# Math

Using numbers, number operators, and math functions.

## Numeric values: 0, 1, 2, 6.7, 10.083…

Just numbers by themselves. Sometimes these are called *numeric literals*.

### Integers: whole numbers

```
let num = 0;
num = 0;
num = 1;
num = 2;
```

### Floating point: numbers with a fractional part

Numbers can have their fractional part too. The decimal point is between the digits of the number.
But, *floating point* numbers have the decimal point at any spot between digits, like: 3.14159 or 651.75.

```
let num = 0
num = 6.7
num = 10.083
```

### Arithmetic binary operation (+, -, *, /)

The operations for basic arithmetic: add, subtract, multiply, and divide.

```
let more = 0+1;
let less = 0-1;
let twice = 1*2;
let divide = 8/4;
```

### Remainder (%)

This is a extra operator for division. You can find out how much is left over if one number doesn’t divide into the other number evenly.

We know that 4 / 2 = 2, so 2 divides into 4 evenly. But, 5 / 2 = 2 with a remainder of 1. So, the remainder operation, 5 % 2 = 1, gives the number that’s left over from a division operation.

`let remainder = 7%4;`

### Exponent (**)

The exponent operator will multiply the number on the left by itself for the amount of times of the number on its right. That is, 4 ** 2 = 4 * 4 and 2 ** 3 = 2 * 2 * 2. The area of a square that has sides with a length of `5`

is equal to one side multiplied by another. For a square, all sides are equal, so:

```
let side = 5;
let area = side * side;
```

But using the exponent operator, this is the same as:

```
let side = 5;
let area = side ** 2;
```

The volume of a cube is three sides multiplied together. The two volumes are the same:

```
let side = 5;
let volume1 = side * side * side;
let volume2 = side ** 3;
```

## Integer multiply and divide

Integer multiply and divide treats the two numbers it operates on as integers. If there is a fractional part for a number, it is truncated before it is used with the other number. The resulting value is always an integer too.

### imul

Interger multiplication of two numbers `3.9`

and `4.2`

results in a value of `12`

since just the values of `3`

and `4`

are used from the numbers multiplied.

```
let myInt = Math.imul(3.9, 4.2)
let myNumber = 3.9 * 4.2
```

### idiv

Interger division of two numbers `7.8`

and `2.6`

results in a value of `3`

since just the values of `7`

and `2`

are used from the numbers multiplied.

```
let myInt = Math.idiv(7.8, 2.6)
let myNumber = 7.8 / 2.6
```

## Square root

The square root of a number is another number that when multiplied by itself it becomes the original number. You know that `2 * 2`

equals `4`

so the square root of `4`

is `2`

. It’s called a *square root* because the area of a *square* is the length of two equal sides multiplied together. The *root* is the length of a side.

```
let side = 5
let square = side * side
let root = Math.sqrt(side)
```

## Absolute value

When you want to know how much a number is without its *sign* (+/-). The absolute value of -5 is 5 and the absolute value of 5 is also 5. The absolute value is sometimes called the *magnitude*.

`let item = Math.abs(-5);`

## Minimum and maximum of two values

You can get the smaller or the bigger of two numbers with the min and max functions.

- The minimum of 2 and 9:
**Math.min(2, 9)**equals 2. - The maximum of 3 and 9:
**Math.max(3, 9)**equals 9.

```
let minval = Math.min(0, 1);
let maxval = Math.max(8, 2);
```

## Round

If a number has a fractional part, you can make the number change to be the closest, next integer value. This is called *rounding*. Rounding the number `6.78`

will make it be `7`

and rounding `9.3`

will give you `9`

. If a number has a fractional part greater than or equal to `0.5`

, the number will round up to the next whole integer value with the higher value. Otherwise, it will round down to the next lowest integer value.

For negative numbers, they round toward the absolute value (the absolute value of `-8`

is `8`

) of the number. So, `-5.23`

rounds to `-5`

and `-2.68`

rounds to `-3`

.

`let rounded = Math.round(5.5)`

## Ceiling

To make a number change to the next higher whole number (integer), get the number’s *ceiling* value. The ceiling value for `1.234`

is `2`

since that is the next higher whole number. For the negative number of `-3.63`

, its ceiling is `-3`

since that’s the next higher whole number.

`let nextup = Math.ceil(8.435)`

## Floor

To make a number change to the next lower whole number (integer), get the number’s *floor* value. The floor value for `8.76`

is `8`

since that is the next lower whole number. For the negative number of `6.17`

, its floor is `-7`

since that’s the next lower whole number.

`let nextdown = Math.floor(4.97)`

## Truncate

The fractional part of a number is removed by *truncating* it. If a number has the value `54.234`

its truncated value is `54`

. Truncation works the same way for a negative number. The truncated value of `-34.913`

is `-34`

.

`let nonfraction = Math.trunc(87.23455)`

## Random value

Make up any number from a minimum value to a some maximum value. If you want a random number up to
100, say: **Math.randomRange(0, 100)**.

`let myRandom = Math.randomRange(0, 5);`

## See also

abs, min, max, randomRange