Pre-Algebra - Integers and Types of Numbers

Which of the following is an odd number?

II.

III.

IV.

II, III, V

I, III, IV

II, V

I, III, V

II, III, IV

Explanation

Odd numbers are integers that have a ones digit that ends in , , , , or . Choices II, III, V are odd numbers because they have a ones digit of , , and respectively.

Which of the following is an integer?

$\sqrt {25}$

$2\pi$

$\textup{No integers are given.}$

Explanation

The correct answer will yield a whole number as a simplified answer. Integers cannot contain decimals quantities.

The only answer that will yield a whole number term is $\sqrt {25}$ since simplifying this root will yield $\pm5$ .

The correct answer is: $\sqrt {25}$

Which is a square number?

Explanation

Square numbers have one factor. If that factor is multiplied by itself, then the number becomes a perfect square. The only number in the selection that meets this requirement is . We can multiply twice to get the perfect square .

What kind of number is $\sqrt{16}$ ?

I. rational

II. irrational

III. integer

IV. imaginary

V. composite

I, III, V

II, IV

II only

III and V only

I and III only

Explanation

Even though it's a radical, we can simplify $\sqrt{16}$ .

$\sqrt{16}=4$

Check the answer.

The answer is .

is an integer and a composite number with factors of . Furthermore, it can be expressed a rational number $(4=\frac{4}{1})$ .

Thus, the final answer is I, III, V.

Which is an integer?

$\sqrt{9}$

$\sqrt{8}$

$\sqrt{6}$

$\sqrt{12}$

$\sqrt{54}$

Explanation

Although all the choices have radicals and we know many radicals are irrational numbers, we can definitely simplify one of them. is a perfect sqaure. The answer to that radical is . is an integer and is our answer.

is an example of _____________.

an integer

an irrational number

a decimal

a fraction

a complex number

Explanation

An integer is any positive or negative whole number.

Therefore, is an integer.

Which of the following is not a natural number?

Explanation

Natural numbers are considered the "counting numbers". They are all of the integers from 1 until infinity. 0 and negative integers are not natural numbers, therefore, the answer to this problem is .

If a and b are even integers, what must be odd?

$\dpi{100} \small a+b-1$

$\dpi{100} \small a+b$

$\dpi{100} \small a\times b$

$\dpi{100} \small a-b$

$\dpi{100} \small a+b-2$

Explanation

The sum (or difference) or 2 even integers is even. Similarly, the product (or quotient) of 2 even integers is also even; therefore the answer must be $\dpi{100} \small a+b-1$ , which can be easily checked by plugging in any two even numbers.

For example, if $\dpi{100} \small a=2\ and\ b=4,\ a+b-1=2+4-1=5$ , which is odd.

What number is found in the set of whole numbers but not in the set of natural numbers?

$\pi$

$\frac{1}{2}$

Explanation

Whole numbers start from and include all positive integers. On the other hand, natural numbers are all positive integers that we can count starting from . The only difference is that is found in whole numbers but not in the natural numbers series. Thus, is the correct answer.