1. What is PEMDAS?

PEMDAS is the order of operations used to evaluate expressions consistently:

P – Parentheses
E – Exponents (powers and roots)
M/D – Multiplication and Division (from left to right)
A/S – Addition and Subtraction (from left to right)

 Multiplication doesn’t always come before division; they are done in order from left to right. Same with addition and subtraction.

2. Step-by-Step Order

1. Parentheses (Grouping Symbols):

   • Simplify inside parentheses, brackets, or absolute values first.

   • Example: $$$\$\$$ → $$$28$.$$

2. Exponents (and roots):

   • Handle squares, cubes, square roots, etc.

   • Example: $$2^3+3^2 = 8 + 9 = 17.

3. Multiplication & Division:

   • Go left to right.

   • Example: $$$20\$\$$

   • NOT $$20÷(5×2)$$ ❌

4. Addition & Subtraction:

   • Go left to right.

   • Example: $$12–4+2=(12–4)+2=8+2=10$$

3. Common ACT Traps

• Left-to-right rule: Many students think “multiplication first, then division.” Wrong → they’re equal priority.

• Negative signs with exponents:

  • $$(-3)^2 = 9$$ but $$-3^2 = -9$$

• Absolute values: Treat them like parentheses.

  • Example: $$|-5+2| = | -3 | = 3.$$

• Fractions with expressions:
  Simplify numerator and denominator separately.

  • Example: $$\frac{6+2}{4-2} = \frac{8}{2} = 4$$

4. Example Problems

1. Evaluate: $$8+12÷4×2$$

   • Step 1: Division and multiplication left to right → $$12÷4=3$$ then $$3×2=6$$.

   • Step 2: Addition → 8+6=14.
     Final Answer: 14.

2. Evaluate: $$2+ (3^2 – 5)$$

   • Step 1: Parentheses: 3^2 = 9, then 9–5=4.

   • Step 2: Add: 2+4=6
     Final Answer: 6.

3. Evaluate: 2^4−24

   • Step 1: Exponent first: $16$.

   • Step 2: Apply negative: = –16.
     Final Answer: –16.

5. Quick Strategies for the ACT

• Underline operations to keep track of order.

• Plug choices back in if it’s an equation problem (Backsolving strategy).

• Estimate first when possible to eliminate wrong answers quickly.

• Watch parentheses and negatives, the ACT loves to test this trap.