[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572392-105":53,"doc-detail-572392-en":120},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":113,"head_meta":115,"extra_data":117,"updated_unix":119},105,"en","integers-absolute-value-and-operations","Integers - absolute value and operations","","Integers explains positive whole numbers, zero, and negative numbers, and how to represent them on a number line. It covers comparing integers (less than/greater than), emphasizing the importance of the negative sign, defining absolute value as distance from 0, and identifying opposites. The document then teaches rules for adding and subtracting integers, including different-sign cases, followed by multiplying integers using signs and absolute values. Examples illustrate outcomes for addition and multiplication.",{"@graph":63,"@context":112},[64,80,95],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/integers-absolute-value-and-operations/572392/",4,{"url":78,"name":59,"@type":81,"author":82,"headline":59,"publisher":85,"fileFormat":88,"inLanguage":57,"description":61,"dateModified":89,"datePublished":89,"encodingFormat":88,"isAccessibleForFree":90,"interactionStatistic":91},"DigitalDocument",{"name":83,"@type":84},"Aldword","Person",{"url":68,"name":86,"@type":87},"DocShare","Organization","application/pdf","2026-10-13",true,{"@type":92,"interactionType":93,"userInteractionCount":4},"InteractionCounter",{"@type":94},"ViewAction",{"@type":96,"mainEntity":97},"FAQPage",[98,104,108],{"name":99,"@type":100,"acceptedAnswer":101},"How do you compare two integers on the number line?","Question",{"text":102,"@type":103},"The integer farther to the right is greater and the one farther to the left is less. This comparison must include the negative sign (e.g., −5 \u003C −3).","Answer",{"name":105,"@type":100,"acceptedAnswer":106},"What is absolute value and how is it written?",{"text":107,"@type":103},"Absolute value is the distance of a number from 0 on the number line. It is written using | |, and it is never negative (e.g., |−3| = 3).",{"name":109,"@type":100,"acceptedAnswer":110},"What are the rules for adding integers with different signs?",{"text":111,"@type":103},"When signs differ, subtract the absolute values (the smaller from the larger) and use the sign of the integer with the larger absolute value. For example, −5 + 2 = −3 because 5 > 2.","https://schema.org",{"og:url":78,"og:type":114,"og:title":59,"og:site_name":86,"og:description":61},"article",{"robots":116,"canonical":78},"index,follow",{"doc_id":118,"site_id":56},572392,1791927120,{"code":4,"msg":5,"data":121},{"doc_id":118,"user_id":122,"nickname":83,"user_avatar":123,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":124,"file_id":125,"file_url":126,"file_type":127,"file_size":128,"view_count":4,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":15,"language":129,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":130,"faqs":131,"seo_title":132,"seo_description":61,"update_tm":119,"read_time":79},2336478940917,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Integers  \nThe integers are the positive whole numbers, 0 , and negative numbers.  \n{ ,−4,−3,−2,−1,0, 1,2,3,4, }  \nThe Number Line and Comparing Integers  \nIntegers can be graphed on the number line:  \n−3 −2 −1 0 1 2 3  \nNegative numbers are to the left of zero and positive numbers are to the right.  \nZero  \n−3 −2 −1 0 1 2 3  \nFor any two integers on a number line, the number to the right is greater, and the number to the right is less than the other number.  \n−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6  \nSince −5 is to the left of −3 , −5 is less than −3 . This is written as:  \n−5 \u003C −3 or − 3 > −5.  \nCareful: The negative sign is important! −3 is greater than −5 even though 3 is less than 5.  \nAbsolute Value  \nThe absolute value of a number is that number’s distance from 0 on the number line.  \n3 units 4 units  \n−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6  \nWe use | | for the absolute value of a number.  \nExamples:  \n+ |4| = 4  \n+ | − 3| = 3  \n+ | − 58| = 58  \nHelpful Hint: The absolute value of a number is never negative, but it can be 0.  \n+ |0| = 0  \nOpposites  \nTwo numbers that are the same distance from 0 on the number line but are on opposite sides of 0  \nare called opposites.  \n5 units 5 units  \n−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6  \n3 units 3 units  \n−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6  \n3 is the opposite of −3 and −3 is the opposite of 3  \nWe use the negative sign − in front of a number to write the opposite of a number. Examples:  \n+ −(5) = −5  \n+ −(3) = −3  \n+ −(−3) = 3  \n5 is the opposite of −5 and −5 is the opposite of 5  \n+ −(−5) = 5  \nHints:  \n+ The opposite of a number is not always negative (even though we put the − sign in front) . For example  \n−(−1) = 1  \n+ The opposite of the opposite of a number is the original number! If n is a number  \n−(−n) = n  \n+ Since there is no distance from 0 to itself, 0 is its own opposite  \n−0 = 0  \nAdding Integers  \n| Hint: Adding two positive numbers is just normal addition.\u003Cbr>Example: 5 + 7 = 12\u003Cbr>Example: −3 + (−4) . Both −3 and −4 are negative. Since the signs are the same, we add the absolute values.\u003Cbr>+ | − 3| = 3 and | − 4| = 4 + 3 + 4 = 7 + The common sign is −\u003Cbr>So −3 + (−4) = −7 |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| 5+( − 2)  5  |  |  |  |  |  |  |\n| |  |  |  |  |  |  |\n| \u003Cbr>|  |  |  |  |  |  |\n|  |  |  |  |  − 2 |  |  |\n|  5  \u003Cbr>\u003Cbr>− 1 0 1 2 3 4 5 6\u003Cbr>|  |  |  |  |  |  |\n|  5 + (− 2) = 3 5 − 2 = 3  |  |  |  |  |  |  |\n| \u003Cbr>|  |  |  |  |  |  |\n| |  | | | |  | |\n|   − 4 + 6 |  |  |  |  |  |  |\n| \u003Cbr>|  |  |  |  |  |  |\n|  6 \u003Cbr>  − 4 \u003Cbr>\u003Cbr>− 6 − 5 − 4 − 3 − 2 − 1 0 1 2 3\u003Cbr>\u003Cbr>|  |  |  |  |  |  |\n|  − 4 + 6 = 2   6 − 4 = 2    |  |  |  |  |  |  |\n| |  |  |  |  |  |  |\n\n| When adding two numbers with different signs, we can get a negative answer. For example if we want −5 + 2 \u003Cbr> Start End \u003Cbr> 2 \u003Cbr>  − 5 \u003Cbr>\u003Cbr>− 6 − 5 − 4 3 − 2 − 1 0 1\u003Cbr>So −5 + 2 = −3 . Notice that the number with bigger absolute value is −5 and the sum is negative. The absolute value of the answer is 5−2 = 3. This is the difference of the absolute values of −5 and 2. \u003Cbr>To add two numbers with different signs: \u003Cbr> + Step 1: Subtract the number with smaller absolute value from the one with bigger absolute value.  + Step 2: Use the sign of the number with larger absolute value as the sign of the sum. \u003Cbr>Hint: When adding two integers, always check to see if the signs are the same or if they are different. Then use the appropriate rule for that case. \u003Cbr>Hint: You might want to draw an arrow sketch like the ones shown above to know what the sign of the answer will be. \u003Cbr>|\n| --- |\n| Example: 15 + (−23)\u003Cbr>The signs are different, so we use the rules for adding numbers with different signs.+ |15| = 15 and | − 23| = 23\u003Cbr>+ 23 is bigger than 15 so we subtract: 23 − 15 = 8\u003Cbr>+ −23 has a bigger absolute value than 15 so the answer should be negative. So 15 + (−23) = −8\u003Cbr>Example: −13 + (−16)\u003Cbr>Now the signs are the same (remember to always check this first) .\u003Cbr>+ | − 13| = 13 and | − 1","cbCaiasOh1QnN7C4","https://ap.wps.com/l/cbCaiasOh1QnN7C4","pdf",1322289,"English","# Integers\n## The number line and comparing integers\n## Zero\n## Absolute value\n## Opposites\n## Adding integers\n## Subtracting integers\n## Multiplying integers","[{\"question\":\"How do you compare two integers on the number line?\",\"answer\":\"The integer farther to the right is greater and the one farther to the left is less. This comparison must include the negative sign (e.g., −5 \\u003c −3).\"},{\"question\":\"What is absolute value and how is it written?\",\"answer\":\"Absolute value is the distance of a number from 0 on the number line. It is written using | |, and it is never negative (e.g., |−3| = 3).\"},{\"question\":\"What are the rules for adding integers with different signs?\",\"answer\":\"When signs differ, subtract the absolute values (the smaller from the larger) and use the sign of the integer with the larger absolute value. For example, −5 + 2 = −3 because 5 \\u003e 2.\"}]","Integers - absolute value and operations | PDF"]