Basic PEMDAS Example

Solve: $3 + 4 \times 2$

Look for Parentheses: No parentheses = Move to next step

Look for Exponents: No exponents = Move to next step

Do Multiplication first: $4 \times 2 = 8$ = $3 + 8$

Do Addition: $3 + 8$ = $11$

Answer: $3 + 4 \times 2 = 11$

Parentheses First

Solve: $(3 + 4) \times 2$

Solve inside Parentheses first: $3 + 4 = 7$ = $7 \times 2$

Do Multiplication: $7 \times 2$ = $14$

Answer: $(3 + 4) \times 2 = 14$

With Exponents

Solve: $2 + 3^2 \times 4$

No Parentheses - check Exponents: $3^2 = 9$ = $2 + 9 \times 4$

Do Multiplication: $9 \times 4 = 36$ = $2 + 36$

Do Addition: $2 + 36$ = $38$

Answer: $2 + 3^2 \times 4 = 38$

Multiple Operations

Solve: $20 - 4 \times 3 + 8 \div 2$

No Parentheses or Exponents - do Multiplication: $4 \times 3 = 12$ = $20 - 12 + 8 \div 2$

Do Division (left to right with multiplication): $8 \div 2 = 4$ = $20 - 12 + 4$

Do Subtraction (left to right): $20 - 12 = 8$ = $8 + 4$

Do Addition: $8 + 4$ = $12$

Answer: $20 - 4 \times 3 + 8 \div 2 = 12$

Nested Parentheses

Solve: $2 \times (3 + (4 - 1))$

Start with innermost parentheses: $4 - 1 = 3$ = $2 \times (3 + 3)$

Solve remaining parentheses: $3 + 3 = 6$ = $2 \times 6$

Do Multiplication: $2 \times 6$ = $12$

Answer: $2 \times (3 + (4 - 1)) = 12$

Mistake: Adding before multiplying

Why: Students often work left to right, doing $3 + 4 = 7$ before the multiplication in $3 + 4 \times 2$

Correct: Always do multiplication and division before addition and subtraction. The answer is $3 + 8 = 11$, not $7 \times 2 = 14$

Mistake: Thinking M comes before D

Why: PEMDAS lists M before D, making students think multiplication always comes first

Correct: Multiplication and Division have EQUAL priority. Work left to right. In $8 \div 2 \times 4$, do $8 \div 2 = 4$ first, then $4 \times 4 = 16$

Mistake: Forgetting to work inside parentheses completely

Why: Students may only do part of what is inside parentheses

Correct: Solve EVERYTHING inside parentheses before moving on. In $(3 + 2 \times 4)$, you must do $2 \times 4 = 8$ first, then $3 + 8 = 11$

Mistake: Ignoring exponents

Why: Students sometimes treat exponents like regular multiplication

Correct: Exponents come before multiplication. In $2 \times 3^2$, first calculate $3^2 = 9$, then $2 \times 9 = 18$

Shopping Discounts

When shopping, you often need to calculate final prices after discounts and additional costs. The order in which you apply these calculations matters!

A 50 dollar shirt is 20% off, then you add 5 dollar shipping. Calculate: $50 \times 0.8 + 5 = 40 + 5 = 45$ dollars

Cooking & Recipes

When scaling recipes or combining ingredients, the order of operations ensures you get the right amounts.

A recipe needs $(2 + 1) \times 3 = 3 \times 3 = 9$ cups total (2 cups flour + 1 cup sugar, tripled)

Video Game Scoring

Video games use mathematical formulas to calculate damage, scores, and rewards. Understanding order of operations helps you predict outcomes.

Damage = base × multiplier + bonus: $10 \times 2 + 5 = 25$ damage

Q: What does PEMDAS stand for?

A: PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Its the order in which you should perform operations in a math expression.

Q: Why does multiplication come before addition?

A: This is a convention mathematicians agreed upon to ensure everyone gets the same answer. Without this rule, 3 + 4 × 2 could equal either 11 or 14 depending on the order.

Q: What is the difference between PEMDAS and BODMAS?

A: They are the same thing! BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is used in UK/Australia, while PEMDAS is used in USA. Both give the same results.

Q: Do I always multiply before dividing?

A: No! Multiplication and division have equal priority. You work from left to right. In 12 ÷ 3 × 2, first divide (12 ÷ 3 = 4), then multiply (4 × 2 = 8).

Q: What if there are no parentheses?

A: If there are no parentheses, skip that step and move to exponents. If no exponents, move to multiplication/division, and so on.

Q: How do I handle nested parentheses?

A: Start with the innermost parentheses and work your way out. For example, in 2 × (3 + (4 - 1)), first solve (4 - 1) = 3, then (3 + 3) = 6, then 2 × 6 = 12.