Math from Words

Chapter Ten - Division

And

Rational Numbers

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**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*.

**Definition** - A *variable* is a number selected from a set of numbers.

**Definition** - A *function* is a rule that associates each permissible input number with one and only one output number.

**Definition** - The *domain of a function* is the set of the function's permissible input numbers.

**Definition** - The *range of a function* is the set of the function's output numbers.

**Definition** - The *independent variable of a function* is a variable whose value is selected from the domain of the function.

**Definition** - The *dependent variable of a function* is a variable whose value is selected from the range of the function.

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