{"id":9426,"date":"2017-05-02T22:26:55","date_gmt":"2017-05-02T22:26:55","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9426"},"modified":"2017-09-23T20:05:41","modified_gmt":"2017-09-23T20:05:41","slug":"summary-multiplying-and-dividing-integers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/summary-multiplying-and-dividing-integers\/","title":{"raw":"Summary: Multiplying and Dividing Integers","rendered":"Summary: Multiplying and Dividing Integers"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"fs-id2654796\">\r\n \t<li><strong>Multiplication of Signed Numbers<\/strong>\r\n<ul id=\"eip-id1168617323909\">\r\n \t<li>To determine the sign of the product of two signed numbers:\r\n<table id=\"eip-id1168467221297\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Same Signs<\/th>\r\n<th>Product<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Two positives\r\n\r\nTwo negatives<\/td>\r\n<td>Positive\r\n\r\nPositive<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468724040\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Different Signs<\/th>\r\n<th>Product<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Positive \u2022 negative\r\n\r\nNegative \u2022 positive<\/td>\r\n<td>Negative\r\n\r\nNegative<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Division of Signed Numbers<\/strong>\r\n<ul id=\"eip-id1172558648335\">\r\n \t<li>To determine the sign of the quotient of two signed numbers:\r\n<table id=\"eip-id1172558648339\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Same Signs<\/th>\r\n<th>Quotient<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Two positives\r\n\r\nTwo negatives<\/td>\r\n<td>Positive\r\n\r\nPositive<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1172558648411\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Different Signs<\/th>\r\n<th>Quotient<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Positive \u2022 negative\r\n\r\nNegative \u2022 Positive<\/td>\r\n<td>Negative\r\n\r\nNegative<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Multiplication by [latex]-1[\/latex] <\/strong>\r\n<ul id=\"eip-id1168466279311\">\r\n \t<li>Multiplying a number by [latex]-1[\/latex] gives its opposite: [latex]-1(a)=-a[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Division by [latex]-1[\/latex] <\/strong>\r\n<ul id=\"eip-id1168467378380\">\r\n \t<li>Dividing a number by [latex]-1[\/latex] gives its opposite: [latex]a\\div(-1)=-a[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"fs-id2654796\">\n<li><strong>Multiplication of Signed Numbers<\/strong>\n<ul id=\"eip-id1168617323909\">\n<li>To determine the sign of the product of two signed numbers:<br \/>\n<table id=\"eip-id1168467221297\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\n<thead>\n<tr valign=\"top\">\n<th>Same Signs<\/th>\n<th>Product<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Two positives<\/p>\n<p>Two negatives<\/td>\n<td>Positive<\/p>\n<p>Positive<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468724040\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\n<thead>\n<tr valign=\"top\">\n<th>Different Signs<\/th>\n<th>Product<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Positive \u2022 negative<\/p>\n<p>Negative \u2022 positive<\/td>\n<td>Negative<\/p>\n<p>Negative<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Division of Signed Numbers<\/strong>\n<ul id=\"eip-id1172558648335\">\n<li>To determine the sign of the quotient of two signed numbers:<br \/>\n<table id=\"eip-id1172558648339\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\n<thead>\n<tr valign=\"top\">\n<th>Same Signs<\/th>\n<th>Quotient<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Two positives<\/p>\n<p>Two negatives<\/td>\n<td>Positive<\/p>\n<p>Positive<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1172558648411\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column states same signs. The second column states product. The first row under same signs states two positives and under that two negatives. In the right column under product, it states positive. Under this row is another column head, this time stating different signs. In the row under this column head, it states positive and negative, and under that, negative and positive. In the right column under product, it states negative.\">\n<thead>\n<tr valign=\"top\">\n<th>Different Signs<\/th>\n<th>Quotient<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Positive \u2022 negative<\/p>\n<p>Negative \u2022 Positive<\/td>\n<td>Negative<\/p>\n<p>Negative<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Multiplication by [latex]-1[\/latex] <\/strong>\n<ul id=\"eip-id1168466279311\">\n<li>Multiplying a number by [latex]-1[\/latex] gives its opposite: [latex]-1(a)=-a[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Division by [latex]-1[\/latex] <\/strong>\n<ul id=\"eip-id1168467378380\">\n<li>Dividing a number by [latex]-1[\/latex] gives its opposite: [latex]a\\div(-1)=-a[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9426\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17535,"menu_order":23,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"8c69a21f-bd87-4a97-af08-3f5867b5f11f","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9426","chapter","type-chapter","status-publish","hentry"],"part":6350,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/17535"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9426\/revisions"}],"predecessor-version":[{"id":15134,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9426\/revisions\/15134"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/6350"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9426\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=9426"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9426"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=9426"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=9426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}