Basic Math Skills Lecture Notes

Topics Covered:

• Addition and Subtraction (including with negative numbers)
• Multiplication (mental math and multiplication tables)
• Division
• Fractions (conversion to decimals, adding, subtracting, multiplying, dividing, and converting to mixed numbers)
• Percentages (mental calculations and simplification of fractions)
• Exponents and exponential fractions
• Order of operations
• Square roots, simplification of radicals, cube roots
• Scientific notation (conversion, multiplying, dividing, square roots)
• Solving equations (linear, involving decimals, fractions, radicals, and cube roots)
• Factoring and quadratic equation
• Graphing linear and quadratic equations
• General parent functions and transformations

Addition and Subtraction

Number Line Method:

• For addition, move right on the number line.
• For subtraction, move left on the number line.

Examples:

• 5 + 4 = 9
• 7 - 3 = 4
• 5 - 8 = -3
• -4 + 5 = 1
• -8 + 3 = -5
• -9 - 4 = -13
• -10 - (-4) = -10 + 4 = -6
• 8 - (-3) = 8 + 3 = 11

Techniques Involving Negative Numbers:

• Change double negatives to a positive: -10 - (-4) = -10 + 4 = -6
• Examples: 8 - (-3) = 8 + 3 = 11

Quiz:

Addition Examples:

• 8 + 7 = 15
• 5 + 9 = 14
• 6 + 7 = 13
• 5 + 12 = 17

Subtraction Examples:

• 9 - 4 = 5
• 12 - 5 = 7
• 14 - 6 = 8
• 22 - 13 = 9

Advanced Subtraction with Larger Negatives:

• Examples: 7 - 9 = -2, 4 - 12 = -8, 5 - 16 = -11, 8 - 19 = -11

Multiplication

Multiplication Table Construction:

• Memorize up to 12x12 for easy calculation
• Patterns identified in columns and rows

Quick Multiplication Techniques:

• Use breaking down larger multipliers into smaller parts (e.g., 15 x 8 -> 10 + 5 x 8)
• Examples: 50 x 100 = 5000
• Multiples of 10: 10 x 100 = 1000, 100 x 100 = 10,000

Multiplication Quiz Examples:

• 8 x 7 = 56
• 9 x 9 = 81
• 7 x 6 = 42
• 10 x 5 = 50
• 12 x 12 = 144
• 8 x 6 = 48
• 4 x 9 = 36
• 3 x 12 = 36

Advanced Multiplication:

• With larger numbers: Break into simpler calculations and add results
  • Example: 20 x 14 -> 20 x 10 + 20 x 4 = 280

Division

Basic Division Techniques:

• Understanding division as reverse multiplication
• Example: 56 ÷ 7 = 8 (because 7 x 8 = 56)

Advanced Division Techniques:

• Long division
• Simplifying with factors
• Examples: 400 ÷ 5 = 80, 3500 ÷ 7 = 500

Fractions

Conversion to Decimals:

• Use long division
• Common fractions and their decimal equivalents should be memorized
  • 1/2 = 0.5
  • 2/3 = 0.67
  • 3/4 = 0.75
  • Example: 1/4 = 0.25

Mixed Numbers:

• Breaking down fractions into parts to simplify calculations
  • Example: 39/6 = 36/6 + 3/6 = 6.5

Fractions Quiz Examples:

• Convert 9/2, 7/3, 5/4, 8/5 to decimals
  • 9/2 = 4.5
  • 7/3 ≈ 2.33
  • 5/4 = 1.25
  • 8/5 = 1.6

Converting Fractions to Percentages:

• Multiply decimal forms by 100
• Example: 4.5 = 450%

Practice Problems

Addition and Subtraction Practice:

• 8 + 7
• 5 + 9
• 6 + 7
• 5 + 12
• 9 - 4
• 12 - 5
• 14 - 6
• 22 - 13

Multiplication Practice:

• 8 x 7
• 9 x 9
• 7 x 6
• 10 x 5
• 12 x 12
• 8 x 6
• 4 x 9
• 3 x 12

Division Practice:

• 56 ÷ 7
• 24 ÷ 6
• 42 ÷ 6
• 20 ÷ 4
• 36 ÷ 6
• 72 ÷ 8
• 144 ÷ 12

Fraction Practice:

• 9/2 -> 4.5
• 7/3 -> 2.33
• 5/4 -> 1.25
• 8/5 -> 1.6

Conversion Practice:

• 54 ÷ 10 -> 5.4
• 23 ÷ 100 -> 0.23
• 8 ÷ 10 -> 0.8
• 4.6 ÷ 10 -> 0.46