Fill the blanks in the table Numbers Closed property under Addition Subtraction Multiplication Division Natural numbers Yes Whole numbers No Integers Yes Rational numbers Yes

Numbers Closed property under Addition Subtraction Multiplication Division Natural numbers Yes No Yes No Whole numbers Yes No Yes No Integers Yes Yes Yes No Rational numbers Yes Yes Yes No When one whole number is subtracted from another, the difference is not always a whole number. This means that the whole numbers are not closed under subtraction.This set is closed only under addition and multiplication An integer is a number that can be written without a fractional component. For example 21 , 0 , - 5 , 11 and − 2786 are integers, while 9 . 75 , 5 4 , and √ 2 are not. The integers are "closed" under addition, multiplication and subtraction, but NOT under division ( 7 ÷ 2 = 3 1 2 ). (a fraction) between two integers. Integers are rational numbers since 7 can be written as the fraction 7 1 . The natural numbers are "closed" under addition and multiplication. A set is closed if and only if the operation on any two elements of the set produces another element of the same set.The division of two natural numbers does NOT necessarily create another natural number ( 1 ÷ 2 = 1 2 ). The rational numbers are "closed" under addition, subtraction, and multiplication. Under division, we run into the problem of division by 0 , which makes the statement that "the rationals are closed under division" false.

Complete the following table. Numbers Commutative with respect to Addition Subtraction Multiplication Division Natural numbers Yes No Yes Whole numbers No Integers Rational numbers No

Numbers Commutative with respect to Addition Subtraction Multiplication Division Natural numbers Yes No Yes No Whole numbers Yes No Yes No Integers Yes No Yes No Rational numbers Yes No Yes No The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is " a + b = b + a "; in numbers, this means 2 + 3 = 3 + 2 . For multiplication, the rule is " a × b = b × a "; in numbers, this means 2 × 3 = 3 × 2 . Whole Numbers - Addition and multiplication of Whole numbers show the commutative property. For example, x + y = y + x and a × b = b × a . Subtraction and division of Whole numbers does not show the commutative property. Integers - Addition and multiplication of Integers show the commutative property. For example, x + y = y + x and a × b = b × a . Subtraction and division of Integers does not show the commutative property. Subtraction does not have a commutative property because a - b gives a different result than does b - a . For example, 3 – 2 = 1 , but 2 – 3 = - 1 . So in the case of subtraction, moving the numbers around produces a different answer. Rational Numbers - Addition and multiplication of Rational numbers show the commutative property. For example, x + y = y + x and a × b = b × a . Subtraction and division of Rational numbers does not show the commutative property.

Complete the following table. Numbers Associative under Addition Subtraction Multiplication Division Natural numbers Yes No Whole numbers No Integers No Yes Rational numbers

Complete the following table. Numbers Associative under Addition Subtraction Multiplication Division Natural numbers Yes No Yes No Whole numbers Yes No Yes No Integers Yes No Yes No Rational numbers Yes No Yes No The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Natural number - The associative property holds true in case of addition and multiplication of natural numbers i.e. a + ( b + c ) = ( a + b ) + c and a × ( b × c ) = ( a × b ) × c . On the other hand, for subtraction and division of natural numbers does not hold the associative property. Whole Number - When we multiply three or more whole numbers, the value of the product remains the same when they are grouped in any manner. The associative property of multiplication holds for whole numbers.Whole number also have associative properties in addition operation. Integers - Adding integers will have the same result regardless of the grouping. The sum will not change even if the integers are grouped differently. Rational Number - Take any three rational numbers a , b and c . Firstly add a and b and then add c to the sum.Addition and multiplication are associative for rational numbers. Subtraction and division are not associative for rational numbers.