{"id":7134,"date":"2022-04-01T10:57:22","date_gmt":"2022-04-01T05:27:22","guid":{"rendered":"http:\/\/conceptsdk.com\/?page_id=7134"},"modified":"2022-04-01T10:58:30","modified_gmt":"2022-04-01T05:28:30","slug":"integer","status":"publish","type":"page","link":"https:\/\/conceptsdk.com\/?page_id=7134","title":{"rendered":"Integer"},"content":{"rendered":"\n<p class=\"has-text-align-center has-white-color has-dark-blue-background-color has-text-color has-background wp-block-paragraph\"><strong>QUICK CONCEPT NOTES<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 You have studied in the earlier class, about the representation of integers on the number line and their addition and subtraction.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 We now study the properties satisfied by addition and subtraction.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(a) Integers are closed for addition and subtraction both. That is, a + b and a \u2013 b are again integers, where a and b are any integers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(b) Addition is commutative for integers, i.e., a + b = b + a for all integers a and b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(c) Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(d) Integer 0 is the identity under addition. That is, a + 0 = 0 + a = a for every integer a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 We studied, how integers could be multiplied, and found that product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer. For example, \u2013 2 \u00d7 7 = \u2013 14 and \u2013 3 \u00d7 \u2013 8 = 24.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 Product of even number of negative integers is positive, whereas the product of odd number of negative integers is negative.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Integers show some properties under multiplication.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(a) Integers are closed under multiplication. That is, a \u00d7 b is an integer for any two integers a and b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(b) Multiplication is commutative for integers. That is, a \u00d7 b = b \u00d7 a for any integers a and b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(c) The integer 1 is the identity under multiplication, i.e., 1 \u00d7 a = a \u00d7 1 = a for any integer a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(d) Multiplication is associative for integers, i.e., (a \u00d7 b) \u00d7 c = a \u00d7 (b \u00d7 c) for any three integers a, b and c.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 Under addition and multiplication, integers show a property called distributive property.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That is, a \u00d7 (b + c) = a \u00d7 b + a \u00d7 c for any three integers a, b and c.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 The properties of commutativity, associativity under addition and multiplication, and the distributive property help us to make our calculations easier.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 We also learnt how to divide integers. We found that.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(b) Division of a negative integer by another negative integer gives a positive integer as quotient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 For any integer a, we have<\/p>\n\n\n\n<ul class=\"has-dark-blue-color has-text-color wp-block-list\"><li>a \u00f7 0 &nbsp;is not defined<\/li><li>a \u00f7 1 = a<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>QUICK CONCEPT NOTES Integers are a bigger collection of numbers which is formed by whole numbers and their negatives. \u2022 You have studied in the earlier class, about the representation of integers on the number line and their addition and subtraction. \u2022 We now study the properties satisfied by addition and subtraction. (a) Integers are [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-7134","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/conceptsdk.com\/index.php?rest_route=\/wp\/v2\/pages\/7134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/conceptsdk.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/conceptsdk.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/conceptsdk.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/conceptsdk.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7134"}],"version-history":[{"count":1,"href":"https:\/\/conceptsdk.com\/index.php?rest_route=\/wp\/v2\/pages\/7134\/revisions"}],"predecessor-version":[{"id":7135,"href":"https:\/\/conceptsdk.com\/index.php?rest_route=\/wp\/v2\/pages\/7134\/revisions\/7135"}],"wp:attachment":[{"href":"https:\/\/conceptsdk.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}