Understanding the Modulus Operator (%)
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Questions and Answers

Given the expression $15 \div 4 * 2 % 3 + 1$, what is the result after applying the order of operations, assuming modulus has the same precedence as multiplication and division and operations are performed left to right?

  • 1
  • 0
  • 2 (correct)
  • 3

Consider the expression $7 % 5 * 3 + 12 \div 4 - 1$. If the modulus operator (%) has the same precedence as multiplication and division, what is the final result of this expression when evaluated from left to right?

  • 7
  • 6 (correct)
  • 8
  • 5

What is the value of the expression 25 % 7 * 3 - 18 / 6 + 5 % 2 assuming the modulus operator has equal precedence with multiplication and division, and operations are performed from left to right?

  • 8 (correct)
  • 6
  • 7
  • 5

In the expression $8 + 12 % 5 * 2 - 6 \div 3$, what would be the outcome if the entire expression is evaluated, considering modulus operation has the same precedence as multiplication and division?

<p>10 (A)</p> Signup and view all the answers

Determine the outcome of the expression $20 \div 4 + 15 % 4 * 2 - 10$, assuming the modulus operator has the same precedence as multiplication and division.

<p>1 (A)</p> Signup and view all the answers

What is the result of the expression 75 % 7, and how does this relate to division?

<p>The result is 5, representing the remainder after division. (C)</p> Signup and view all the answers

Consider x = 12345. What will print(x % 1000) output, and why?

<p>345, because it isolates the last three digits. (A)</p> Signup and view all the answers

If number % 2 evaluates to 1, what can be definitively concluded about the variable number?

<p><code>number</code> is an odd number. (C)</p> Signup and view all the answers

Given that x = 7 and y = 2, what would x % y * x + y evaluate to, following order of operations?

<p>9 (B)</p> Signup and view all the answers

How can the modulus operator be effectively utilized to cycle through a fixed set of indices (e.g., for array access) without exceeding the array bounds?

<p>By using the index modulus the array length. (D)</p> Signup and view all the answers

In a scenario where you need to determine if a year is a leap year (divisible by 4, but not divisible by 100 unless also divisible by 400), which expression correctly determines if year is a leap year?

<p><code>year % 4 == 0 and (year % 100 != 0 or year % 400 == 0)</code> (D)</p> Signup and view all the answers

What would be the result of print((-15) % 4) in Python, and how does this behavior differ from some other programming languages?

<p><code>3</code>, because Python's modulus operator returns a non-negative result with the same sign as the divisor. (B)</p> Signup and view all the answers

You are given the task to distribute n identical candies among k children as fairly as possible. Using the modulus operator, how can you determine how many candies will be left over after the fairest possible distribution?

<p>By calculating <code>n % k</code> (B)</p> Signup and view all the answers

Flashcards

What is the Modulus?

The modulus operator (%) returns the remainder of a division.

10 % 2 = ?

10 % 2 = 0 (No remainder)

17 % 5 = ?

17 % 5 = 2 (Remainder of 2)

Order of Operations Acronym

The order is: Parentheses, Exponents, Multiplication/Modulus, Division, Addition, Subtraction.

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Modulus Priority

Modulus, multiplication, and division have equal priority and are executed from left to right.

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What is modulus?

The modulus operator (%) returns the remainder of a division.

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10 % 3 equals what?

The result of 10 divided by 3 is 3 with a remainder of 1.

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What is 29 % 5?

The result of 29 divided by 5 is 5 with a remainder of 4.

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How to check if a number is even or odd using modulus?

If a number % 2 equals 0, it's even; otherwise, it's odd.

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What is an even number % 2?

Even numbers have no remainder when divided by 2, so num % 2 == 0.

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What does a non-zero modulus mean?

It means it has a remainder when divided by 2.

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What does number % 100 do?

It returns the last two digits of a number.

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What are the last two digits in 245 % 100?

The last two digits are 45 because 245 divided by 100 leaves a remainder of 45.

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Study Notes

  • The modulus (%) returns the remainder of a division operation

Basic Usage

  • 10 % 3 equals 1 because 10 divided by 3 is 3 with a remainder of 1
  • The code fruits = 10 % 3 followed by print(fruits) will output 1
  • 29 % 5 equals 4 because 29 divided by 5 is 5 with a remainder of 4
  • The code fruits = 29 % 5 followed by print(fruits) will output 4

Determining Even or Odd Numbers

  • The modulus can determine if a number is even or odd
  • Even numbers are divisible by 2 with no remainder, so even_number % 2 equals 0
  • If number % 2 equals 0, the variable "number" is even
  • If number % 2 equals 1, the variable "number" is odd

Finding the Last Two Numbers

  • The modulus can extract the last two digits of a number
  • number % 100 returns the remainder when "number" is divided by 100
  • If number = 245, then number % 100 equals 45, which are the last two digits of 245

Practice Problems

  • 10 % 2 = 0
  • 17 % 5 = 2
  • 4 % 4 = 0
  • 125 % 10 = 5
  • 30 % 3 = 0
  • 19 % 4 = 3
  • 156 % 100 = 56

Order of Operations

  • The order of operations is Parentheses, Exponents, Multiplication/Modulus, Division, Addition, Subtraction
  • Modulus operations have the same priority as multiplication and division
  • In a program, modulus, division, and multiplication operations are performed from left to right based on their order of appearance

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Description

Learn how to use the modulus operator (%) in programming to find remainders. Explore applications such as determining even or odd numbers and extracting the last digits of a number. Includes examples and practice problems.

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