# Arithmetic Keywords

Arithmetic keywords perform mathematical operations on numbers. Each has both a textual form (readable) and symbolic form (concise).

## Keywords

| Keyword    | Symbol | Operation      |
| ---------- | ------ | -------------- |
| PLUS       | `+`    | Addition       |
| MINUS      | `-`    | Subtraction    |
| TIMES      | `*`    | Multiplication |
| DIVIDED BY | `/`    | Division       |
| MODULO     | None   | Remainder      |

## PLUS

Adds two numbers.

### Syntax

```l4
value1 PLUS value2
value1 + value2
```

### Examples

**Example file:** 

```l4-file
-- Arithmetic keyword examples

-- PLUS (Addition)

#EVAL 5 PLUS 3
#EVAL 5 + 3
#EVAL 10.5 + 2.5
#EVAL (-3) + 8

-- MINUS (Subtraction)

#EVAL 10 MINUS 4
#EVAL 10 - 4
#EVAL 5 - 8
#EVAL 0 - 5

-- TIMES (Multiplication)

#EVAL 6 TIMES 7
#EVAL 6 * 7
#EVAL 3.14 * 2
#EVAL (-3) * 4

-- DIVIDED BY (Division)

#EVAL 15 DIVIDED BY 3
#EVAL 15 / 3
#EVAL 10 / 4
#EVAL 7 / 2

-- MODULO (Remainder)

#EVAL 17 MODULO 5
#EVAL 10 MODULO 3
#EVAL 8 MODULO 2

-- Operator Precedence

-- Multiplication before addition
#EVAL 2 + 3 * 4

-- Parentheses override precedence
#EVAL (2 + 3) * 4

-- Division before subtraction
#EVAL 10 - 4 / 2

-- With parentheses
#EVAL (10 - 4) / 2

-- Complex Expressions

-- Circle area: pi * r^2
GIVEN r IS A NUMBER
circleArea r MEANS 3.14159 TIMES r TIMES r

#EVAL circleArea 5

-- Quadratic formula discriminant: b^2 - 4ac
GIVEN a IS A NUMBER
      b IS A NUMBER
      c IS A NUMBER
discriminant a b c MEANS
  b TIMES b MINUS 4 TIMES a TIMES c

#EVAL discriminant 1 5 6

-- Practical Examples

-- Calculate tax
GIVEN price IS A NUMBER
      taxRate IS A NUMBER
calculateTax price taxRate MEANS
  price TIMES taxRate / 100

#EVAL calculateTax 100 8.5

-- Calculate discount
GIVEN originalPrice IS A NUMBER
      discountPercent IS A NUMBER
applyDiscount originalPrice discountPercent MEANS
  originalPrice MINUS (originalPrice TIMES discountPercent / 100)

#EVAL applyDiscount 200 25

-- Combining with Comparisons

ASSUME income IS A NUMBER
ASSUME expenses IS A NUMBER

DECIDE profit IS income MINUS expenses
DECIDE isProfitable IS profit GREATER THAN 0

#CHECK isProfitable
```



```l4
#EVAL 5 PLUS 3        -- 8
#EVAL 5 + 3           -- 8
#EVAL 10.5 + 2.5      -- 13
```

## MINUS

Subtracts the second number from the first.

### Syntax

```l4
value1 MINUS value2
value1 - value2
```

### Examples

```l4
#EVAL 10 MINUS 4      -- 6
#EVAL 10 - 4          -- 6
#EVAL 5 - 8           -- -3
```

## TIMES

Multiplies two numbers.

### Syntax

```l4
value1 TIMES value2
value1 * value2
```

### Examples

```l4
#EVAL 6 TIMES 7       -- 42
#EVAL 6 * 7           -- 42
#EVAL 3.14 * 2        -- 6.28
```

## DIVIDED BY

Divides the first number by the second.

### Syntax

```l4
value1 DIVIDED BY value2
value1 / value2
```

### Examples

```l4
#EVAL 15 DIVIDED BY 3    -- 5
#EVAL 15 / 3             -- 5
#EVAL 10 / 4             -- 2.5 (rational result)
```

**Note:** Division returns exact rational numbers, not truncated integers.

## MODULO

Returns the remainder after division.

### Syntax

```l4
value1 MODULO value2
```

### Examples

```l4
#EVAL 17 MODULO 5     -- 2
#EVAL 10 MODULO 3     -- 1
```

## Operator Precedence

Standard mathematical precedence:

1. Parentheses `()` (highest)
2. Multiplication, Division, Modulo
3. Addition, Subtraction (`+`, `-`) (lowest)

### Examples

```l4
#EVAL 2 + 3 * 4        -- 14 (not 20)
#EVAL (2 + 3) * 4      -- 20
#EVAL 10 - 4 / 2       -- 8 (not 3)
#EVAL (10 - 4) / 2     -- 3
```

## Combining with Other Operators

Arithmetic results can be used with comparisons and logic:

```l4
ASSUME price IS A NUMBER
ASSUME quantity IS A NUMBER

-- Calculate total and check threshold
DECIDE total IS price TIMES quantity
DECIDE needsApproval IS total GREATER THAN 10000
```

## Math Library Functions

For advanced operations, import the math library:

```l4
IMPORT math

#EVAL sqrt 16          -- 4
#EVAL exp 1            -- 2.718...
```

See **[Libraries Reference](/l4/reference/libraries.md)** for more functions.

## Related Keywords

- **[COMPARISONS](/l4/reference/operators/comparisons.md)** - Compare arithmetic results
- **[IF](/l4/reference/control-flow/IF.md)** - Conditional arithmetic

## See Also

- **[Operators Reference](/l4/reference/operators.md)** - Full operator documentation
- **[Types: NUMBER](/l4/reference/types.md)** - Numeric types
- **[Syntax: Precedence](/l4/reference/syntax.md)** - Operator precedence rules