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

1. Exam

2. No homework, enjoy a 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