Modular Arithmetic Basics in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the remainder of 10 divided by 3.

DSA Javascript

const result = 10 [1] 3;
console.log(result);

Drag options to blanks, or click blank then click option'

A+

B/

C*

D%

Attempts:

3 left

💡 Hint

Common Mistakes

Using division operator instead of modulus

Using multiplication or addition by mistake

The % operator gives the remainder of division, so 10 % 3 equals 1.

2fill in blank

medium

Complete the code to check if a number is even using modular arithmetic.

DSA Javascript

const isEven = (num) => num [1] 2 === 0;
console.log(isEven(4));

Drag options to blanks, or click blank then click option'

A%

B/

C*

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using division operator instead of modulus

Using multiplication or subtraction

The modulus operator % returns the remainder. If num % 2 === 0, the number is even.

3fill in blank

hard

Fix the error in the code to correctly compute (a + b) modulo m.

DSA Javascript

function modAdd(a, b, m) {
  return (a + b) [1] m;
}
console.log(modAdd(7, 5, 6));

Drag options to blanks, or click blank then click option'

A/

B*

C%

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using division instead of modulus

Using multiplication or subtraction

The modulus operator % is needed to get the remainder after addition.

4fill in blank

hard

Fill both blanks to create a function that returns (a * b) modulo m.

DSA Javascript

function modMultiply(a, b, m) {
  return (a [1] b) [2] m;
}
console.log(modMultiply(4, 5, 3));

Drag options to blanks, or click blank then click option'

A*

B%

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping operators

Using addition or subtraction instead of multiplication

Multiplication is done first, then modulus to get the remainder.

5fill in blank

hard

Fill all three blanks to create a function that returns (a - b) modulo m, ensuring the result is non-negative.

DSA Javascript

function modSubtract(a, b, m) {
  return ((a [1] b) [2] m) [3] m;
}
console.log(modSubtract(2, 5, 7));

Drag options to blanks, or click blank then click option'

A-

B+

C%

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Not adding modulus before applying modulus

Using multiplication instead of addition

Subtract first, add modulus to avoid negative, then apply modulus again.

Practice

1. What is the result of 7 % 3 in modular arithmetic?

easy

A. 2

B. 3

C. 1

D. 0

Solution

1. Step 1: Understand the modulus operation

   The modulus operator (%) gives the remainder after division of the first number by the second.

2. Step 2: Calculate 7 divided by 3

   7 divided by 3 is 2 with a remainder of 1.

3. Final Answer:

   1 -> Option C

4. Quick Check:

   7 % 3 = 1 [OK]

Hint: Modulus gives remainder after division [OK]

Common Mistakes:

• Confusing modulus with division
• Using 3 instead of remainder
• Thinking modulus returns quotient

2. Which of the following is the correct syntax to compute the remainder of a divided by b in JavaScript?

easy

A. a % b

B. a mod b

C. mod(a, b)

D. a // b

Solution

1. Step 1: Recall JavaScript modulus syntax

   In JavaScript, the modulus operator is the percent sign (%) placed between two numbers or variables.

2. Step 2: Identify correct syntax

   Only a % b correctly computes the remainder of a divided by b.

3. Final Answer:

   a % b -> Option A

4. Quick Check:

   Use % for modulus in JavaScript [OK]

Hint: Use % operator for modulus in JavaScript [OK]

Common Mistakes:

• Using 'mod' keyword
• Using integer division operator //
• Calling a non-existent mod() function

3. What is the output of the following JavaScript code?

const x = 15;
const y = 4;
console.log(x % y);

medium

A. 4

B. 3

C. 0

D. 1

Solution

1. Step 1: Calculate 15 divided by 4

   15 divided by 4 is 3 with a remainder of 3.

2. Step 2: Apply modulus operator

   The expression 15 % 4 returns the remainder, which is 3.

3. Final Answer:

   3 -> Option B

4. Quick Check:

   15 % 4 = 3 [OK]

Hint: Modulus returns remainder after division [OK]

Common Mistakes:

• Confusing remainder with quotient
• Expecting 4 instead of remainder
• Mistaking modulus for division

4. Find the error in the following code snippet that tries to compute the modulus of two numbers:

let a = 10;
let b = 3;
let result = a % b();
console.log(result);

medium

A. Missing semicolon after console.log

B. Modulus operator should be replaced with division

C. Variables a and b should be strings

D. Using parentheses after b causes an error

Solution

1. Step 1: Analyze the modulus expression

   The code uses a % b(), which treats b as a function call, but b is a number, not a function.

2. Step 2: Identify the error

   Parentheses after b cause a runtime error because numbers cannot be called like functions.

3. Final Answer:

   Using parentheses after b causes an error -> Option D

4. Quick Check:

   Variables are not functions, so no () after b [OK]

Hint: Don't add () after variables unless they are functions [OK]

Common Mistakes:

• Adding () after number variables
• Confusing modulus with division
• Ignoring runtime errors

5. You want to find the remainder when the sum of two numbers a = 123456789 and b = 987654321 is divided by 1000. Which expression correctly computes this using modular arithmetic properties?

hard

A. ((a % 1000) + (b % 1000)) % 1000

B. (a % 1000) + (b % 1000)

C. a + b % 1000

D. a % (b % 1000)

Solution

1. Step 1: Recall modular addition property

   The remainder of a sum modulo m equals the sum of remainders modulo m: (a + b) % m = ((a % m) + (b % m)) % m.

2. Step 2: Apply property to given numbers

   Compute (a % 1000) and (b % 1000), add them, then take modulo 1000 again to get correct remainder.

3. Final Answer:

   ((a % 1000) + (b % 1000)) % 1000 -> Option A

4. Quick Check:

   Use modular addition: ((a%m)+(b%m))%m [OK]

Hint: Add remainders then mod again for sum modulus [OK]

Common Mistakes:

• Skipping final modulus after addition
• Adding without modulus
• Using wrong modulus order