Everyday calculations

5.1Add, subtract, multiply and divide#

The two operands are on levels 2 and 1. Level 2 is the first number, level 1 the second: 10 ENTER 4 − gives 6 and 20 ENTER 5 ÷ gives 4.

Example 5.1

Divide 20 by 5

$$20\div5=4$$

1. Type 20, ENTER, 5, then divide.

   20ENTER5÷

Example 5.2

Subtract: 10 minus 4

1. Type 10, ENTER, 4, then subtract.

   10ENTER4−

Example 5.3

One third

1. Divide 1 by 3. Results show 12 digits.

   1ENTER3÷

5.2Negative numbers and changing the sign#

Type the digits, then press +/− to make the number negative. When there is no command line, +/− changes the sign of level 1.

Example 5.4

Enter a negative number and add

1. Type 5, +/−, ENTER, 3 and +.

   5+/−ENTER3+

Example 5.5

Change the sign of a result

1. Subtract 3 from 8, then press +/−.

   8ENTER3−+/−

5.3Square, square root, power, reciprocal and roots#

√x takes the square root, left shift √x squares, yˣ raises level 2 to the power in level 1, left shift ÷ is the reciprocal and right shift √x is XROOT, which takes the x-th root.

Example 5.6

2 to the power 10

$$2^{10}=1024$$

1. Type 2, ENTER, 10, press the power key.

   2ENTER10yˣ

Example 5.7

Square root of 144

1. Type 144 and press the root key.

   144√x

Example 5.8

Square of 5

1. Type 5, left shift, root key.

   5◀x²√x

Example 5.9

Reciprocal of 2

1. Type 2, left shift, divide.

   2◀1/x÷

Example 5.10

Cube root of 27

$$\sqrt[3]{27}=3$$

1. Type 27, ENTER, 3 and press right shift root key (XROOT).

   27ENTER3▶ˣ√y√x

5.4Calculate a percentage#

Right shift × is %: level 1 percent of level 2. Both numbers are used up and only the percentage is left, so copy the base number with ENTER first if you still need it. The MTH menu also has %T (what percent one number is of another) and %CH (percent change from one number to another).

Example 5.11

15 percent of 200

1. Type 200, ENTER, 15, then right shift multiply.

   200ENTER15▶%×

Example 5.12

Add 15 percent

$$200+0.15\times200=230$$

1. Copy the 200 first with ENTER, take the percentage of the copy, then add.

   200ENTERENTER15▶%×+

Example 5.13

What percent is 30 of 200?

1. Open MTH, go to page 2 and press %T (fifth key).

   200ENTER30◀MTHAPPSNXTF5

Example 5.14

Percent change from 50 to 60

1. Press %CH (sixth key on MTH page 2).

   50ENTER60◀MTHAPPSNXTF6

5.5Pi, e and i#

Right shift TAN puts $\pi$ on the stack, right shift 2 puts e, and left shift 2 puts the imaginary unit i. Pi and e stay symbolic (shown as π and e) until you convert them. Left shift EVAL (→NUM) turns them into decimal numbers.

Example 5.15

The value of pi

1. Press right shift TAN, then left shift EVAL.

   ▶πTAN◀→NUMEVAL

Example 5.16

Area of a circle of radius 5

$$A=\pi r^{2}$$

1. Type 5, square it, push pi and multiply, then convert to a number.

   5◀x²√x▶πTAN×◀→NUMEVAL

See also Convert between polar and rectangular

5.6Evaluate and approximate#

EVAL runs the object on level 1: it evaluates an expression, runs a program, and looks up a name. →NUM (left shift EVAL) evaluates and converts to decimals.

Example 5.17

Evaluate an expression with a stored variable

1. Store 3 in x.

   3'αα◀1/x÷αENTERSTO▶

2. Type the expression x squared plus 1 and press EVAL.

   'αα◀1/x÷αTyˣ2+1ENTEREVAL

5.7Look back at earlier calculations#

The app records calculations in the History panel, with what you entered and the top of the stack. For reuse inside the calculator, use HIST, LASTARG and UNDO.

See also See your past calculations in HistoryReuse an earlier result