Operator precedence and evaluation order in Python - Step-by-Step Execution

Concept Flow - Operator precedence and evaluation order

Start Expression

↓

Identify Operators

↓

Check Precedence

↓

Evaluate Highest Precedence Operator

↓

Replace Result in Expression

↓

More Operators?

Yes→Repeat Check Precedence

No↓

Final Result

The program looks at the expression, finds the operator with the highest priority, evaluates it first, replaces it with the result, and repeats until done.

Execution Sample

Python

result = 3 + 4 * 2
print(result)

Calculates 3 plus 4 times 2, showing how multiplication happens before addition.

Execution Table

Step	Expression	Operator Evaluated	Operation	Intermediate Result
1	3 + 4 * 2	*	4 * 2	8
2	3 + 8	+	3 + 8	11
3	11	None	None	11

💡 No more operators left, final result is 11

Variable Tracker

Variable	Start	After Step 1	After Step 2	Final
result	undefined	undefined	11	11

Key Moments - 3 Insights

Why does multiplication happen before addition in the expression?

Because multiplication has higher precedence than addition, as shown in step 1 of the execution_table where 4 * 2 is evaluated first.

What if we want addition to happen first?

We can use parentheses to change order, like (3 + 4) * 2, which forces addition before multiplication.

Does evaluation always go left to right?

No, operators with higher precedence are evaluated first regardless of position, but operators with the same precedence are evaluated left to right.

Visual Quiz - 3 Questions

Look at the execution_table, what is the intermediate result after evaluating the first operator?

A 11

B 8

C 6

D None

💡 Hint

Check the 'Intermediate Result' column in step 1 of the execution_table.

At which step does the addition operator get evaluated?

A Step 1

B Step 3

C Step 2

D Never

💡 Hint

Look at the 'Operator Evaluated' column in the execution_table.

If the expression was changed to (3 + 4) * 2, what would be the first operator evaluated?

A Addition (+)

B Multiplication (*)

C None

D Both at the same time

💡 Hint

Parentheses change evaluation order; check key_moments about parentheses.

Concept Snapshot

Operator precedence decides which part of an expression runs first.
Multiplication and division have higher precedence than addition and subtraction.
Use parentheses () to change the order.
Operators with the same precedence run left to right.
Python evaluates expressions step-by-step following these rules.

Full Transcript

This lesson shows how Python decides which part of a math expression to calculate first. It looks at the operators and their priority. For example, multiplication happens before addition. We traced the expression 3 + 4 * 2. First, 4 times 2 equals 8. Then 3 plus 8 equals 11. We also learned that parentheses can change this order. Operators with the same priority are done left to right. This helps us understand how Python calculates results step by step.

Practice

1. Which operator has the highest precedence in the expression 3 + 4 * 2?

easy

A. Multiplication (*)

B. Addition (+)

C. Subtraction (-)

D. Division (/)

Solution

1. Step 1: Recall operator precedence rules

   Multiplication (*) has higher precedence than addition (+), subtraction (-), and division (/).

2. Step 2: Identify highest precedence operator in expression

   In 3 + 4 * 2, multiplication (*) runs before addition (+).

3. Final Answer:

   Multiplication (*) -> Option A

4. Quick Check:

   Highest precedence = Multiplication (*) [OK]

Hint: Multiplication and division run before addition and subtraction [OK]

Common Mistakes:

• Thinking addition runs before multiplication
• Ignoring operator precedence
• Assuming left to right always applies

2. Which of the following expressions is syntactically correct in Python?

easy

A. 5 + * 3

B. 4 + (3 * 2)

C. 7 / / 2

D. 8 - -

Solution

1. Step 1: Check each expression for syntax errors

   5 + * 3 has two operators in a row without operand: invalid.
   4 + (3 * 2) uses parentheses correctly and valid operators.
   7 / / 2 has double division operator which is invalid.
   8 - - ends with operator without operand: invalid.

2. Step 2: Confirm correct syntax

   Only 4 + (3 * 2) is syntactically correct: 4 + (3 * 2).

3. Final Answer:

   4 + (3 * 2) -> Option B

4. Quick Check:

   Valid syntax = 4 + (3 * 2) [OK]

Hint: Check for missing operands or extra operators [OK]

Common Mistakes:

• Using two operators in a row
• Missing parentheses around expressions
• Ending expression with an operator

3. What is the output of the following code?

result = 10 - 3 * 2 + 4 // 2
print(result)

medium

A. 5

B. 8

C. 6

D. 4

Solution

1. Step 1: Apply operator precedence and evaluate multiplication and floor division first

   3 * 2 = 6
   4 // 2 = 2

2. Step 2: Evaluate the expression left to right with addition and subtraction

   10 - 6 + 2 = 4 + 2 = 6

3. Final Answer:

   6 -> Option C

4. Quick Check:

   10 - 6 + 2 = 6 [OK]

Hint: Multiply and divide before add and subtract [OK]

Common Mistakes:

• Adding before multiplying
• Using normal division instead of floor division
• Ignoring left to right evaluation for same precedence

4. Find the error in this expression:

value = 5 + (3 * 2

medium

A. No error, expression is correct

B. Wrong operator used

C. Extra operator before 2

D. Missing closing parenthesis

Solution

1. Step 1: Check parentheses balance

   Expression has an opening parenthesis '(' but no matching closing parenthesis ')'.

2. Step 2: Identify syntax error

   Missing closing parenthesis causes syntax error in Python.

3. Final Answer:

   Missing closing parenthesis -> Option D

4. Quick Check:

   Parentheses must be balanced [OK]

Hint: Count opening and closing parentheses carefully [OK]

Common Mistakes:

• Ignoring missing parentheses
• Assuming expression is valid without closing parenthesis
• Confusing operator errors with syntax errors

5. Given the expression result = (2 + 3) * (4 - 1) ** 2 // 5, what is the value of result?

hard

A. 9

B. 15

C. 5

D. 25

Solution

1. Step 1: Evaluate parentheses and exponentiation first

   (2 + 3) = 5
   (4 - 1) = 3
   3 ** 2 = 9

2. Step 2: Multiply and then floor divide

   5 * 9 = 45
   45 // 5 = 9

3. Final Answer:

   9 -> Option A

4. Quick Check:

   Parentheses and exponent first, then multiply, then floor divide [OK]

Hint: Do parentheses and powers before multiply/divide [OK]

Common Mistakes:

• Ignoring exponentiation precedence
• Dividing before multiplying
• Not applying floor division correctly