Math 6A, Lesson 1, Spring 2019, 2/3/2019

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Simplification of Linear Algebraic Expressions

1. The distributive law is applicable when removing parentheses in an algebraic expression. Examples in class:

  • 2(3x + 4y) =
  • -4(5a – 3b) + 7a
  • a(2x + 7y + 5z)
  • (2p + 3q -4r)(-6b)
  • 2[x- 5(3-x)]

2. Express each of the following as a single fraction in the simplest form. Recall LCM of denominators.

  • -p + p/3 +(3p)/5
  • (3p + 10)/4 -2
  • (3x – 4)/4 + (2x+5)/3
  • (1 – 2x)/3 + (3x + 1)/5 + (4x -3)/6

3. Home Work:

  • Handout:
    • two pages
  • Workbook: correct last week’s HW problem of
    • page 21: 3, 4, 5
    • Page 23: 11, 12, 13, 14, 15
    • Page 24: 21
    • Page 25: 22, 23

4. Hand out the report card for Fall 2018

 

Math 6A, Lesson 16, Fall 2018, 1/27/2019

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Distributive Law, Addition and Subtraction of Linear Algebraic Expressions

1. Snow day on 1/20/2019

2. Use of parentheses and distributive law

  • a(x + y) = ax + ay
  • (x + y)a = a(x + y) = ax + ay = xa + xy
  • a(x – y) = a{x + (-y)] = ax + a(-y) = ax – ay
  • a(x + y + z) = ax + ay + az
  • x – (a – b) = a -a + b

3. Addition and subtraction of linear algebraic expressions: explained in class

  • (2a +3b) + (5a -4b) =
  • Find the sum of -2p + 3q – 4 and p + 5q – 3
  • (4x – 5) – (7x – 3)

4. Home Work:

  • Handout:
    • one pages
  • Workbook:
    • page 21: 3, 4, 5
    • Page 23: 11, 12, 13, 14, 15
    • Page 24: 21
    • Page 25: 22, 23

Math 6A, Lesson 15, Fall 2018, 1/13/2019

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Like Terms and Unlike Terms

1. Go over the exam problem one by one.

2. Terms, coefficient, and constant terms

  • The expression 2x – 3y + 8 consists of three terms. They are 2x, -3y and 8. The numerical part, including the sign, of a term is called the coefficient of the variable.
  • Term 2x, the coefficient of x is 2
  • Term -3y, the coefficient of y is -3
  • Term 8, is called constant term

3. Classify the like terms and unlike terms: explained in class

4. Simplify the algebraic expression by combining (or collecting) like terms

  • 2x + 3x = 5x
  • 8y – 3y = 5y
  • 3a + 4b – 2a + 5b = (3a -2a) + (4b +5b) = a + 9b

5. Home Work:

  • Handout: two pages
  • Workbook:
    • page 21: 1, 2
    • Page 22: 6, 9, 10

 

Math 6A, Lesson 14, Fall 2018, 01/06/2019

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1. Exam on chapter 3 “Introduction to Algebra”

2. Home Work: 

  • Redo all the problems you got wrong in last three homework assignment.

 

Math 6A, Lesson 13, Fall 2018, 12/16/2018

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Writing Algebraic Expressions to Represent Real-world Situation

1. We may use algebraic expressions and formulas to express the relationship between two or more quantities in our daily life

  • Lots of examples teaching in the classroom, and lots of exercise on whiteboard
  • Visualizing, drawing
  • Variables are representing quantities with similar units.

2. Home Work:

  • Handout: three pages
  • Workbook:
    • page 17: 15, 16, 17, 18, 19
    • Page 18: 20, 21, 22, 23, 24
    • Page 19: 25

 

Math 6A, Lesson 12, Fall 2018, 12/9/2018

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Evaluation of algebraic expressions and formulas

1. Evaluation of algebraic expressions

  • The process of replacing each variable with its value to find the actual value of an algebraic expression is called substitution.

2. Formulas

  • The area of a rectangle is given by
    • Area = Length x Width
    • A = lw
  • This equality of connecting two or more variables is called a formula. When the values of l and w are known, we can find the value of A in the formula by substitution.

3. Home Work:

  • Handout: two pages
  • Workbook:
    • page 15: 3, 4, 5
    • Page 16: 11, 12, 13
    • Page 17: 14
    • Page 19: 26, 27
    • Page 20: 28

 

Math 6A, Lesson 11, Fall 2018, 12/02/2018

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The use of letters in algebra

1. The use of letters

  • In general, an algebraic expression involves numbers and letters that are connected with operation symbols such as “+”, “-”, “x” and “/”
  • In 10 + 8n, we call n a variable and 10 + 8n an algebraic expression

2. Basic notation in algebra

  • In algebra, there are rules for writing algebraic expressions. The operation symbols “+”, “-”, “x”, “/”  and “=” have the same meanings in both algebra and arithmetic.
  • Add a to b: sum = a + b = b + a
  • Subtract c from d: difference = d – c != c -d
  • Multiply g by h: product = g x h = h x g = gh
  • Divide x by y where y != 0: quotient = x/y

3. Exponential notation

  • Teach in the class on white board

4. Simplify algebraic expressions

  • Teach in the class on white board

5. Home Work:

  • Handout: two pages
  • Workbook:
    • page 15: 1, 2
    • page 16: 6, 7, 8, 9, 10

 

Math 6A, Lesson 10, Fall 2018, 11/18/2018

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1. Exam

2. No homework, no class next week. Happy Thanksgiving break.

 

Math 6A, Lesson 9, Fall 2018, 11/11/2018

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1. No quiz today, exam next week.

2. Real numbers and use of calculators:.

  • Rational number: can be expressed as a decimal by dividing the numerator of the rational number by its denominator
  • Terminating decimal: has a finite number of digits: ⅜, 5/16
  • Repeating decimal: 9/11, 7/11
  • Irrational number: non-terminating and non-repeating decimals
  • Use of calculators

3. Rounding numbers to decimal places

  • Mark the cut-off point after the desired place value
  • Rule of rounding up: the first digit after the cut-off point,  is >=5
  • Rule of rounding don: the first digit after the cut-off point, is  < 5
  • Nearest 10, 100, 1000, one million, …
  • Nearest tenth, hundredth, or thousandth, …
  • 1 decimal place, two decimal places, 3 decimal places, …

4. Home Work:

  • Handout: two pages
  • Workbook:
    • page 11: 24, 25, 26, 27, 28, 29
    • page 12-13: 30, 31, 32, 33, 34, 35, 36

 

Math 6A, Lesson 8, Fall 2018, 11/04/2018

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1. Quiz on negative number, addition and subtraction of integers

2. Multiplication, division and combined operations of integers:.

3. Rational numbers: rational numbers are numbers that can be expressed in the form of a/b, where a and b are integers, and b != 0

4. Addition, subtraction, multiplication and division of rational numbers

5. Home Work:

  • Handout: three pages
  • Workbook:
    • page 8: 6, 8, 9, 10, 11
    • page 10: 18, 19, 20, 21, 22, 23