# Evaluate Expressions in TI-Nspire Using Primary and Secondary Keys

With the TI-Nspire, you can evaluate mathematical expressions directly from the *primary* keys (as defined by the functions or characters located directly on the keys themselves) and the *secondary* keys (as defined by the colored functions or characters located toward the top of some keys).

For example, **[***x*^{2}**]** is the primary key for squaring an expression and the secondary key for taking the square root of an expression. To access a secondary key, press **[CTRL]** followed by the primary key.

To add a Calculator page, press **[CTRL][****I****]**→Add Calculator.

Start with a very simple expression, entered and evaluated by pressing only primary keys. In the first screen, typing

finds the value of

The result of this calculation, found by pressing **[ENTER]**, is shown in the second screen.

Notice that two things happen after you press **[ENTER]**. The original typed expression is shown with a stacked fraction, and the result is also expressed as a stacked fraction. When possible, TI-Nspire displays expressions and results in *pretty print* — that is, in the format that you typically see in a math textbook or other print source.

But why force the TI-Nspire to convert your expression to *pretty print**?* Typing the secondary key for division

gives you a Fraction template. This template allows you to type intense math problems (like the complex fraction in the third screen) with minimal use of parentheses. Students who use this template avoid the parentheses errors that used to be very common in my math classroom because the expression they type on the Calculator page looks exactly like the problem in their textbook.

As for the fractional result, TI-Nspire attempts to display all rational values as fractions. In the second screen, typing **[3][CTRL][***x*^{2}**][1][2]**** **finds the value of 3 times the square root of 12. Notice that the result is expressed as a decimal, which happens any time a result is an *irrational* number (that is, when the decimal portion neither terminates nor repeats and thus can’t be written in fractional form).

This result is shown to four decimal places. To change the number of displayed digits, press **[ON]**→Settings→Settings→General. A dialog box opens and the first field, Display Digits, allows for changing the number of displayed digits.

Pressing OK affects only the settings within the current document (and doesn’t change the Scratchpad settings). Choose Make Default every time you make a change so that the Scratchpad settings change as well as future documents that you create.

Consider that you want to evaluate log_{5}25. The logarithm function is a secondary key located on the **[10**^{x}**]** key. The first screen shows that a Logarithm template appears after pressing **[CTRL][10**^{x}**]**.

Notice the two small dashed rectangular (fields) with the cursor located in the leftmost field. The first field defines the base of the logarithm, and the second field gives the value for which you want to evaluate this logarithm. Type **[****5****]** to specify the base. To move to the next box, press **[TAB]**. Type **[****2****][****5****]** and press **[ENTER]** to complete the calculation, as shown in the second screen.

Always use the **[TAB]** key to move from field to field in a mathematical expression just like you do on a computer. Pressing **[SHIFT][TAB]** moves your cursor to the previous field.

If you leave the first field in the Logarithm template blank, TI-Nspire uses a default base of 10.