Pre-Algebra : Integers and Types of Numbers

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #31 : Integers And Types Of Numbers

What is a composite number?

Possible Answers:

A positive integer with at least one other factor besides one and itself

Cubic numbers

A positive integer with just factors of one and itself

Irrational numbers

Negative integers

Correct answer:

A positive integer with at least one other factor besides one and itself

Explanation:

Composite numbers have at least one factor other than one and itself. For example,  is a composite number. The factors are 

Example Question #41 : Number Theory

What do you get when you multiply an even number with an odd number?

Possible Answers:

Prime number

Irrational number

Imaginary number

Even number

Odd number

Correct answer:

Even number

Explanation:

For example, take an even number like  and an odd number like . Their product is  which is an even number. No matter what examples we use; we will find that the answer is always even. Furthermore, it can never be a square number because the multiplicand and multiplier will be two different numbers (one odd and one even).

Example Question #32 : Integers And Types Of Numbers

What kind of number is ?

I. rational

II. irrational

III. integer

IV. imaginary

V. composite

Possible Answers:

III and V only

and III only

II, IV

I, III, V

II only

Correct answer:

I, III, V

Explanation:

Even though it's a radical, we can simplify.

Check the answer.

The answer is 

 is an integer and a composite number with factors of . Furthermore, it can be expressed a rational number .

Thus, the final answer is I, III, V.

Example Question #43 : Number Theory

Which is a square number?

Possible Answers:

Correct answer:

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

Example Question #44 : Number Theory

What are odd numbers?

Possible Answers:

Integers that have a ones digit that ends in , or  

All the digits of the integer must have , or   

Integers that have a ones digit that ends in , or  

Integers that have a ones digit that ends in , or 

Integers that have a ones digit that ends in , or  

Correct answer:

Integers that have a ones digit that ends in , or 

Explanation:

In order to determine if a number is odd, we will check the ones digit. It must contain , or . The answer is integers that have a ones digit that ends in , or 

Example Question #33 : Integers And Types Of Numbers

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

Possible Answers:

Correct answer:

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. 

Example Question #34 : Integers And Types Of Numbers

Which of the following is an odd number?

I. 

II. 

III. 

IV. 

V. 

Possible Answers:

II, V

I, III, V

II, III, IV

I, III, IV

II, III, V

Correct answer:

II, III, V

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. 

Example Question #35 : Integers And Types Of Numbers

What is the product of two nonidentical prime numbers?

Possible Answers:

Composite number

Square number

Zero

Prime number

Cubic number

Correct answer:

Composite number

Explanation:

When you take two prime numbers, you are creating a composite number. A compositie number has at least one more factor than one and itself. Since you multiply two prime numbers, you are increasing the factors of the new number. 

Example Question #47 : Number Theory

What do you get when you divide two negative integers?

Possible Answers:

Integers

Zero

Irrational number

One

Rational numbers

Correct answer:

Rational numbers

Explanation:

For example, we can take the negative integers  and . When we divide , we get an answer of . This is an integer and a rational number. However, if we reverse it , we get an answer of . This is not an integer but it is a rational number. Integers can be rational numbers as they are expressed as any number over one. Futhermore, rational numbers are defined as the expression of any quotient or fraction possessing a non-zero denominator. Thus, our answer is rational numbers. 

Example Question #36 : Integers And Types Of Numbers

Given the following set of numbers:

Which numbers in the set are whole numbers?

Possible Answers:

Correct answer:

Explanation:

A whole number is any number without a fraction or decimal, but negative numbers are NOT whole numbers. Therefore, the only correct choices from this set are  and , which are neither negative nor have decimals. 

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