Which of the following statements is true if p is an internet and q is a nonzero integer? a. an irrational number can be written as a fraction p/q. b. a rational number can not be written as a fraction p/q. c. all numbers can be written as a fraction p/q. d. a rational number can be written as a fraction p/q.

D. A rational number can be written as a fraction p/q

Step-by-step explanation:

All real numbers are classified into two major categories namely rational and irrational numbers.

A number which can be written in the form , p and q are integers and q ≠ 0 is called a rational number.

Ex:

is a rational number

5 is a rational number since 5 can be written as and clearly, 1 ≠ 0

0 is also rational since 0 can be written as .

A number which cannot be written in the form is called an irrational number.

Ex:

is an irrational number since it cannot be written in form,

Hence, the correct option is D.

The remainder when 4z is divided by 8 is 4

From the question, when z is divide by 8, the remainder is 5. But we do not know the quotient.

From the formula

Here, the dividend is z, divisor is 8, and the remainder is 5.

Let the quotient be x, then we can write that

Now, to determine the remainder when 4z is divided by 8,

Multiply both sides of the equation by 4

Then,

(NOTE: must be a proper fraction)

Compare this to the formula

The remainder is 4

Hence, the remainder when 4z is divided by 8 is 4.

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