# Order of Operations and the TI-84 Plus Calculator

The order in which the TI-84 Plus calculator performs operations is the standard order that you are all used to. Spelled out in detail, here is the order in which the calculator performs operations:

The calculator simplifies all expressions surrounded by parentheses.

The calculator evaluates all functions that are followed by the argument.

These functions supply the first parenthesis in the pair of parentheses that must surround the argument. An example is sin

*x.*When you press**[SIN]**to access this function, the calculator inserts**sin(**on-screen. You then enter the argument and press**[ ) ]**.The calculator evaluates all functions entered after the argument.

An example of such a function is the square function. You enter the argument and then press

**[**to square it.*x*^{2}]Evaluating –3

^{2}may not give you the expected answer. You think of –3 as being a single, negative number. So when you square it, you expect to get +9. But the calculator gets –9. This happens because the normal way to enter –3 into the calculator is by pressing**[(-)][3]**— and pressing the**[(-)]**key is equivalent to multiplying by –1.Thus, in this context, –3

^{2}= –1 * 3^{2}= –1 * 9 = –9. To avoid this potentially hazardous problem, always surround negative numbers with parentheses*before*raising them to a power.The calculator evaluates powers entered using the [^] key and roots entered using the

**Function, found in the Math menu.**You can also enter various roots by using fractional exponents — for example, the cube root of 8 can be entered as 8^(1/3).

The calculator evaluates all multiplication and division problems as it encounters them, proceeding from left to right.

The calculator evaluates all addition and subtraction problems as it encounters them, proceeding from left to right.

Well, okay, what does the phrase “*x* plus 1 divided by *x* minus 2” actually *mean* when you say it aloud? Well, that depends on how you say it. Said without pausing, it means (*x* + 1)/(*x* – 2). Said with a subtle pause after the “plus” and another before the “minus,” it means *x* + (1/*x*) – 2.

The calculator can’t hear speech inflection, so make good use of those parentheses when you’re “talking” to the calculator.