# Magic Number

# Sticky Operators

## Less bracketing. More speed.

# What are they?

Let’s say you want to calculate

It’s natural to type ‘11 + 33 / 2’.

But doing so gives you

As division has higher precedence than addition, it acts like glue —

it bonds 33 and 2.

As a workaround, we use parentheses, ( 11 + 33 ) / 2.

While workable, it’s also unnatural and slows us down.

Ideally we want ‘+’ to act upon 11 and 33.

We want it to bond 11 and 33.

We want it to be *sticky*.

# How?

### ⌥ (option) is the key

Or rather, ⌥ is the sticky key.

To enter a sticky ‘+’, press
`⌥`` + `

So to calculate

just enter 11 *⌥ +* 33 / 2

### Subtraction

As you have guessed, the shortcut is `⌥`` – `

For example:

Enter: 33 *⌥ –* 11 / 2

(Don’t go away yet. There is a little twist in our story.)

### Multiplication

To avoid confusion with the standard multiplication sign ‘×’, the lower-case x,

and the upper-case X, Magic Number uses the dot ( • ) notation from math.

Shortcut: `⌥`` . `

Example: To convert 3600 minutes into days, we want

For that, we enter 3600 / 60 *⌥ .* 24

### Division

No drama here, the shortcut is `⌥`` / `

Previously, to calculate

you had to use parentheses, 8 ^ (2 / 3).

And now, 8 ^ 2 *⌥ /* 3.

*What’s next?*

You are almost an expert.

With the next 2 tips, you can handle any sticky situation.

# Sensing sticky

With great power comes great responsibility…

When you have *2 × 3 + 4 =* 14, and without knowing ‘+’ is sticky,
you might think something is wrong. How can you tell something is sticky?

Let’s look at standard and sticky operators side by side.

*Addition*

Standard

Sticky

*Subtraction*

Standard

Sticky

*Multiplication*

Standard

Sticky

*Division*

Standard

Sticky

*See the bond*

You can also tell by double-clicking the operator.

This selects the operator and its operands as a group.

Standard

Left operand | 2 × 3 = 6 |

Right operand | 4 |

Left + Right | 10 |

Sticky

Left operand | 3 |

Right operand | 4 |

Left + Right | 7 |

*Avoid misunderstanding*

Whether it is for someone or for your future self, parentheses are still essential to make your expressions understandable.

Here is a quick way to bracket a sticky for clarity:

1. Double-click to select it as a group.

2. Press ⌘ ) or ⌘ ] to bracket the group.

# Semi-sticky

There are times you need a less sticky operator.

To see why, let’s start with the *standard* ‘+’.

Enter √ 3 *+* 4 and you get

For comparison, let’s try the *sticky* ‘+’.

Enter √ 3 *⌥+* 4

You can see sticky ‘+’ bonds directly to 3.

That is, it bonds directly to whatever comes before it.

To get a better insight, enter 8 ^ 2 *⌥+* 3

As expected sticky ‘+’ bonds directly to 2.

This is better than entering 8 ^ (2 + 3).

However when dealing with expressions like

Using a sticky ‘+’ for √ 3 ^ 2 ⌥+ … yields

And using a standard ‘+’ doesn’t help either.

You are stuck.

Sticky ‘+’ won’t do as it bonds with 2 — it’s too sticky.

Standard ‘+’ won’t do as it bonds with √ 3 ² — it’s not sticky.

You need something in between.

You need a semi-sticky ‘+’ that bonds with 3 ².

You can achieve that by pressing ⌥+ twice.

That is, by entering √ 3 ^ 2 **⌥+ ⌥+** 4 ^ 2.

# Your turn

Well done for getting this far.

Let’s put what you’ve learned to the test.

Here’s a quadratic equation

And here’s the quadratic formula.

Your task: Solve x by entering

Your extra challenge: Do it with Apple’s calculator. Do it in RPN mode.