Integers and Types of Numbers - Pre-Algebra

Natural numbers are the counting numbers from to 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 number is an integer.

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 , which can be easily checked by plugging in any two even numbers.

For example, if , which is odd.

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

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

Integers are all counting numbers, and include both and all negative counting numbers. Thus, keeping this definition in mind, we can see that the value which is not an integer is since it has digits after the decimal point.

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.

An integer is any number without a fractional component, such as the following:

A whole number is any positive number with no fractional component, such as the following:

The major difference between the two groups of numbers is that there are no negative whole numbers, while there are negative integers.

The first step of this problem is to eliminate any choices that are not integers. The choices , , and , are all fractions or contain fractional components, so none of these values can be considered integers.

Of the remaining choices, falls under the categories of whole number and integer, so it cannot be the answer.

fufills both requirements of the question. It is an integer by having no fractional component, and it is not a whole number because it is a negative value, so it must be the correct answer.

A number is rational if it is possible to express it as a fraction with integers as the numerator and denominator. 25 and -1 are integers, and could be written as fractions: . is already expressed as a fraction. At first glance,

looks like an irrational number becasue it repeats forever. This is different from an irrational number because an irrational number will go on forever but without a repeating pattern. could actually be expressed as the fraction . This leaves us with the correct answer of which goes on forever \[is non-terminating\] but without any clear pattern or repeating part.

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.

An integer is a number that is whole and doesn't have a decimal or a fraction. The number can be positive, negative, or zero.

An integer is a number that has no decimals or fractions. They must be whole numbers whether positive, negative or zero. is an irrational number which means it doesn't have a definite value. All the other choices have definite value.

Positive integers start from one onward. No matter what number you multiply with, the answer is always positive and an integer. A positive integer multiplied by a positive integer is always a positive integer.

Natural numbers are numbers that occur naturally meaning they range from zero onwards. Negative numbers dont occur naturally.

When you add two negative numbers, the answer is always negative. When adding negative numbers, we treat as an addition problem but we need to add the negative sign afterwards. Two negative numbers can never add to zero.

For a number to be rational, the numerator and denominator have to be integers. The exception is the denominator must not equal zero. It can be negative, positive, or zero.

All the numbers are irrational numbers. They are basically numbers that can't be expressed as fractions. They dont have definite values. is an imaginary number that contains the letter .

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.

It is true when we divide two rational numbers, we should get a rational number. The exception is when let's say we divide and . If the denominator is , the answer is undefined. Undefined is a class of its own. This is the only exception so our answer is mostly rational numbers.

Counting numbers are numbers you can count with your hands. We start from one and onward. They are the same as positive integers.

Example of prime numbers are . Their factors are one and itself. They are also positive integers.