# TI-84 Plus Calculator’s Math MATH Submenu

Press [MATH] to access the Math MATH submenu on your TI-84 Plus calculator. This submenu contains general mathematical functions you can insert into an expression.

## Converting between decimals and fractions on the TI-84 Plus

The **Frac** function always converts a finite decimal to a fraction. If your calculator can’t convert a decimal to a fraction, it lets you know by redisplaying the decimal. Be sure to enter the decimal before inserting the **Frac** function. Press [MATH][ENTER][ENTER] to quickly convert a decimal answer to a fraction as shown in the first screen.

How do you convert an infinite repeating decimal into a fraction? Just type at least ten digits of the repeating decimal and press [MATH][ENTER][ENTER]. See the second screen.

The **Dec** function converts a fraction to a decimal. Enter the fraction before you insert the **Dec** function. See the third screen.

If you are in Automatic mode, include a decimal in an expression to produce a decimal answer.

## Cubing and taking cube roots on the TI-84 Plus

The cube function cubes the value that precedes the function. The cube function is rarely used because it is easier to press [^][3] to cube an expression. The cube-root template

finds the cube root of a value that follows the function. See the first screen.

## Taking the *x*th root on the TI-84 Plus calculator

The *x*th root template

finds the *x*th root of the value that follows the function. To use this function, first enter the root *x*, then insert the

function, and then enter the argument. Alternatively, on the TI-84 Plus C you can insert the *x*th root template first. Then type the root, press the right-arrow key, and type the expression. This is illustrated in the second screen.

## Finding the location of maximum and minimum values on the TI-84 Plus

The **fMin** and **fMax **functions approximate *where* the minimum or maximum value of a function occurs in a specified interval. *They do not compute the minimum or maximum value of the function;* they just give you the *x*-coordinate of the minimum or maximum point.

The **fMin** and **fMax **functions are stand-alone functions in the sense that they cannot be used in an expression. To use these functions, insert the appropriate function, **fMin** or **fMax**, at the beginning of a new line on the Home screen. Then enter the definition of the function whose minimum or maximum you want to locate. Press [,] and enter the variable used in the definition of the function you just entered. Press [,] and enter the lower limit of the specified interval. Then press [,], enter the upper limit, and press [)].

Finally, press [ENTER] to *approximate* the location of the minimum or maximum in the specified interval. This is illustrated in the third screen. In this screen the calculator is *approximating* the location of the maximum value of the function *x*^{2} in the interval

## Using numerical differentiation and integration templates on the TI-84 Plus

The calculator cannot perform symbolic differentiation and integration. For example, it can’t tell you the derivative of *x*^{2} is 2*x*, nor can it evaluate an indefinite integral. But the **nDeriv** template will approximate the derivative (slope) of a function at a specified value of the variable, and the **fnInt** template will approximate a definite integral.

Insert the **nDeriv** template. Templates are intuitive to use. First, enter the variable you want to take the derivative with respect to and then press the right-arrow key. Enter the function whose derivative you want to find and then press the right-arrow key. Then enter the value at which the derivative is to be taken. Finally, press [ENTER] to *approximate* the derivative. This is illustrated in the first screen.

To use the **fnInt** template, insert **fnInt**. Enter the lower limit and press the right-arrow key, then enter the upper limit and press the right-arrow key. Enter the function you’re integrating and press the right-arrow key. Enter the variable used in the definition of the function you just entered. Finally, press [ENTER] to *approximate* the definite integral. This is illustrated in the second screen.

The calculator may give you an error message or a false answer if **nDeriv** is used to find the derivative at a nondifferentiable point or if **fnInt** is used to evaluate an improper integral.

## Using the TI-84 Plus calculator’s summation and logarithm templates

These templates can be found by pressing the up-arrow key to scroll in the MATH menu, or by pressing [ALPHA][WINDOW] to access the templates in the shortcut menu.

The summation template can be used to find the sum of a sequence. In math classrooms, this is commonly known as *Sigma notation.* The template should look exactly like a Sigma notation problem in your math textbook.

To use the summation template, insert

Notice the cursor has a blinking “A” indicating your calculator is in Alpha mode. Press the key that corresponds to the variable you want to use and press the right-arrow key. Enter the lower limit, press the right-arrow key, then enter the upper limit and press the right-arrow key again. Enter the expression and press [ENTER] to find the sum of the sequence as shown in the first line of the last screen.

Using the logarithm template, you can change the base of a logarithm! Press the following keys to insert the **logBASE** template:

Simply enter the base, press the right-arrow key, and enter the number you wish to take the logarithm of. Press [ENTER] to display the answer. Isn’t that easy and fun?