Lesson 1-1 Properties of Real Number

Each quotient must have a denominator

A quotient is found by dividing two numbers and a quotient with a denominator of zero is infinity which is not a real number

The word that complete the sentence is therefore;

Each quotient must have a nonzero denominator

The reason by which the above word is selected is as follows;

The set of Real Numbers include;

Rational numbers; a/b, where b = nonzero number

Integers; Positive and negative whole numbers, including zero

Whole numbers; 0, 1, 2

Natural numbers; Positive whole numbers excluding zero

Irrational number; Numbers that cannot be expressed as a/b

A quotient is the outcome of dividing two numbers, x by y

Therefore;

Quotient = x/y

A quotient can be a rational or irrational number, however, a quotient that has a denominator of zero (y = 0) is infinity, which is not a real number

When y = 0, x/y = x/0 = ∞ (∞ is not a real number)

Therefore, from the properties of Real Numbers,

Each quotient must have a nonzero denominator to be a Real Number

Learn more about Real Numbers here;

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