---
title: Rational
---

Utilities for working with the Rational type.

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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```grain
from "rational" include Rational
```

```grain
1/2r
```

```grain
3/4r
```

## Values

Functions and constants included in the Rational module.

### Rational.**fromNumber**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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```grain
fromNumber: (number: Number) => Rational
```

Converts a Number to a Rational.

Parameters:

| param    | type     | description          |
| -------- | -------- | -------------------- |
| `number` | `Number` | The value to convert |

Returns:

| type       | description                          |
| ---------- | ------------------------------------ |
| `Rational` | The Number represented as a Rational |

### Rational.**toNumber**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
toNumber: (rational: Rational) => Number
```

Converts a Rational to a Number.

Parameters:

| param      | type       | description          |
| ---------- | ---------- | -------------------- |
| `rational` | `Rational` | The value to convert |

Returns:

| type     | description                          |
| -------- | ------------------------------------ |
| `Number` | The Rational represented as a Number |

### Rational.**numerator**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
numerator: (x: Rational) => Number
```

Finds the numerator of the rational number.

Parameters:

| param | type       | description                    |
| ----- | ---------- | ------------------------------ |
| `x`   | `Rational` | The rational number to inspect |

Returns:

| type     | description                          |
| -------- | ------------------------------------ |
| `Number` | The numerator of the rational number |

### Rational.**denominator**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
denominator: (x: Rational) => Number
```

Finds the denominator of the rational number.

Parameters:

| param | type       | description                    |
| ----- | ---------- | ------------------------------ |
| `x`   | `Rational` | The rational number to inspect |

Returns:

| type     | description                            |
| -------- | -------------------------------------- |
| `Number` | The denominator of the rational number |

### Rational.**toIntegerRatio**

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<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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```grain
toIntegerRatio: (x: Rational) => (Number, Number)
```

Gets the numerator and denominator of the rational.

Parameters:

| param | type       | description           |
| ----- | ---------- | --------------------- |
| `x`   | `Rational` | The rational to split |

Returns:

| type               | description                                   |
| ------------------ | --------------------------------------------- |
| `(Number, Number)` | The numerator and denominator of the rational |

Examples:

```grain
Rational.toIntegerRatio(1/2r) == (1, 2)
```

```grain
Rational.toIntegerRatio(2/8r) == (1, 4)
```

### Rational.**fromIntegerRatio**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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```grain
fromIntegerRatio: (numerator: Number, denominator: Number) => Rational
```

Creates a rational from a numerator and denominator.

Parameters:

| param         | type     | description     |
| ------------- | -------- | --------------- |
| `numerator`   | `Number` | The numerator   |
| `denominator` | `Number` | The denominator |

Returns:

| type       | description          |
| ---------- | -------------------- |
| `Rational` | The reduced rational |

Throws:

`InvalidArgument(String)`

* If the numerator is not an integer
* If the denominator is not an integer

Examples:

```grain
Rational.fromIntegerRatio(1, 2) == 1/2r
```

```grain
Rational.fromIntegerRatio(2, 8) == 1/4r
```

### Rational.**(+)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(+): (x: Rational, y: Rational) => Rational
```

Computes the sum of its operands.

Parameters:

| param | type       | description        |
| ----- | ---------- | ------------------ |
| `x`   | `Rational` | The first operand  |
| `y`   | `Rational` | The second operand |

Returns:

| type       | description                 |
| ---------- | --------------------------- |
| `Rational` | The sum of the two operands |

Examples:

```grain
use Rational.{ (+) }
assert 1/2r + 1/4r == 3/4r
```

### Rational.**(-)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(-): (x: Rational, y: Rational) => Rational
```

Computes the difference of its operands.

Parameters:

| param | type       | description        |
| ----- | ---------- | ------------------ |
| `x`   | `Rational` | The first operand  |
| `y`   | `Rational` | The second operand |

Returns:

| type       | description                        |
| ---------- | ---------------------------------- |
| `Rational` | The difference of the two operands |

Examples:

```grain
use Rational.{ (-) }
assert 1/2r - 1/4r == 1/4r
```

### Rational.**(*)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(*): (x: Rational, y: Rational) => Rational
```

Computes the product of its operands.

Parameters:

| param | type       | description        |
| ----- | ---------- | ------------------ |
| `x`   | `Rational` | The first operand  |
| `y`   | `Rational` | The second operand |

Returns:

| type       | description                     |
| ---------- | ------------------------------- |
| `Rational` | The product of the two operands |

Examples:

```grain
use Rational.{ (*) }
assert 1/2r * 1/4r == 1/8r
```

### Rational.**(/)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(/): (x: Rational, y: Rational) => Rational
```

Computes the quotient of its operands.

Parameters:

| param | type       | description        |
| ----- | ---------- | ------------------ |
| `x`   | `Rational` | The first operand  |
| `y`   | `Rational` | The second operand |

Returns:

| type       | description                      |
| ---------- | -------------------------------- |
| `Rational` | The quotient of the two operands |

Examples:

```grain
use Rational.{ (/) }
assert 1/2r / 1/4r == 2/1r
```

### Rational.**(==)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(==): (x: Rational, y: Rational) => Bool
```

Checks if the first value is equal to the second value.

Parameters:

| param | type       | description      |
| ----- | ---------- | ---------------- |
| `x`   | `Rational` | The first value  |
| `y`   | `Rational` | The second value |

Returns:

| type   | description                                                                 |
| ------ | --------------------------------------------------------------------------- |
| `Bool` | `true` if the first value is equal to the second value or `false` otherwise |

Examples:

```grain
use Rational.{ (==) }
assert 1/2r == 1/2r
```

### Rational.**(!=)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(!=): (x: Rational, y: Rational) => Bool
```

Checks if the first value is not equal to the second value.

Parameters:

| param | type       | description      |
| ----- | ---------- | ---------------- |
| `x`   | `Rational` | The first value  |
| `y`   | `Rational` | The second value |

Returns:

| type   | description                                                                     |
| ------ | ------------------------------------------------------------------------------- |
| `Bool` | `true` if the first value is not equal to the second value or `false` otherwise |

Examples:

```grain
use Rational.{ (!=) }
assert 1/2r != 1/4r
```

### Rational.**(<)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(<): (x: Rational, y: Rational) => Bool
```

Checks if the first value is less than the second value.

Parameters:

| param | type       | description      |
| ----- | ---------- | ---------------- |
| `x`   | `Rational` | The first value  |
| `y`   | `Rational` | The second value |

Returns:

| type   | description                                                                  |
| ------ | ---------------------------------------------------------------------------- |
| `Bool` | `true` if the first value is less than the second value or `false` otherwise |

Examples:

```grain
use Rational.{ (<) }
assert 1/4r < 1/2r
```

### Rational.**(>)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(>): (x: Rational, y: Rational) => Bool
```

Checks if the first value is greater than the second value.

Parameters:

| param | type       | description      |
| ----- | ---------- | ---------------- |
| `x`   | `Rational` | The first value  |
| `y`   | `Rational` | The second value |

Returns:

| type   | description                                                                     |
| ------ | ------------------------------------------------------------------------------- |
| `Bool` | `true` if the first value is greater than the second value or `false` otherwise |

Examples:

```grain
use Rational.{ (>) }
assert 1/2r > 1/4r
```

### Rational.**(<=)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
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</details>

```grain
(<=): (x: Rational, y: Rational) => Bool
```

Checks if the first value is less than or equal to the second value.

Parameters:

| param | type       | description      |
| ----- | ---------- | ---------------- |
| `x`   | `Rational` | The first value  |
| `y`   | `Rational` | The second value |

Returns:

| type   | description                                                                              |
| ------ | ---------------------------------------------------------------------------------------- |
| `Bool` | `true` if the first value is less than or equal to the second value or `false` otherwise |

Examples:

```grain
use Rational.{ (<=) }
assert 1/4r <= 1/2r
```

```grain
use Rational.{ (<=) }
assert 1/2r <= 1/2r
```

### Rational.**(>=)**

<details disabled>
<summary tabindex="-1">Added in <code>0.6.0</code></summary>
No other changes yet.
</details>

```grain
(>=): (x: Rational, y: Rational) => Bool
```

Checks if the first value is greater than or equal to the second value.

Parameters:

| param | type       | description      |
| ----- | ---------- | ---------------- |
| `x`   | `Rational` | The first value  |
| `y`   | `Rational` | The second value |

Returns:

| type   | description                                                                                 |
| ------ | ------------------------------------------------------------------------------------------- |
| `Bool` | `true` if the first value is greater than or equal to the second value or `false` otherwise |

Examples:

```grain
use Rational.{ (>=) }
assert 1/2r >= 1/4r
```

```grain
use Rational.{ (>=) }
assert 1/2r >= 1/2r
```