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

1. Exam on chapter 3 “Introduction to Algebra”

2. Home Work: 

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

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

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

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

6. Extra: What is Super Moon? What are King tides? When does it happen?

1. Exam

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

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

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

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

• If two numbers have the same sign, their product/quotient is positive
• If two numbers have opposite signs, their product/quotient is negative
• Any integer multiplies 0, the product is 0: a x 0 = 0
• 0/a = 0, given a !=0
• a/0 is undefined
• How about 0/0? https://www.khanacademy.org/math/algebra/introduction-to-algebra/division-by-zero/v/undefined-and-indeterminate
• Combined operation: PEMDAS

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

1. Quiz on negative number and addition of integers

2. Subtraction of integers:.subtraction is the reverse process of addition. Using a number line:

• Subtraction of a positive number is taken as a movement to the LEFT of the number line
• Subtraction of a negative number is taken as a movement to the RIGHT of the number line

(-3)  – 4

2 –  3

(-1) –  (-3)

2 –  (-5)

0 – (-4)

3. Rule for subtraction: to subtract integers, we change the sign of the integer being subtracted and add them together according to the rule for addition of integers.

For any integers a, and,b,

a – b = a + (-b)

4. Absolute value of the difference:

For any integers a, and,b,

|a – b| = |b – a|

5. Home Work:

• Handout: two pages
• Workbook:
  • page 8: 7
  • page 9: 17
  • page 10: 20

1. Quiz about GCF and LCM

2. Opposite Numbers (additive inverse): is a number that when added to a given number yields 0. The opposite number for any number x is -x. Note that x may be positive or negative.

(-5) + 5 = 0

x + (-x) = 0

On the number line, the numbers 5 and -5 are located at the same distance from zero. We say that the numbers 5 and -5 are opposites. We can also say that -5 is opposite to 5, and 5 is opposite to -5 on the number line.

3. Addition of integers:

• Addition of a positive number is taken as a movement to the RIGHT of the number line
• Addition of a negative number is taken as a movement to the LEFT of the number line

(-3) + 4

2 + 3

(-1) + (-3)

2 + (-5)

0 + (-4)

4. Rule for addition:

• If the signs of the integers being added are the same, the sum has the same sign as the integers and we add the absolute values of the integers

For any a > 0, and b > 0,

a + b = a + b;        3 + 5 = 8

(-a) + (-b) = -(a+b);         (-3) + (-5) = – (3 + 5) = -8

• If the signs of the integers being added are different,, the sum takes the sign of the integer with the greater absolute value and we find the difference of the absolute values of the integers.

For any a > 0, and b > 0,

a + (-b) = +(a – b) if a >=b;        9 + (-6) = +(9 – 6) = +3 = 3

a + (-b) = – (b -a) if b > a;         15 + (-20) = -(20 -15) = -5

-a + b = -(a – b) if a >= b;         -18 + 12 = -(18 -12) = -6

-a + b = +(b -a) if b > a;          -23 + 27 = +(27 – 23) = +4 = 4

5. Home Work:

• Handout: one page
• Workbook: page 7: 4