in the expression this type of notation is referred to as infix since the operator is in between the two operands that it is working on consider another infix examplea the operators and still appear between the operandsbut there is problem which operands do they work ondoes the work on and or does the take and cthe expression seems ambiguous in factyou have been reading and writing these types of expressions for long time and they do not cause you any problem the reason for this is that you know something about the operators and each operator has precedence level operators of higher precedence are used before operators of lower precedence the only thing that can change that order is the presence of parentheses the precedence order for arithmetic operators places multiplication and division above addition and subtraction if two operators of equal precedence appearthen left-to-right ordering or associativity is used let' interpret the troublesome expression using operator precedence and are multiplied firstand is then added to that result ( bc would force the addition of and to be done first before the multiplication in expression cby precedence (via associativity)the leftmost would be done first although all this may be obvious to youremember that computers need to know exactly what operators to perform and in what order one way to write an expression that guarantees there will be no confusion with respect to the order of operations is to create what is called fully parenthesized expression this type of expression uses one pair of parentheses for each operator the parentheses dictate the order of operationsthere is no ambiguity there is also no need to remember any precedence rules the expression can be rewritten as (( ( )dto show that the multiplication happens firstfollowed by the leftmost addition can be written as ((( bcdsince the addition operations associate from left to right there are two other very important expression formats that may not seem obvious to you at first consider the infix expression what would happen if we moved the operator before the two operandsthe resulting expression would be +ab likewisewe could move the operator to the end we would get abthese look bit strange these changes to the position of the operator with respect to the operands create two new expression formatsprefix and postfix prefix expression notation requires that all operators precede the two operands that they work on postfixon the other handrequires that its operators come after the corresponding operands few more examples should help to make this bit clearer (see table would be written as + bc in prefix the multiplication operator comes immediately before the operands and cdenoting that has precedence over the addition operator then appears before the and the result of the multiplication in postfixthe expression would be abc againthe order of operations is preserved since the appears immediately after the and the cdenoting that has precedencewith coming after although the operators moved and now appear either before or after their respective operandsthe order of the operands stayed exactly the same relative to one another now consider the infix expression ( bc recall that in this caseinfix requires the parentheses to force the performance of the addition before the multiplication howeverwhen basic data structures