Pre-Algebra : Number Theory

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #51 : Number Theory

Which if the following is not an integer?

Possible Answers:

None of the other answers.

Correct answer:

None of the other answers.

Explanation:

Integers comprise negative numbers as well as positive numbers. Even zero is an integer. The caveat of integers is that they must be able to be expressed without fractions. They have to be whole. While   is a fraction, it is equivalent to 1, which is a whole number.

Example Question #52 : Number Theory

Which of the following is an integer?

Possible Answers:

Correct answer:

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  since simplifying this root will yield .

The correct answer is:  

Example Question #53 : Number Theory

Simplify, if possible:  

Possible Answers:

The expression is already simplified

Correct answer:

Explanation:

Combine like-terms.  

The square roots cannot be combined unless they are multiplied, which means they must be separate terms.

The answer is:  

Example Question #54 : Number Theory

Which of the following is NOT an integer?

Possible Answers:

Correct answer:

Explanation:

An integer is a whole number, or a number that is not a fraction.

Therefore, since   is a fraction, it is NOT an integer.

Example Question #55 : Number Theory

Which of the following is NOT a natural number?

Possible Answers:

Correct answer:

Explanation:

Natural numbers are numbers are referred to as counting numbers or positive integers.  When we count objects, we do not include the number zero.  Therefore, the number zero is NOT a natural number.

Example Question #56 : Number Theory

Which of the following is an integer?

Possible Answers:

Correct answer:

Explanation:

Which of the following is an integer?

An integer is any positive or negative whole number including zero.

So, the only integer provided must be "4," because no other option fits the definition.

Example Question #57 : Number Theory

Which set of numbers is considered to be whole numbers? Choose the best answer.

 

Possible Answers:

Correct answer:

Explanation:

Whole numbers are considered any positive whole number including 0.

The best answer is : 

Example Question #1 : The Number System

Which of the following expressions is irrational?

Possible Answers:

Correct answer:

Explanation:

An irrational number is defined as any number that cannot be expressed as a simple fraction or does not have terminating or repeating decimals. Of the answer choices given, the only number that cannot be expressed as a simple fraction or with repeating or terminating decimals is .

 

Example Question #2 : The Number System

Which of the following is an irrational number?

Possible Answers:

Correct answer:

Explanation:

An irrational number is any number that can not be expressed as a ratio of integers, i.e. a fraction. Therefore, the only irrational number listed is .

Example Question #3 : The Number System

Which of these expressions is not irrational?

Possible Answers:

Correct answer:

Explanation:

The square root of an integer is either an irrational number or an integer. The latter is the case if and only if there is an integer which, when multiplied by itself, or squared, yields the number inside the symbol (the radicand) as the product. Of , only 81 is the square of an integer (9).

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