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Project: Fractions

Unit: DelphiDabbler.Lib.Fractions

Record: TFraction

Applies to: ~>0.1

``````class operator Modulus(const A, B: TFraction): TFraction;
``````

## Description

This operator overload permits the `mod` operator to be applied to TFraction operands. It calculates the remainder after dividing A by B.

The result of the operation is returned as a new TFraction instance, reduced to its lowest terms.

One of the operands may be either an integer or floating point value. The Implicit operator takes care of converting the integer and floating point operands to a TFraction before performing the modulus operation.

The second operand must not be zero. In the case of a TFraction this means the Numerator must not be zero.

### Example

``````var
F1, F2, FRes: TFraction;
begin
// 7/8 mod 1/3 = 7/8 - 2 * 1/3 = 7/8 - 2/3 = 21/24-16/24 = 5/24
F1 := TFraction.Create(7, 8);
F2 := TFraction.Create(1, 3);
FRes := F1 mod F2;
Assert(FRes.Numerator = 5) and (FRes.Denominator = 24));

// 4/3 mod 2/3 = 4/3 - 2 * 2/3 = 4/3 - 4/3 = 0
F1 := TFraction.Create(4, 3);
F2 := TFraction.Create(2, 3);
FRes := F1 mod F2;
Assert(FRes.Numerator = 0) and (FRes.Denominator = 1));

// 32/5 mod 3 = 32/5 - 2 * 3 = 32/5 - 6/1 = 32/5 - 30/5 = 2/5
F1 := TFraction.Create(32, 5);
FRes := F1 mod 3;
Assert(FRes.Numerator = 2) and (FRes.Denominator = 5));

// 5 mod 2/3 = 5 - 7 * 2/3 = 5/1 - 14/3 = 15/3 - 14/3 = 1/3
F2 := TFraction.Create(2, 3);
FRes := 5 mod F2;
Assert(FRes.Numerator = 1) and (FRes.Denominator = 3));

// 10 7/8 mod 3.75 = 87/8 mod 15/4 = 87/8 mod 30/8 = 87/8 - 60/8 = 27/8
F1 := TFraction.Create(87, 8);
FRes := F1 mod 3.75;
Assert(FRes.Numerator = 27) and (FRes.Denominator = 8));
end;
``````