Math from Words
Chapter Ten - Division
And
Rational Numbers

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Definition - The sign of an integer p is the plus sign (+) appended on the left, if p is a positive integer (+p), and the sign is the hyphen (-) appended on the left, if p is a negative integer (-p).

Definition - Integer C is integer A divided by integer B that is computed by the following procedure:

Procedure

Q is 0.

R is |A|.

AA. If R is less than |B|, Go to EE.

BB. |B| subtracted from R is the whole number that R becomes now.

CC. Increment Q.

DD. Go to AA.

EE. If both A and B, or neither A and ,B are less than 0, then Go to HH.

FF. The product of -1 and Q is the integer that Q becomes now.

GG. The product of -1 and R is the integer that R becomes now.

HH. Q is the integer that C becomes now.

II. C is the quotient, R is the remainder, and this procedure is ended.

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Definition - An item is a fraction if and only if it is an integer divided by an integer.

Definition - The numerator in the fraction that is integer A divided by integer B is the integer A.

Definition - The denominator in the fraction that is integer A divided by integer B is the integer B.

Notation - A fraction is notated this way: A/B.

Definition - A rational number is a fraction that is integer A divided by integer B, where B is not zero.

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Definition - The non-negative rational number A/B is greater than the non-negative rational number C/D if and only if the product of |A| and |D| is greater than the product of |B| and |C|.

Definition - The non-negative rational number A/B is always greater than the negative rational number C/D.

Definition - The negative rational number A/B is greater than the negative rational number C/D if and only if the product of |B| and |C| is greater than the product of |A| and |D|.

Definition - The negative rational number A/B is never greater than the non-negative rational number C/D.

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