal. Keywords in word problems for equal are: • Once we translate the given equation into a mathematical expression, we can find the solution Equals Equals Equal to Is equal to Amounts to Represents

  12. Section 11.6 – Translating Sentences into Equations and Solving • Example • Translate “three more than twice a number is seventeen”, then solve the equation. • Three more than  3+ • Twice a number  2n • Is seventeen  = 17 • Put these together  3 + 2n = 17 • Now solve this equation for n • 3 – 3 + 2n = 17 – 3; subtract 3 from each side • 2n = 14 • 2n/2 = 14/2; divide both sides by 2 • n = 7; is the solution to the equation. • We say “the number is 7”

  13. Section 11.6 – Translating Sentences into Equations and Solving • Example • Translate “a number decreased by 6 equals fifteen” into an equation, then solve. • A number decreased by 6  n - 6 • Equals 15  = 15 • Put these together  n – 6 = 15 • Now solve this equation for n • n – 6 + 6 = 15 + 6; add 6 to each side • n = 21 • We say “the number is 21”

  14. Section 11.6 – Translating Sentences into Equations and Solving • Example • Translate “eight decreased by twice a number is four” find the number. • Eight decreased by  8 - • Twice a number  2n • Is four  = 4 • Putting these together  8 – 2n = 4 • Now solve this equation for n • 8 – 8 – 2n = 4 – 8 ; subtract 8 from each side • -2n = -4 • -2n/(-2) = -4/(-2) ; divide both sides by -2 • n = 2 • We say “the number is 2”

  15. Section 11.6 – Translating Sentences into Equations and Solving • Class Example • Translate “the product of two and a number is ten” then find the number. • The product of two and a number  2n • Is ten  = 10 • Putting these together  2n = 10 • Now solve this equation for n • 2n /2 = 10 /2; divided both sides by 2 • n = 5 • We say “the number is 5”

  16. Section 11.6 – Translating Sentences into Equations and Solving • Class Example • Translate “three more than one-half a number is nine” find the number. • Three more than  3 + • One-half of a number  ½ n • Is nine  = 9 • Putting these together  3 + ½ n = 9 • Now solve this equation for n • 3 – 3 + ½ n = 9 – 3 ; subtract 3 from each side • ½ n = 6 • ½ n (2) = 6 (2) ; multiply both sides by 2 • n = 12 • We say “the number is 12”

  17. Final Exam Review • What to study? • Practice final • Lecture notes • Sections in the book

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