{"id":2270,"date":"2026-05-26T22:39:57","date_gmt":"2026-05-26T17:09:57","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=2270"},"modified":"2026-05-26T22:40:01","modified_gmt":"2026-05-26T17:10:01","slug":"ncert-class-9-maths-exercise-3-2-solutions-world-of-numbers","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-3-2-solutions-world-of-numbers\/","title":{"rendered":"NCERT Class 9 Maths Exercise 3.2 Solutions | World of Numbers"},"content":{"rendered":"<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2270?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2270?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 3.2 of <strong>\u201cThe World of Numbers\u201d<\/strong> focuses on integers, negative numbers, and Brahmagupta\u2019s arithmetic laws. Students learn how to solve real-life problems involving temperature changes, debts, profits, and operations with negative numbers. These step-by-step solutions are written in simple English for easy understanding and exam preparation.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Topic<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Chapter<\/td><td>The World of Numbers<\/td><\/tr><tr><td>Exercise<\/td><td>3.2<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Class<\/td><td>Grade 9<\/td><\/tr><tr><td>Main Concept<\/td><td>Integers &amp; Brahmagupta\u2019s Laws<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Easy<\/td><\/tr><tr><td>Useful For<\/td><td>School Exams &amp; Practice<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Positive and Negative Numbers<\/li>\n\n\n\n<li>Integers<\/li>\n\n\n\n<li>Brahmagupta\u2019s Laws<\/li>\n\n\n\n<li>Multiplication of Integers<\/li>\n\n\n\n<li>Division of Integers<\/li>\n\n\n\n<li>Real-life Applications of Integers<\/li>\n\n\n\n<li>Temperature Problems<\/li>\n\n\n\n<li>Profit and Loss Using Integers<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Integer Set<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"double-struck\">Z<\/mi><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><mo>\u2212<\/mo><mn>3<\/mn><mo separator=\"true\">,<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mn>3<\/mn><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mtext>\u2009<\/mtext><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbb{Z}=\\{\\dots,-3,-2,-1,0,1,2,3,\\dots\\}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Product Rules of Integers<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mi>a<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mo>+<\/mo><mi>b<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mi>a<\/mi><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">(-a)\\times(+b)=-ab<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mi>a<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mi>b<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>+<\/mo><mi>a<\/mi><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">(-a)\\times(-b)=+ab<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Zero Property<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>+<\/mo><mn>0<\/mn><mo>=<\/mo><mi>a<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>a<\/mi><mo>\u2212<\/mo><mn>0<\/mn><mo>=<\/mo><mi>a<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>a<\/mi><mo>\u00d7<\/mo><mn>0<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a+0=a,\\ a-0=a,\\ a\\times0=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-Step Solutions<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Question 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The temperature in Ladakh is 4\u00b0C at noon. By midnight, it drops by 15\u00b0C. Find the midnight temperature.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Initial temperature = 4\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Temperature drop = 15\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mo>\u2212<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4 &#8211; 15<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= -11<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The midnight temperature is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mo>\u2212<\/mo><msup><mn>11<\/mn><mo>\u2218<\/mo><\/msup><mi>C<\/mi><\/mrow><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{-11^\\circ C}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Question 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A spice trader takes a loan of \u20b9850. The next day he earns a profit of \u20b91200. Later he incurs a loss of \u20b9450. Find his final financial standing.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Loan = \u2212850<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Profit = +1200<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Loss = \u2212450<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Equation:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>\u2212<\/mo><mn>850<\/mn><mo>+<\/mo><mn>1200<\/mn><mo>\u2212<\/mo><mn>450<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">-850 + 1200 &#8211; 450<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>\u2212<\/mo><mn>850<\/mn><mo>+<\/mo><mn>1200<\/mn><mo>=<\/mo><mn>350<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">-850 + 1200 = 350<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>350<\/mn><mo>\u2212<\/mo><mn>450<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>100<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">350 &#8211; 450 = -100<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Final financial standing:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mo>\u2212<\/mo><mtext>\u20b9<\/mtext><mn>100<\/mn><\/mrow><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{-\u20b9100}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This means the trader still has a debt of \u20b9100.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Question 3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Calculate the following using Brahmagupta\u2019s laws:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(i) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>12<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-12) \\times 5<\/annotation><\/semantics><\/math><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using integer multiplication rule:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Negative \u00d7 Positive = Negative<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>12<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mn>5<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-12)\\times5=-60<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mo>\u2212<\/mo><mn>60<\/mn><\/mrow><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{-60}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>8<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>7<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(-8) \\times (-7)<\/annotation><\/semantics><\/math>(\u22128)\u00d7(\u22127)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Negative \u00d7 Negative = Positive<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>8<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>7<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>56<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-8)\\times(-7)=56<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mn>56<\/mn><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{56}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>14<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">0 &#8211; (-14)<\/annotation><\/semantics><\/math><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Subtracting a negative means adding a positive.<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>14<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><mo>+<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0-(-14)=0+14<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=14<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mn>14<\/mn><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{14}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>20<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00f7<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-20) \\div 4<\/annotation><\/semantics><\/math><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Negative \u00f7 Positive = Negative<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>20<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00f7<\/mo><mn>4<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-20)\\div4=-5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mo>\u2212<\/mo><mn>5<\/mn><\/mrow><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{-5}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Question 4<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Explain using a real-life example why subtracting a negative number is the same as adding a positive number.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose you owe your friend \u20b95.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Your current money = \u20b910<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mathematically:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>10<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">10-(-5)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtracting a negative means removing debt.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If your \u20b95 debt is removed, your financial condition improves by \u20b95.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>10<\/mn><mo>+<\/mo><mn>5<\/mn><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">10+5=15<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>10<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">10-(-5)=15<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, subtracting a negative number is the same as adding a positive number.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Forgetting sign rules while multiplying integers<\/li>\n\n\n\n<li>Confusing subtraction of negative numbers<\/li>\n\n\n\n<li>Writing positive answers for negative operations<\/li>\n\n\n\n<li>Ignoring real-life meaning of debts and fortunes<\/li>\n\n\n\n<li>Division sign mistakes with integers<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Remember:\n<ul class=\"wp-block-list\">\n<li>Positive \u00d7 Positive = Positive<\/li>\n\n\n\n<li>Negative \u00d7 Negative = Positive<\/li>\n\n\n\n<li>Positive \u00d7 Negative = Negative<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Practice temperature and money-based questions<\/li>\n\n\n\n<li>Always write signs carefully<\/li>\n\n\n\n<li>Learn Brahmagupta\u2019s laws properly<\/li>\n\n\n\n<li>Use step-by-step calculation in exams<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. What is the value of:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>6<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(-6)\\times(-4)<\/annotation><\/semantics><\/math>(\u22126)\u00d7(\u22124)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A) \u221224<br>B) 24<br>C) \u221210<br>D) 10<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">B) 24<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. What is:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>9<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">0-(-9)<\/annotation><\/semantics><\/math>0\u2212(\u22129)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A) \u22129<br>B) 0<br>C) 9<br>D) \u221218<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C) 9<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. Which of the following is an integer?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac12<\/annotation><\/semantics><\/math>21\u200b<br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mn>2<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt2<\/annotation><\/semantics><\/math>2\u200b<br>C) \u22127<br>D) 3.5<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C) \u22127<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. The result of:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>15<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00f7<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-15)\\div3<\/annotation><\/semantics><\/math>(\u221215)\u00f73<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A) 5<br>B) \u22125<br>C) 45<br>D) \u221245<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">B) \u22125<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. What are integers?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Integers are positive numbers, negative numbers, and zero.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Who introduced negative numbers formally?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Brahmagupta formally introduced negative numbers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Why does negative \u00d7 negative become positive?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Because removing a debt improves financial value.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Is zero a positive number?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">No, zero is neither positive nor negative.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. Can integers be represented on a number line?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Yes, integers are represented on a number line.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">CTA (Call To Action)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Master integers and number systems with detailed NCERT solutions, mock tests, and chapter-wise practice questions. Keep practicing daily to improve your Mathematics score and build strong concepts for higher classes.<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2270?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2270?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p> Short Intro Exercise 3.2 of \u201cThe World of Numbers\u201d focuses on integers, negative numbers, and<\/p>\n","protected":false},"author":1,"featured_media":2271,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[22,4,11],"tags":[954,955,959,957,953,951,960,958,961,952,956],"class_list":["post-2270","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","category-class-9","category-maths-class-9","tag-brahmagupta-laws-questions-answers","tag-class-9-maths-chapter-3-solutions","tag-grade-9-maths-solutions","tag-integer-operations-class-9","tag-integers-class-9-solutions","tag-ncert-class-9-maths-exercise-3-2-solutions","tag-ncert-maths-chapter-3-answers","tag-negative-numbers-questions","tag-real-life-integer-problems","tag-world-of-numbers-exercise-3-2","tag-world-of-numbers-solutions"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2270","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=2270"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2270\/revisions"}],"predecessor-version":[{"id":2272,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2270\/revisions\/2272"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/2271"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=2270"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=2270"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=2270"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}