# # Ratio Math Functions

These functions let you apply a **Ratio** (a fraction) to an amount, multiplying or
dividing an amount by a ratio of two natural numbers.

The Ratio Math functions have to be imported.

## # assertIsRatio(ratio)

**ratio**:**Ratio**- Returns: None.

Throws an error if the argument is not a valid **Ratio**.

Throws messages for errors:

**Ratio ${ratio} must be a record with 2 fields.****Parameter must be a Ratio record, but ${ratio} has ${q(name)**

```
assertIsRatio(aRatio);
```

## # makeRatio(numerator, numeratorBrand, denominator?, denominatorBrand?)

**numerator**:**BigInt****numeratorBrand**:**Brand****denominator**:**BigInt**- Optional, defaults to 100n.**denominatorBrand)**:**Brand**- Optional, defaults to the*numeratorBrand*value.- Returns:
**Ratio**

Returns a **Ratio** based on the arguments passed into the function.

By default, the *denominator* is 100n (i.e., the **Ratio** is a percent).

```
// Use default values to create a ratio of 50 / 100 Quatloos
const ratio = makeRatio(50n, quatloosBrand);
// Specify all values to create a ratio of 75 Quatloos / 4 Moolas (the current exchange rate)
const ratio = makeRatio(75n, quatloosBrand, 4n, moolasBrand);
```

## # makeRatioFromAmounts(numeratorAmount, denominatorAmount)

Returns a **Ratio**, representing a fraction and consisting of an immutable pair
of two **Amounts**. The *numeratorAmount* is the **Ratio's** numerator and
the *denominatorAmount* is the **Ratio's** denominator.

```
const fiftyCents = AmountMath.make(centsBrand, 50n);
const dollar = AmountMath.make(centsBrand, 100n);
const halfADollar = makeRatioFromAmounts(fiftyCents, dollar);
```

## # floorMultiplyBy(amount, ratio)

Returns an immutable **Amount**. Its **Brand** is the *ratio*'s
numerator's **Brand**. Note that the denominator **Brand** has to be the same as the *amount* **Brand**.

The resulting **Amount** is determined by:

- Multiplying the
*amount*value by the*ratio*'s numerator's value. - Dividing the result from step 1 by the
*ratio*'s denominator's value. - If that results in an integer, that value is returned. Otherwise, the value is rounded down to the next integer.

For example, if the *amount* value is 47 and the *ratio* is 3 / 5, the calculation
would go

- 47 * 3 = 141
- 141 / 5 = 28.2
- Floor(28.2) = 28

Throws errors with messages:

**Expected an amount: ${amount})**: First argument isn't an**Amount**.**amount's brand ${q(amount.brand)} must match ratio's denominator ${q( ratio.denominator.brand**: The amount and ratio's denominator must have the same brand.

```
const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 28 Swiss francs
const exchange = floorMultiplyBy(dollars47, exchangeRatio);
```

## # ceilMultiplyBy(amount, ratio)

Returns an immutable **Amount**. Its **Brand** is the *ratio*'s
numerator's **Brand**. Note that the denominator **Brand** has to be the same as the *amount* **Brand**.

The resulting **Amount** is determined by:

- Multiplying the
*amount*value by the*ratio*'s numerator's value. - Dividing the result from step 1 by the
*ratio*'s denominator's value. - If that results in an integer, that value is returned. Otherwise, the value is rounded up to the next integer.

For example, if the *amount* value is 47 and the *ratio* is 3 / 5, the calculation
would go

- 47 * 3 = 141
- 141 / 5 = 28.2
- Ceiling(28.2) = 29

Throws errors with messages:

**Expected an amount: ${amount})**: First argument isn't an**Amount**.**amount's brand ${q(amount.brand)} must match ratio's denominator ${q( ratio.denominator.brand**: The amount and ratio's denominator must have the same brand.

```
const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 29 Swiss francs
const exchange = ceilMultiplyBy(dollars47, exchangeRatio);
```

## # multiplyBy(amount, ratio)

Returns an immutable **Amount**. Its **Brand** is the *ratio*'s
numerator's **Brand**. Note that the denominator **Brand** has to be the same as the *amount* **Brand**.

The resulting **Amount** is determined by:

- Multiplying the
*amount*value by the*ratio*'s numerator's value. - Dividing the result from step 1 by the
*ratio*'s denominator's value. - If that results in an integer, that value is returned. Otherwise, the value is rounded to the nearest integer according to banker's rounding rules (opens new window).

For example, if the *amount* value is 47 and the *ratio* is 3 / 5, the calculation
would go

- 47 * 3 = 141
- 141 / 5 = 28.2
- BankersRounding(28.2) = 28

Throws errors with messages:

**Expected an amount: ${amount})**: First argument isn't an**Amount**.**amount's brand ${q(amount.brand)} must match ratio's denominator ${q( ratio.denominator.brand**: The amount and ratio's denominator must have the same brand.

```
const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 28 Swiss francs
const exchange = multiplyBy(dollars47, exchangeRatio);
```

## # floorDivideBy(amount, ratio)

Returns an immutable **Amount**. Its **Brand** is the *ratio*'s denominator's **Brand**.

The resulting value is determined by:

- Multiplying the
*amount*value by the*ratio*'s denominator's value. - Dividing the result from step 1 by the
*ratio*'s numerator's value. - If that results in an integer, that value is returned. Otherwise, the value is rounded down to the next integer.

For example, if the *amount* value is 47 and the *ratio* is 3 / 5, the calculation
would go

- 47 * 5 = 235
- 235 / 3 = 78.33333...
- Floor(78.3333...) = 78

Throws errors with messages:

**Expected an amount: ${amount})**: First argument isn't an**Amount**.**amount's brand ${q(amount.brand)} must match ratio's numerator ${q(ratio.numerator.brand**: The amount and ratio's numerator must have the same brand.

```
const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 78 dollars
const exchange = floorDivideBy(dollars47, exchangeRatio);
```

## # ceilDivideBy(amount, ratio)

Returns an immutable **Amount**. Its **Brand** is the *ratio*'s denominator's **Brand**.

The resulting value is determined by:

- Multiplying the
*amount*value by the*ratio*'s denominator's value. - Dividing the result from step 1 by the
*ratio*'s numerator's value. - If that results in an integer, that value is returned. Otherwise, the value is rounded up to the next integer.

For example, if the *amount* value is 47 and the *ratio* is 3 / 5, the calculation
would go

- 47 * 5 = 235
- 235 / 3 = 78.33333...
- Ceiling(78.3333...) = 79

Throws errors with messages:

**Expected an amount: ${amount})**: First argument isn't an**Amount**.**amount's brand ${q(amount.brand)} must match ratio's numerator ${q(ratio.numerator.brand**: The amount and ratio's numerator must have the same brand.

```
const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 79 dollars
const exchange = ceilDivideBy(dollars47, exchangeRatio);
```

## # divideBy(amount, ratio)

Returns an immutable **Amount**. Its **Brand** is the *ratio*'s denominator's **Brand**.

The resulting value is determined by:

- Multiplying the
*amount*value by the*ratio*'s denominator's value. - Dividing the result from step 1 by the
*ratio*'s numerator's value. - If that results in an integer, that value is returned. Otherwise, the value is rounded to the nearest integer according to banker's rounding rules (opens new window).

For example, if the *amount* value is 47 and the *ratio* is 3 / 5, the calculation
would go

- 47 * 5 = 235
- 235 / 3 = 78.33333...
- BankersRounding(78.3333...) = 78

Throws errors with messages:

**Expected an amount: ${amount})**: First argument isn't an**Amount**.**amount's brand ${q(amount.brand)} must match ratio's numerator ${q(ratio.numerator.brand**: The amount and ratio's numerator must have the same brand.

```
const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 78 dollars
const exchange = divideBy(dollars47, exchangeRatio);
```

## # invertRatio(ratio)

**ratio**:**Ratio**- Returns:
**Ratio**

Returns a **Ratio** such that the *ratio* argument's numerator is the returned value's
denominator and the *ratio* argument's denominator is the returned value's numerator.

```
const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, usDollarBrand);
// Returns a ratio of 5 US dollars / 3 swiss Francs
const invertedRatio = invertRatio(exchangeRatio);
```

## # addRatios(left, right)

**left**:**Ratio****right**:**Ratio**- Returns:
**Ratio**

Returns a **Ratio** that's the sum of the *left* and *right* parameters.

The **Brands** of the *numerators* of *left* and *right* must be
identical. similarly, the **Brands** of the *denominators* of *left* and
*right* must also be identical. If either of these conditions aren't met, then no **Ratio** is returned
and an error is thrown instead.

If the *denominator* values aren't identical, then both **Ratios** are multiplied by the lowest common
denominator, and then the **Ratios** are added.

For example:

- Let's assume
*left*= {numerator: 44n kilometers, denominator: 3n hours} and*right*= {numerator: 25n kilometers, denominator: 2n hours}. *left*would be multiplied by 2/2, and*right*would be multiplied by 3/3, resulting in*left*= {numerator: 88n kilometers, denominator: 6n hours} and*right*= {numerator: 75n kilometers, denominator: 6n hours}*left*and*right*would then be added together, resulting in {numerator: 163n kilometers, denominator: 6n hours}. This**Ratio**would then be returned.

## # subtractRatios(left, right)

**left**:**Ratio****right**:**Ratio**- Returns:
**Ratio**

Returns a **Ratio** that's the result when the *right* parameter is subtracted from the *left* one.

The **Brands** of the *numerators* of *left* and *right* must be
identical. similarly, the **Brands** of the *denominators* of *left* and
*right* must also be identical. If either of these conditions aren't met, then no **Ratio** is returned
and an error is thrown instead.

If the *denominator* values aren't identical, then both **Ratios** are multiplied by the lowest common
denominator, and then *right* is subtracted from *left*.

For example:

- Let's assume
*left*= {numerator: 44n kilometers, denominator: 3n hours} and*right*= {numerator: 25n kilometers, denominator: 2n hours}. *left*would be multiplied by 2/2, and*right*would be multiplied by 3/3, resulting in*left*= {numerator: 88n kilometers, denominator: 6n hours} and*right*= {numerator: 75n kilometers, denominator: 6n hours}*right*would then be subtracted from*left*would then be added together, resulting in {numerator: 13n kilometers, denominator: 6n hours}. This**Ratio**would then be returned.

## # multiplyRatios(left, right)

**left**:**Ratio****right**:**Ratio**- Returns:
**Ratio**

Returns a **Ratio** that's the product of the *left* and *right* parameters.

The **Brands** of the *numerators* of *left* and *right* must be
identical. similarly, the **Brands** of the *denominators* of *left* and
*right* must also be identical. If either of these conditions aren't met, then no **Ratio** is returned
and an error is thrown instead.

## # oneMinus(ratio)

**ratio**:**Ratio**- Returns:
**Ratio**

Subtracts the *ratio* argument from 1 and returns the resultant **Ratio**.

This function requires the *ratio* argument to be between 0 and 1. It also requires the numerator and denominator **Brands** to be the same. If either of these conditions aren't met, an error is thrown and no **Ratio** is returned.

## # ratioGTE(left, right)

**left**:**Ratio****right**:**Ratio**- Returns:
**Boolean**

Returns **true** if *left* is larger than or equal to *right*, **false** otherwise.

An error is returned if the **Brands** of *left* and *right*
aren't identical.

## # ratiosSame(left, right)

**left**:**Ratio****right**:**Ratio**- Returns:
**Boolean**

Returns **true** if the *left* and *right* **Ratios** are the same, **false** otherwise. Note that for
the two **Ratios** to be considered the same, the
**Value** and **Brand**
of both the *numerator* and *denominator* of one **Ratio** must be identical to the **Value** and
**Brand** of the *numerator* and *denominator* of the other **Ratio**.

## # quantize(ratio, newDen)

**ratio**:**Ratio****newDen**:**BigInt**- Returns:
**Ratio**

Creates and returns a new **Ratio** that's equivalent to the *ratio* argument, but with a new denominator specified by the *newDen* argument.

## # parseRatio(numeric, numeratorBrand, denominatorBrand?)

**numeric**:**ParsableNumber****numeratorBrand**:**Brand****denominatorBrand**:**Brand**- Optional, defaults to*numeratorBrand*.- Returns:
**Ratio**

Creates a **Ratio** from the *numeric* argument, and returns that **Ratio**.

## # assertParsableNumber(specimen)

**specimen**:**Object**- Returns: None.

Throws an error if the argument is not a **ParsableNumber**.