Math 010: Verbal expressions & Intro to Equations

1. Math 010: Verbal expressions & Intro to Equations October 9, 2013

2. Pre-test on Verbal Expressions First page of worksheet

3. 5.7 Verbal -> Variable Expressions • Verbal means words, variable means algebraic/math language • Memorize terms, also understand meaning in context

4. Addition Terms • “added to” • “more than” – adding numbers makes them more • Except when negatives are involved • “the sum of” • “increased by” – adding will create an increased quantity • “the total of” – to find a total, add all quantities together

5. Subtraction Terms • “minus” • “the difference between” • “decreased by” – subtracting will create a decreased quantity • “less than” • Note: 5 less than y means y - 5 • “subtract… from” • Note: 2 subtracted from xmeans x - 2

6. Multiplication Terms • “times” • “twice” means two times • “of” – used with fractions • “ of x” means times x or x • “the product of” • “multiplied by”

7. Division Terms • “divided by” • “the quotient of” • “the ratio of” • ratios can be division problems or fractions

8. “t increased by 9” • A study published by the Nature Climate Change journal last year predicted that by the year 2100, the global temperature will be increased by 9 degrees Fahrenheit. • Let t represent the current global temperature. • Write an expression for the predicted future temperature. • Current global temperature, plus 9 degrees • t + 9

9. “twice w” • According to the Wall Street Journal, a waiter working in San Francisco makes twice as much as a waiter working in New York City. • Let w be the wages of a waiter working in New York City. • Write an expression for the wages of a waiter in San Francisco. • twice as much means two times as much • 2w – remember, no symbol means multiplication.

10. “the product of y and z” • The amount of gas money used on a trip is the product of the number of gallons of gas used and the price of gas per gallon. • Let y be the number of gallons used, and let z be the price of gas per gallon. • Write a formula for the amount of gas money used. • Product means multiply! • yz

11. “7 less than t” • What operation? • Subtraction. • With subtraction, always ask “Does the order of numbers stay the same or get reversed? • In the case of less than, it gets reversed. • t - 7

12. “the difference between y and 4” • Difference means subtraction. • Reverse or stay the same? • Order stays the same. • y - 4

13. “the quotient of y and z” • Speed is defined as the quotient of distance and time. Let y represent distance and z represent time. • Write an expression for speed. • Quotient means division! • y ÷ z • Can also write as a fraction:

14. “the fifth power of a” • A decateron, or 5-cube, is a hypercube that exists in five dimensions. The 5-dimensional volume of a decateron with side length a is defined as the fifth power of a. • Power means exponent. • - that means a · a · a · a · a

15. “x minus 2” • Pretty obvious here • But ask: Does order stay the same or reverse? • Stays the same. • x - 2

16. “x divided by 12” • Another obvious one • Or write as a fraction:

17. “8 more than x” • I don’t remember our test scores, but I know I got 8 more points than you did. • Let x represent your test score. • Write an expression for my test score. • More means addition • x + 8

18. “the total of 5 and y” • I went to a restaurant and ordered one item for 5 dollars, and another item for y dollars. • Write an expression to represent the total of the bill. • Total means addition • 5 + y

19. “ymultiplied by 11” • Just a note here on order… • Dictated word for word, you get y · 11 • In multiplication, constant terms come first • 11y

20. “the sum of x and z” • Sum means addition. • x + z

21. “6 added to y” • Obvious, but note order again… • Dictated: 6 + y • In addition, variable terms come before constant terms. • y + 6

22. “m decreased by 3” • Decreased by means minus. • Order stays the same or reverses? • Same • m - 3

23. “the cube of r” • The volume of a cube with side length r is defined as the cube of r. • That means

24. “subtract 9 from z” • We know the operation is subtraction… • But does the order stay the same or reverse? • It reverses. • z - 9

25. “10 times t” • Dictated: 10 · t • 10t

26. “one-half of x” • In fractions, of means… • Multiply • =

27. “the ratio of t and 9” • For every t pairs of shoes in my closet, I have 9 pairs of socks. • Find the ratio of shoes to socks. • Ratio means division • Can write t ÷ 9 or

28. “the square of x” • The area of a square with side length x is defined as the square of x.

29. Adding more layers • Translate “three times the sum of c and five” into math. • “3 times the sum of cand 5” • 3 is not just multiplied by one object, it is multiplied by the sum. • So we need parentheses around the sum: (c + 5) • 3 (c + 5)

30. “The difference between four times w and nine” • Two parts to the difference: “four times w” minus “nine” • Difference means subtract, order stays the same • 4w - 9

31. “Five less than the product of n and eight” • Less than means subtraction, order reverses… • So it’s “the product of n and eight” minus 5 • 8n - 5

32. “The quotient of r and the sum of r and four” • Quotientis the blanket term here – applies to the rest of the sentence • Use a fraction • r is the numerator • “the sum of r and four” is the denominator

33. “Twice x divided by the difference between x and 7” • Think of the division problem as a fraction. • “divided by” is the fraction bar. • “Twice x” is the numerator. • “The difference between x and 7” is the denominator.

34. Do your homework for 5.7 • Recommended to work ahead. Check your answers to odd #s in the back of the book • Send me an email before midnight on Sunday with at least 3 verbal -> variable expressions from the 5.7 HW you want me to go over next Wednesday • YOUR EMAIL MESSAGE WILL COUNT AS TODAY’S QUIZ GRADE

35. Review: Multiplying Fractions • Evaluate • Multiplication is the easiest fraction operation. • Multiply numbers across the top and across the bottom

36. Dividing Fractions • Evaluate • Flip the second fraction!! • Then multiply

37. Adding fractions = If denominators are the same, keep the denominator and add across the top only.

38. Adding fractions Evaluate

39. Subtracting fractions • Evaluate

40. Simplify fractions • Simplify • Do 4 and 10 share a common factor? • Ask starting with 2. • Yes, they are both divisible by 2.

41. 6.1 Intro to Equations • In an equation, goal is to get the variable (letter) by itself. • Ask “What operation is being done to x?” then do the opposite. • Perform the same operation on both sides OF THE EQUALS SIGN

42. x – 6 = -11. Solve for x. • What operation is being done on x? • Subtraction of 6. • So add 6 to both sides.

43. 6 + t = 14. Solve for t. • What operation is being done to t? • Addition of 6. • 6 comes first, OK because addition is commutative. • Subtract 6 from each side.

44. 2x = -26. Solve for x. • What operation is being performed on x? • Multiplication by 2. • So divide each side by 2.

45. -7m = 56. Solve for m. • What operation is being performed on m? • Multiplication by -7. • So divideeach side by -7.

46. . Solve for y. • What operation is being done on y? • Fraction bar means… • Division by 8. • So multiply each side by 8.

47. . Solve for x. • What operation is being done to x? • Division by 7. • So multiply each side by 7.

48. Goodnight • Don’t forget to email me before midnight on Sunday with at least 3 verbal -> variable expressions from the 5.7 HW you want me to go over next Wednesday • kianxie@gmail.com • See you next Wednesday