to get division that returns an integer resultyou can use the integer division operation /integer division always produces an integer think of integer division as "gozinta the expression produces because three gozinta (goes intoten three times (with remainder of onewhile the result of integer division is always an integerthe data type of the result depends on the data type of the operands float integer-divided by float produces float with fractional component the last two interactions demonstrate the remainder operation the remainder of integer-dividing by is notice again that the data type of the result depends on the type of the operands depending on your math backgroundyou may not have used the integer division or remainder operations before the thing to keep in mind is that these two operations are closely related integer division tells you how many times one number goes into anotherand the remainder tells you how much is left over mathematically you could write the idea like thisa ( // )( )+( %bas an example applicationsuppose we calculated the value of our loose change in cents (rather than dollarsif have centsthen can find the number of whole dollars by computing // and the remaining change is % thusi must have total of three dollars and cents in change by the wayalthough pythonas of version treats regular division and integer division as two separate operatorsmany other computer languages (and earlier python versionsjust use to signify both when the operands are intsmeans integer divisionand when they are floatsit signifies regular division this is common source of errors for examplein our temperature conversion program the formula / celsius would not compute the proper resultsince / would evaluate to using integer division in these "old-fashionedlanguagesyou need to be careful to write this expression as celsius so that the proper form of division is usedyielding fractional result using the math library besides the operations listed in table python provides many other useful mathematical functions in special math library library is just module that contains some useful definitions our next program illustrates the use of this library to compute the roots of quadratic equations quadratic equation has the form ax bx such an equation has two solutions for the value of given by the quadratic formula- + ac let' write program that can find the solutions to quadratic equation the input to the program will be the values of the coefficients aband the outputs are the two values given by the quadratic formula here' program that does the job quadratic py program that computes the real roots of quadratic equation illustrates use of the math library