The first equals 8/3, the second equals 2/3. Thus (a – b) – c does not equal a – (b – c). The first equals 1/24, the second equals 1/12. However, if the order of the numbers is changed in subtraction and division, the result will vary as well. The associative characteristic of rational numbers asserts that no matter how numbers are grouped, the outcome remains the same when any three rational numbers are added or multiplied. The first equals 4/3, and the second equals 3/4. With division: 1/3 ÷ 1/4 is not the same as 1/4 ÷ 1/3.With multiplication: 1/3 x 1/4 and 1/4 x 1/3 both equal 1/12.The first equals 1/12 while the second is -1/12. With subtraction: 1/3 – 1/4 is not the same as 1/4 – 1/3.With addition: 1/3 + 1/4 is the same as 1/4 + 1/3 as both equal 7/12.The commutative property of rational numbers states that adding or multiplying any two rational numbers in any order produces the same result. When two rational numbers are combined in any way together, the outcome is another rational number.Īll the above answers meet the criteria for a rational number. Let’s look at how this property affects all of the basic arithmetic operations. The closure property of rational numbers asserts that any two rational numbers added, subtracted, multiplied, or divided will produce a rational number in all four circumstances. Let’s take a closer look at these characteristics whilst also exploring a list of rational numbers. The following are some of the most important properties of rational numbers.

Whole numbers are fractions, decimals, and negative values that are not included in real numbers. A set of numbers that includes all positive integers and 0 is known as a whole number. Whole Numbersīecause every whole number can be written as a fraction, every whole number is a rational number. A collection of real numbers is made up of these many types of numbers. Natural numbers are used to count things, rational numbers are used to represent fractions, irrational numbers are used to calculate the square root of a number, and integers are used to measure temperature, among other things.

A real number is one that can be discovered in the real world. Real numbers include all rational numbers. If the numerator and denominator have a different sign (i.e., one is a positive integer and the other is a negative integer), the rational number is said to be negative.įor example, the following rational numbers are negative: -1/7, 4/5, -25/11, 10/19, -13/23 while these rational numbers are positive: -11/-14, 2/3, -3/-4, and 1/2. In this case, 0.2 can be expressed as 1/5 and 6 as 6/1. Positive rational numbers include figures like 0.2, 6 or 2/5. In other words, if the numerator and denominator of a rational number have the same sign, it is positive. If the numerator and denominator of a rational number are both positive integers or both negative integers, the number is said to be positive. Here are the different types of rational numbers: Positive rational numbers We should not assume that only rational numbers are fractions with integers. All rational numbers are whole numbers.ĭifferent sets of rational numbers exist.We can determine whether the number’s decimal expansion is terminating or non-terminating.The given number can be represented as a fraction of integers.To determine whether a given number is rational, check if it meets any of the following criteria: As a result, each of these figures is a rational figure. Because it is non-recurring and non-terminating, 0.212112111…is an irrational number.Ī rational number can be expressed as a fraction of integers.Because it cannot be simplified, the square root of 2 is an irrational number.Π is an irrational number as it is a non-repeating, never-ending number.

The denominator of 5/0 is zero, making it an irrational number.0.7777777 is a rational number with recurring decimals.√81 is a rational number since it can be reduced to 9.In all terminating decimal forms, 0.5 can be written as 1/2, 5/10, or 10/20.The number 9 can be expressed as 9/1, with both 9 and 1 being integers.

Are all rational numbers real numbers