PEMDAS Order

BODMAS Order (Alternative)

• Always solve parentheses FIRST

• Multiplication and Division have equal priority - work from LEFT to RIGHT

• Addition and Subtraction have equal priority - work from LEFT to RIGHT

• The order stays the same for decimals as it does for whole numbers

Step 1: Look for PARENTHESES ( ) and solve what's inside first

Step 2: Solve any EXPONENTS (powers)

Step 3: Do all MULTIPLICATION and DIVISION from left to right

Step 4: Do all ADDITION and SUBTRACTION from left to right

Step 5: Write your final answer

Example 1: 5.2 + 3.6 × 2.5

Example 2: (8.5 - 3.2) × 2.0 + 4.6

Example 3: 18.0 ÷ 3.6 - 1.5 × 0.4

Example 4: 12.5 - 4.2 ÷ 6.0 + 1.3 × 0.4

✗ DON'T work from left to right for all operations

✗ DON'T forget parentheses come first

✗ DON'T do addition before multiplication

✓ DO follow PEMDAS/BODMAS order strictly

Step 1: Read the problem carefully (maybe twice!)

Step 2: Identify what you need to find (the question)

Step 3: Find the important numbers and information

Step 4: Determine which operation(s) to use

Step 5: Set up the equation

Step 6: Solve using the correct order of operations

Step 7: Check if your answer makes sense

Step 8: Write your answer with the correct unit

Example 1 (Addition & Multiplication):

"Sarah bought 3 notebooks for $2.45 each and a pen for $1.75. How much did she spend in total?"

Example 2 (Subtraction & Division):

"A 6.5-meter rope is cut into 5 equal pieces. If 0.8 meters is wasted, how long is each piece?"

Example 3 (Mixed Operations):

"A store sells juice boxes for $0.75 each. Tom bought 8 boxes and paid with a $10 bill. How much change did he receive?"

1. Break it down: Identify each step needed to solve

2. Order matters: Determine which calculation to do first, second, third, etc.

3. Write intermediate steps: Write down each step's answer before moving to the next

4. Use parentheses: Group operations that should be done together

5. Check your work: Make sure the final answer makes sense

Step 1: Read the entire problem carefully

Step 2: Underline or highlight important information

Step 3: Identify what the question is asking

Step 4: List all the steps needed in order

Step 5: Solve one step at a time

Step 6: Use each answer in the next step

Step 7: Write the final answer with units

Example 1:

"Maria went to the grocery store with $50.00. She bought 4 apples for $1.25 each, 2 loaves of bread for $3.50 each, and a gallon of milk for $4.75. How much money does she have left?"

Example 2:

"A rectangular garden is 12.5 meters long and 8.4 meters wide. If fencing costs $6.50 per meter, how much will it cost to fence the entire garden?"

Example 3:

"A pizza parlor charges $12.75 for a large pizza plus $1.50 for each topping. If 3 friends split the cost of a pizza with 4 toppings equally, how much does each person pay?"

TRUE: Both sides equal the same value

FALSE: The sides equal different values

Step 1: Look at the equation (it has an = sign)

Step 2: Evaluate the LEFT side using order of operations

Step 3: Evaluate the RIGHT side using order of operations

Step 4: Compare the two answers

Step 5: If they're equal → TRUE; if different → FALSE

Always use PEMDAS/BODMAS to evaluate each side! The order of operations must be followed on BOTH sides of the equation.

Example 1: Is this equation TRUE or FALSE?

3.5 + 2.0 × 4.0 = 11.5

Example 2: Is this equation TRUE or FALSE?

(10.0 - 4.5) × 2.0 = 10.0

Example 3: Is this equation TRUE or FALSE?

15.6 ÷ 2.0 + 3.2 = 7.8 × 1.5 - 3.9

Example 4: Is this equation TRUE or FALSE?

20.0 - 5.0 × 2.0 = (20.0 - 5.0) × 2.0

Order of Operations (PEMDAS)

✓ Always follow the order of operations (PEMDAS/BODMAS)

✓ Parentheses are your best friend - they tell you what to do first

✓ Multiplication and Division are equal - do whichever comes first from left to right

✓ Addition and Subtraction are equal - do whichever comes first from left to right

✓ In word problems, underline important numbers and circle key words

✓ For multi-step problems, solve one step at a time and write it down

✓ For true/false equations, solve both sides separately before comparing

✓ Check your answer - does it make sense for the problem?

✓ Always include units in your final answer (dollars, meters, etc.)

Step 1: Master Each Operation Separately
Make sure you're comfortable with adding, subtracting, multiplying, and dividing decimals before mixing them.

Step 2: Practice Order of Operations
Start with simple problems with 2-3 operations, then work up to more complex ones.

Step 3: Work on Word Problems
Read carefully, identify what you're looking for, and decide which operations to use.

Step 4: Try Multi-Step Problems
Break complex problems into smaller steps and solve one at a time.

Step 5: Check Your Work
Always ask yourself: "Does my answer make sense?"