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3.2 — Arithmetic operators

Unary arithmetic operators

There are two unary arithmetic operators, plus (+), and minus (-). If you remember, unary operators are operators that only take one operand.

Operator Symbol Form Operation
Unary plus + +x Value of x
Unary minus - -x Negation of x

The unary plus operator returns the value of the operand. In other words, +5 = 5, and +x = x. Generally you won’t need to use this operator since it’s redundant. It was added largely to provide symmetry with the unary minus operator.

The unary minus operator returns the operand multiplied by -1. In other words, if x = 5, -x = -5.

For best effect, both of these operators should be placed immediately preceding the operand (eg. -x, not - x).

Do not confuse the unary minus operator with the binary subtraction operator, which uses the same symbol. For example, in the expression x = 5 - -3;, the first minus is the subtraction operator, and the second is the unary minus operator.

Binary arithmetic operators

There are 5 binary arithmetic operators. Binary operators are operators that take a left and right operand.

Operator Symbol Form Operation
Addition + x + y x plus y
Subtraction - x - y x minus y
Multiplication * x * y x multiplied by y
Division / x / y x divided by y
Modulus (Remainder) % x % y The remainder of x divided by y

The addition, subtraction, and multiplication operators work just like they do in real life, with no caveats.

Division and modulus (remainder) need some additional explanation.

Integer and floating point division

It is easiest to think of the division operator as having two different “modes”. If both of the operands are integers, the division operator performs integer division. Integer division drops any fractions and returns an integer value. For example, 7 / 4 = 1 because the fraction is dropped. Note that integer division does not round.

If either or both of the operands are floating point values, the division operator performs floating point division. Floating point division returns a floating point value, and the fraction is kept. For example, 7.0 / 3 = 2.333, 7 / 3.0 = 2.333, and 7.0 / 3.0 = 2.333.

Note that trying to divide by 0 (or 0.0) will generally cause your program to crash, as the results are undefined!

Using static_cast<> to do floating point division with integers

In section 2.7 -- Chars, we showed how we could use the static_cast<> operator to cast a char to an integer so it would print correctly.

We can similarly use static_cast<> to convert an integer to a floating point number so that we can do floating point division instead of integer division. Consider the following code:

This produces the result:

int / int = 1
double / int = 1.75
int / double = 1.75
double / double = 1.75

Modulus (remainder)

The modulus operator is also informally known as the remainder operator. The modulus operator only works on integer operands, and it returns the remainder after doing integer division. For example, 7 / 4 = 1 remainder 3, thus 7 % 4 = 3. As another example, 25 / 7 = 3 remainder 4, thus 25 % 7 = 4.

Modulus is very useful for testing whether a number is evenly divisible by another number: if x % y == 0, then we know that y divides evenly into x.

For example, say we wanted to write a program that printed every number from 1 to 100 with 20 numbers per line. We could use the modulus operator to determine where to do the line breaks. Even though you haven’t seen a while statement yet, the following program should be pretty comprehensible:

This results in:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

We’ll discuss while statements in a future lesson.

A warning about integer division and modulus with negative numbers prior to C++11

Prior to C++11, if either of the operands of integer division are negative, the compiler is free to round up or down! For example, -5 / 2 can evaluate to either -3 or -2, depending on which way the compiler rounds. However, most modern compilers truncate towards 0 (so -5 / 2 would equal -2). The C++11 specification changed this to explicitly define that integer division should always truncate towards 0 (or put more simply, the fractional component is dropped).

Also prior to C++11, if either operand of the modulus operator is negative, the results of the modulus can be either negative or positive! For example, -5 % 2 can evaluate to either 1 or -1. The C++11 specification tightens this up so that a % b always resolves to the sign of a.

Arithmetic assignment operators

Operator Symbol Form Operation
Assignment = x = y Assign value y to x
Addition assignment += x += y Add y to x
Subtraction assignment -= x -= y Subtract y from x
Multiplication assignment *= x *= y Multiply x by y
Division assignment /= x /= y Divide x by y
Modulus assignment %= x %= y Put the remainder of x / y in x

Up to this point, when you’ve needed to add 5 to a variable, you’ve likely done the following:

This works, but it’s a little clunky, and takes two operators to execute.

Because writing statements such as x = x + 5 is so common, C++ provides 5 arithmetic assignment operators for convenience. Instead of writing x = x + 5, you can write x += 5. Instead of x = x * y, you can write x *= y.

Where’s the exponent operator?

Astute readers will note that there is no exponent operator. Instead, you have to use the pow() function that lives in the cmath library. pow(base, exponent) is the equivalent of baseexponent. It’s worth noting that the parameters to pow() are doubles, so it can handle non-integer exponents.

Quiz
1) What does the following expression evaluate to? 6 + 5 * 4 % 3

2) Write a program that asks the user to input an integer, and tells the user whether the number is even or odd. Write a function called isEven() that returns true if an integer passed to it is even. Use the modulus operator to test whether the integer parameter is even.

Hint: You’ll need to use if statements and the comparison operator (==) for this program. See section 2.7 -- Chars if you need a refresher on how to do this.

Answers

1) Show Solution

2) Show Solution

3.3 -- Increment/decrement operators, and side effects
Index
3.1 -- Operator precedence and associativity

108 comments to 3.2 — Arithmetic operators

  • Daniel

    After reading this multiple times, I still have no idea how the modulus (remainder) works. Could you explain it differently or post a link that explains it in depth?

    EDIT:
    Even though I’m not quite understanding the modulus, I managed to complete the second quiz haha 😀
    [code]#include

    using namespace std;

    bool isEven(int number)
    {
    if (number % 2 == 0)
    return true;
    else
    return false;
    }

    int main()
    {
    cout <> number;
    if (isEven(number))
    cout << number << " is even.n";
    else
    cout << number << " is odd.n";

    return 0;
    }[code]

    • Alex

      Modulus is just another name for the remainder left over after doing an integer division.

      So, 7 / 4 = 1, because the fraction is dropped.
      7 % 4 = 3, because 7 / 4 is 1, leaving a remainder of 3. That 3 is the result of the modulus.

  • Hema

    The output was 1 when val was equal to 9.
    Can you explain me how?

    • Alex

      1/2 does integer division and results in 0 (1/2 is 0.5, but integer division drops the fractional portion, so you’re left with 0). Any number to the 0th power is 1.

      You probably meant to do 1.0/2.0 instead of 1/2, so you get floating point division.

  • Hema

    Why can’t we use integers in the place of chars?

  • Nicolas

    Well this was my first attempt at question 2, but I think I missed the point about having a function return true 😛 great tutorial again!

  • Mitch

    Couldn’t the isEven function be simplified further?

    bool isEven(int x)
    {
        return (x % 2);
    }

    It still returns the correct true/false information.

    • Alex

      It could be simplified to the following:

      • MSteven

        Why This? Can you explain me, please!

        • Alex

          If x is even, then x % 2 = 0, which the ! flips to a 1, which becomes boolean true.
          If x is odd, then x % 2 = 1, which the ! flips to a 0, which becomes boolean false.

        • MSteven

          Hi Alex and I thanks you for your reply, but:
          It seems like i the function below !(x % 2) evaluates to 1 as function return value. Consequently By default, a bool function return 0(false) while I think the opposite

          Enlighten me, please!

      • MSteven

        Hi Alex, here’s a code, can you tell me if the code is pretty , a good code factorized and commented if no, how do I do for ameliorating it?

        • Alex

          main() and continueOrStop() are pretty redundant -- you could consolidate them.

          I’d also put the comments on the actual functions rather than the forward declarations.

          Other than that, I don’t see anything particularly noteworthy.

  • Greetings,

    Your quiz question 2 stated that we will need to use if statements in our code. However I coded this without if statements. Perhaps I misunderstood the question? The following is my code:

    • Alex

      Your program doesn’t tell the user whether the number is even or odd, it tells them 1 or 0 representing whether the number is even or odd.

      But that’s also fixable without using an if statement (by using the conditional operator), so yes, there is a valid solution that doesn’t use “if”.

  • James Ray

    I posted an answer to a question about code for this tutorial here.

  • Jim Smith

    I like to make loops to allow the user to decide when the program should end.

  • antiriad7

    On exercises 2’s answer, why?:

    Why not simply?:

    ‘%’ has higher precedence than ‘==’, it will be better practice to use without parentheses.

    • Alex

      return x % 2 == 0 assumes both the code author the reader remembers that % has higher precedence than ==. Even though the parenthesis in this case are superfluous, they both make your intent clear and ensure you haven’t misremembered the prioritization. In general, you should be optimizing your code for readability, correctness, and maintainability -- consequently, I would say it’s a better practice to use the parenthesis in this case than not (there’s no runtime performance penalty for using them).

  • harbie

  • Harbie

    I am trying to learn the c++ modulo. I was able to get the positive integers to run and compile… But whenever I try the negative divisor it doesn’t compile …..

    I just found your page and would post my program in a few….

    Thanks and looking to learn from here as others have…

  • Gabriel Netto Ferreira

    I did that code "on my way", but the compiler accuses an error in lines 8 and 9.
    What can it be? I never used string like data type, so… probably it’s a lil mistake

    ty, and sorry for my bad english. I’m not american, so english isn’t mine/my (idk, but I think it’s mine ahuauha) mother tongue :s

    • Gabriel Netto Ferreira

      Obs: I’m using Netbeans IDE, in Ubuntu 16.04

    • Alex

      I’m not sure which specific lines are causing errors, but just inspecting your program, a few things jump out at me:
      A few thoughts here:
      1) Your isEven() function is returning a string -- if it’s going to return a string, it should return a std::string.
      2) Your isEven() function should really be returning a boolean.
      3) Also make sure you’ve #included the string header.

  • Olvin Lizama

    Well, I think now your tutorials are mature enough to write a book, it may not be a best seller, but you can leave your legacy in C++ history, people will quote your work, your examples, and teach with your material.

    You have such a great didactic and is really easy to understand what you want to teach and very few people has that gift.

    For sure it could be a struggle to do it, but never will be worthless.

    I thank you for this project, is awesome and maybe you are used to people saying this, but I’m learning a lot thanks to  you.

    Sorry for my English it’s not my native language.

    Best wishes,

    • Alex

      Thank you for your kind words. The biggest problem with books is they are expensive, and that makes them inaccessible to a large portion of the world. The great thing about this website is that it is accessible for everyone with internet (since it’s ad-sponsored, something I can’t do with a book)! My goal isn’t to be famous or quoted -- my goal is to help others learn C++, just like others once helped me. This is my little mark on the world, and I’m proud that so many people from all countries of the world, rich or poor, have been able to visit.

  • Olvin Lizama

    Hi Alex,

    Perhaps you wanted us to use the functions and everything you taught us, but in think this is the simple way to make this program,

  • M Hassan Tahir

    #include "stdafx.h"
    #include <iostream>

    int userInput()
    {
        std::cout << "Enter an integer and know whether it is even or odd: ";
        int integer;
        std::cin >> integer;
        return integer;
    }

    void  isEven(int x)
    {
        if ( x % 2 == 0)
            std::cout << "The entered integer is even";
        else
            std::cout << "The entered integer is odd";
    }

    int main()
    {
        int input = userInput();
        isEven(input);

        return 0;
    }

    Another simple way. I hope it will work fine everywhere.
    Getting a hang of programming in C++ now.
    Thanks Alex!

  • ihowa

    i wrote a code for the second question and it is way different from what you wrote but it works fine. i want to know your take on my code pls and thank you

    • Alex

      Did you test this program? If so, you’d know that it doesn’t work. It starts off good, getting a number from function enternum(), which is passed back to main. But that value (x) is never used. Instead, iseven() declares its own local uninitialized variable x and then uses that to try to determine even or not. That will lead to undefined results.

      You need to pass the variable x in main to function iseven() as a function parameter, and have iseven() use that variable. Then your program will not only be well structured, it will actually work too. 🙂

      • Ihowa

        I understand what you’re getting at. but the first program did work.

        • Olvin Lizama

          Ihowa,

          It doesn’t work, I tried to compile it and gave me warnings about x not being used, Alex is right in order to work you need to pass x to iseven() function, should be like this,

  • Travis

    Is there any reason someone shouldn’t do:

  • Rammwurst

    Or you know

        return!(x % 2);

    cause you already taught us that everything !=0 bool sees as true.

    • J3ANP3T3R

      Interesting. but in his example

      return (x % 2) == 0;

      it will only either return a zero for FALSE and a non-zero value for TRUE. did you mean add ! in case the remainder is a negative ? i dont see what else could be missing return (x % 2) == 0; looks fine.

  • in your example above, you forgotten to insert "return 0"
    if i compile it says error

    #include <iostream>

    int main()
    {
        // count holds the current number to print
        int count = 1; // start at 1

        // Loop continually until we pass number 100
        while (count <= 100)
        {
            std::cout << count << " "; // print the current number

            // if count is evenly divisible by 20, print a new line
            if (count % 20 == 0)
                std::cout << "\n";

            count = count + 1; // go to next number
        } // end of while
    } // end of main()

  • Kyle Roth

    why does this ask me for an integer 4 times?

    [#include "stdafx.h"
    #include <iostream>

    int getNumber()
    {
        std::cout << "enter and integer";
        int x;
        std::cin >> x;
        return x;

    }

    int main()
    {
        
        getNumber();
        
        
        if (((getNumber()) % 2) == 0)
            std::cout << getNumber() << "is even\n";
        else
            std::cout << getNumber() << "is odd\n";
    } ]

    • Alex

      4 times? It should only ask 3 times. And this happens because getNumber() asks the user to enter an integer each time it is called. And you’re calling it 3 times (only one of the conditional statements gets executed).

      What you should do is assign the return value of getNumber() to a temporary variable, and use that variable instead of calling getNumber() again.

  • sharaf

    why can’t we use in this way?

  • Simon

    My version ; still too messy but added a twist 😉

    • Simon

      And here is a different version of your counting, C++ starts to get funny… thanks a lot for all the tutorial and really really well done quizz.

  • Nortski

    Thank you so much for these tutorials. I’ve tried a number of times to get my head around programming over the years. Decided to give it another go and these tutorials are fantastic!

    This was my solution to question 2. More coding than was needed but works fine. Streamlining will come with experience 🙂

  • Josh

    Is this acceptable? Or really, is this less efficient in any way?

    • Alex

      Is it acceptable from what perspective? Does it work? Yes. Does it meet the quiz requirements? No. The quiz asked you to create a function named isEven() and you didn’t.

  • Pravasi Meet

    The semantics of += (add assignment operator) are different in C & C++. += operator returns lvalue (locator value) in C++ but not in C. That’s why following program is valid in C++ but invalid in C.

    When you compile above program in C the compiler gives you following error:
    [Error] lvalue required as left operand of assignment

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