Operator precedence in Rust - Step-by-Step Execution

Concept Flow - Operator precedence

Start Expression

↓

Identify Operators

↓

Check Precedence

↓

Evaluate Higher Precedence

↓

Replace Result

↓

Evaluate Next Operator

↓

Final Result

The program reads an expression, identifies operators, evaluates them in order of precedence from highest to lowest, and combines results step-by-step until the final value is computed.

Execution Sample

Rust

let result = 2 + 3 * 4 - 5 / 5;
println!("{}", result);

Calculates the expression 2 + 3 * 4 - 5 / 5 following Rust's operator precedence rules.

Execution Table

Step	Expression	Operation	Precedence	Result	Explanation
1	2 + 3 * 4 - 5 / 5	3 * 4	Multiplication (High)	12	Multiply 3 and 4 first
2	2 + 12 - 5 / 5	5 / 5	Division (High)	1	Divide 5 by 5 next
3	2 + 12 - 1	2 + 12	Addition (Lower)	14	Add 2 and 12
4	14 - 1	14 - 1	Subtraction (Lower)	13	Subtract 1 from 14
5	13	None	None	13	Final result after all operations

💡 All operators evaluated in precedence order; final result is 13

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
result	undefined	2 + 12 - 5 / 5	2 + 12 - 1	14 - 1	13	13

Key Moments - 3 Insights

Why is multiplication done before addition in the expression?

Because multiplication has higher precedence than addition, as shown in execution_table steps 1 and 3 where multiplication is evaluated first.

Why does division happen before subtraction?

Division has higher precedence than subtraction, so it is evaluated earlier as seen in execution_table step 2 before subtraction in step 4.

What happens if we ignore operator precedence and evaluate left to right?

The result would be different and incorrect; operator precedence ensures correct order, as shown by the stepwise evaluation in the execution_table.

Visual Quiz - 3 Questions

Look at the execution_table, what is the result after step 2?

A 2 + 12 - 1

B 2 + 3 * 4 - 1

C 14 - 1

D 13

💡 Hint

Check the 'Expression' column in execution_table row for step 2

At which step is the addition operation evaluated?

A Step 1

B Step 3

C Step 4

D Step 2

💡 Hint

Look at the 'Operation' column in execution_table to find when '2 + 12' is calculated

If the division operator had lower precedence than subtraction, which step would change?

A Step 4

B Step 3

C Step 2

D Step 1

💡 Hint

Consider when division is evaluated in execution_table and how precedence affects order

Concept Snapshot

Operator precedence determines the order in which parts of an expression are calculated.
Higher precedence operators like * and / are done before + and -.
Rust follows standard math precedence rules.
Evaluate operators from highest to lowest precedence step-by-step.
Parentheses can override precedence to group operations.

Full Transcript

This example shows how Rust evaluates the expression 2 + 3 * 4 - 5 / 5 by following operator precedence rules. Multiplication and division have higher precedence than addition and subtraction, so 3 * 4 and 5 / 5 are calculated first, resulting in 12 and 1 respectively. Then addition and subtraction are performed left to right: 2 + 12 equals 14, and 14 - 1 equals 13. The final result printed is 13. This stepwise evaluation ensures correct calculation order and result.

Practice

1. In Rust, which operator has the highest precedence among these: +, *, -, /?

easy

A. Multiplication (*) and division (/) have higher precedence than addition (+) and subtraction (-).

B. Addition (+) and subtraction (-) have higher precedence than multiplication (*) and division (/).

C. All operators have the same precedence and are evaluated left to right.

D. Subtraction (-) has the highest precedence among all.

Solution

1. Step 1: Recall Rust operator precedence rules

   Multiplication (*) and division (/) operators have higher precedence than addition (+) and subtraction (-).

2. Step 2: Compare given operators

   Among the given operators, * and / are evaluated before + and - in expressions.

3. Final Answer:

   Multiplication (*) and division (/) have higher precedence than addition (+) and subtraction (-). -> Option A

4. Quick Check:

   *, / > +, - [OK]

Hint: Remember: multiply/divide before add/subtract [OK]

Common Mistakes:

• Thinking addition has higher precedence than multiplication
• Assuming all operators have equal precedence
• Confusing subtraction precedence with multiplication

2. Which of the following Rust expressions is correctly written to add 2 and 3, then multiply the result by 4?

easy

A. 2 + 3 * 4

B. (2 + 3) * 4

C. 2 + (3 * 4)

D. 2 * 3 + 4

Solution

1. Step 1: Understand operator precedence and parentheses

   Multiplication (*) has higher precedence than addition (+), so without parentheses, multiplication happens first.

2. Step 2: Check each expression

   (2 + 3) * 4 uses parentheses to add 2 and 3 first, then multiplies by 4, which matches the requirement.

3. Final Answer:

   (2 + 3) * 4 -> Option B

4. Quick Check:

   Parentheses force addition first [OK]

Hint: Use parentheses to change default order [OK]

Common Mistakes:

• Ignoring parentheses and relying on default precedence
• Misplacing parentheses causing wrong order
• Assuming left-to-right always applies

3. What is the output of this Rust code?

let result = 10 - 4 / 2 + 3 * 2;
println!("{}", result);

medium

A. 13

B. 10

C. 11

D. 14

Solution

1. Step 1: Apply operator precedence to expression

   Division and multiplication happen before addition and subtraction:
   4 / 2 = 2
   3 * 2 = 6

2. Step 2: Calculate left to right with results

   Expression becomes: 10 - 2 + 6
   10 - 2 = 8
   8 + 6 = 14

3. Final Answer:

   14 -> Option D

4. Quick Check:

   */ before +- gives 14 [OK]

Hint: Calculate * and / first, then + and - left to right [OK]

Common Mistakes:

• Doing operations strictly left to right ignoring precedence
• Adding before multiplying
• Miscomputing division or multiplication

4. Identify the error in this Rust expression:

let value = 5 + 3 * / 2;

medium

A. No error, expression is valid

B. Logical error: multiplication should be addition

C. Syntax error due to misplaced operator '/'

D. Runtime error due to division by zero

Solution

1. Step 1: Analyze the expression syntax

   The expression has * / operators together without a number between them, which is invalid syntax in Rust.

2. Step 2: Confirm error type

   This causes a syntax error because Rust expects an operand between operators.

3. Final Answer:

   Syntax error due to misplaced operator '/' -> Option C

4. Quick Check:

   Operators must have operands between them [OK]

Hint: Check for missing operands between operators [OK]

Common Mistakes:

• Assuming expression is valid without checking syntax
• Confusing syntax error with runtime error
• Ignoring operator placement rules

5. Given the Rust expression:

let x = 2 + 3 * 4 - 6 / 3 + (8 - 5) * 2;

What is the correct value of x after evaluation?

hard

A. 18

B. 20

C. 19

D. 21

Solution

1. Step 1: Evaluate parentheses and high precedence operators

   Calculate inside parentheses:
   (8 - 5) = 3
   Then multiplication and division:
   3 * 4 = 12
   6 / 3 = 2
   3 * 2 = 6 (from parentheses result * 2)

2. Step 2: Substitute and calculate addition and subtraction left to right

   Expression becomes: 2 + 12 - 2 + 6
   2 + 12 = 14
   14 - 2 = 12
   12 + 6 = 18

3. Final Answer:

   18 -> Option A

4. Quick Check:

   Parentheses and */ first, then +- left to right [OK]

Hint: Calculate parentheses first, then * and /, then + and - left to right [OK]

Common Mistakes:

• Ignoring parentheses and calculating in wrong order
• Doing addition before multiplication
• Mixing up left-to-right evaluation for + and -