Math Quiz: Order of Operations & LCM

Arithmetic Calculations

• For the expression (8 + 2 \times 5 - 3):
  • Apply the order of operations (PEMDAS/BODMAS).
  • First, multiply (2 \times 5) to get (10).
  • Then, add (8 + 10) to obtain (18).
  • Finally, subtract (3) to arrive at (15).

Lowest Common Denominator (LCD)

• The fractions (\frac{1}{4}) and (\frac{1}{6}) require finding the least common multiple (LCM) of their denominators (4 and 6).
• The LCM of (4) and (6) is (12), making it the lowest common denominator.
• This allows the fractions to be expressed with a numerator adjustment.

Exponential and Multiplicative Expression Evaluation

• Evaluating (2^3 + 4 \times (3 - 1)):
  • Calculate (2^3) to get (8).
  • Simplify the expression in parentheses: (3 - 1) equals (2).
  • Then, compute (4 \times 2) resulting in (8).
  • Finally, add (8 + 8) for a total of (16).

Addition of Fractions with Common Denominator

• To add (\frac{3}{8}) and (\frac{1}{2}), convert (\frac{1}{2}) to a fraction with a common denominator of (8).
• Rewriting (\frac{1}{2}) as (\frac{4}{8}) allows for easy addition.
• Thus, (\frac{3}{8} + \frac{4}{8} = \frac{7}{8}).

Expression with Parentheses and Division

• Evaluating (6 + (4 + 2) \div 2 - 3):
  • First calculate the expression in parentheses: (4 + 2 = 6).
  • Then divide (6 \div 2) to get (3).
  • Finally, compute (6 + 3 - 3) with a result of (6).