Calculations and answers

3.1Order of operations#

Classic CAS follows the standard order: brackets, powers, multiplication and division, then addition and subtraction. Use brackets to force a different order.

Example 3.1

Brackets change the order

$$(2+3)\times 4=20$$

1. Type (2 + 3) × 4 and press enter.

   (2+3)×4enter

Example 3.2

Powers before negation

1. Type negative 3, then ^2.

   (−)3^2enter

The power happens first, so the answer is −9. Write (−3)² with brackets to get 9.

3.2Add fractions and keep exact answers#

Whole numbers and fractions give exact answers. Type a fraction with ÷, or build a stacked fraction with /: type the top, press ▼, type the bottom, then ▶ to leave the fraction.

Example 3.3

Add fractions with the divide key

$$\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{47}{60}$$

1. Type 1/3 + 1/4 + 1/5.

   1÷3+1÷4+1÷5enter

Example 3.4

Add fractions with the fraction template

1. Press frac, type 1, down, 3, right, then +.

   /1▼3▶+

2. Build the second fraction and press enter.

   /1▼6▶enter

Example 3.5

Convert an improper fraction

1. Use propFrac to write 7/3 as a mixed number.

   propfrac(7÷3)enter

Example 3.6

Mixed number template

$$1\tfrac{1}{2}=\frac{3}{2}$$

1. Open templates, choose Mixed number (e), type 1, right, 1, right, 2, right.

   templatese1▶1▶2▶enter

3.3Get a decimal answer#

Press ctrl≈enter instead of enter to get a decimal answer once. A number typed with a decimal point already gives a decimal result, and the Approximate setting makes every answer a decimal (see Modes).

Example 3.7

Decimal answer for one line

1. Type 1/3 and press ctrl then enter.

   1÷3ctrl≈enter

Example 3.8

Square root as a decimal

1. Type √12 (ctrl sq), press right, then ctrl enter.

   ctrl√x²12▶ctrl≈enter

Example 3.9

A decimal input gives a decimal answer

1. Type 0.5 + 1/4 and press enter.

   0.5+1÷4enter

Example 3.10

Turn a decimal into a fraction

1. Use exact( to convert 0.75 to a fraction.

   exact(0.75)enter

3.4Negative numbers versus subtraction#

Use (−) for a negative sign and − for subtraction. They are different keys: − needs a number on its left.

Example 3.11

Subtract a negative

$$5-(-3)=8$$

1. Type 5, subtract, negative 3.

   5−(−)3enter

3.5Scientific notation#

Press EE to type "times ten to the power". Type the mantissa, press EE, then the exponent. Very large or small answers are displayed as 1.E20 style numbers.

Example 3.12

Enter 2 × 10³

$$2\times 10^{3}=2000$$

1. Type 2, ee, 3 and press enter.

   2EE3enter

Example 3.13

A tiny number

1. Type 1, ee, negative 7.

   1EE(−)7enter

3.6Use the last answer#

Start a new entry with an operator (+, −, ×, ÷, ^, x² or factorial) and the calculator types ans for you. You can also press ctrlans(−) to type ans anywhere.

Example 3.14

Continue from the last answer

1. Type 6, enter, then × 7 and enter.

   6enter×7enter

Example 3.15

Place ans inside an expression

1. Type 9, enter, then ctrl (−), + 1, enter.

   9enterctrlans(−)+1enter

3.7Reuse and edit earlier lines#

Press ▲ on an empty entry line to select the last answer; press ▲ again to select the entry above it. Press ▲ or ▼ to move around. Press enter to paste the selected entry or answer into the entry line so you can edit it. Press del to delete the selected line, or esc to leave the selection.

Example 3.16

Paste an old answer

1. Type 2+3, enter, press up, enter, then ×2.

   2+3enter▲enter×2enter

Example 3.17

Edit an old entry

1. Press up twice to select the entry, press enter, then add +10.

   2+3enter▲▲enter+10enter

The history keeps the last 60 lines. Choose Clear History in the Home menu or in the Actions menu to wipe the screen without deleting variables.