Pre-Algebra : Number Theory

Study concepts, example questions & explanations for Pre-Algebra

varsity tutors app store varsity tutors android store

Example Questions

Example Question #2 :Integers And Types Of Numbers

Which of the following isnota natural number?

Possible Answers:

Correct answer:

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.

Example Question #1 :Integers And Types Of Numbers

Which of the following describes the number?

Possible Answers:

all of the other choices

whole number

natural number

integer

Correct answer:

integer

Explanation:

Natural numbers are the counting numbers fromto infinity (all positive numbers). Whole numbers are the natural numbers plus. Integers are the positive and negative counting numbers, including. Therefore, the most accurate term to describe the numberis an integer.

Example Question #4 :Integers And Types Of Numbers

Which of these numbers is an integer but not a whole number?

Possible Answers:

Correct answer:

Explanation:

The whole numbers are the elements of the set

.

The integers are the the elements of the set

.

The numbers that belong to the former but not the latter are exactly the set of negative integers. Of the given choices, onlyis such a number. It is the correct choice.

Example Question #5 :Integers And Types Of Numbers

Evaluate:

Possible Answers:

Correct answer:

Explanation:

First evaluate everything inside of the absolute value. 3-5=-2.

The absolute value then turns all negative numbers into a positive number, so the -2 becomes a positive 2.

Example Question #6 :Integers And Types Of Numbers

Ifaandbare even integers, what must be odd?

Possible Answers:

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

\dpi{100} \small a+b

\dpi{100} \small a\times b

\dpi{100} \small a-b

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

Correct answer:

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

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.

Example Question #7 :Integers And Types Of Numbers

What is the greatest prime factor of

Possible Answers:

Correct answer:

Explanation:

The only prime factors are 3 and 5, therefore, 5 will be the greatest prime factor.

Example Question #53 :High School Math

Isan integer, decimal, or a fraction?

Possible Answers:

Decimal

None

Integer

Fraction

Correct answer:

Fraction

Explanation:

A fraction is a number with a numerator and denominator that can not be simplified into an integer so the numberis a fraction.

Example Question #54 :High School Math

Which of the following is an integer?

Possible Answers:

1.5

-100.1

Correct answer:

Explanation:

Integers are any number that doesn't have anything in the decimal places. They are also known as whole numbers. The cubed root of 64 is 4, which is the only whole number out of the answer choices.

Example Question #55 :High School Math

Which of the following is NOT an integer?

Possible Answers:

-4

1024

Correct answer:

Explanation:

An integer is simply a whole negative or positive number, which means it can be expressed without decimal places. Any number can be considered an integer as long as it fits this criteria. They can be expressed as square roots, fractions, or anything else, as long as the final answer is a whole number. In this question, the only answer that is not a whole number is, which is 1.6.

Example Question #58 :High School Math

Which of the following isnotan integer?

Possible Answers:

Correct answer:

Explanation:

By definition, an integer is a whole number that is either positive or negative. Negative numbers such asandare integers, as are 10 and 5.

, however, is not an integer because it isn't a whole number.

Learning Tools by Varsity Tutors