{"id":602463,"date":"2022-05-14T08:42:49","date_gmt":"2022-05-14T08:42:49","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=602463"},"modified":"2022-05-17T04:27:28","modified_gmt":"2022-05-17T04:27:28","slug":"ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/","title":{"rendered":"ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions"},"content":{"rendered":"\n<p>Class 7: Maths Chapter 8 solutions. Complete Class 7 Maths Chapter 8 Notes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\">ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions<\/h2>\n\n\n\n<p>ML Aggarwal 7th Maths Chapter 8, Class 7 Maths Chapter 8 solutions<\/p>\n\n\n\n<p><strong>1. From the algebraic expressions using variables, constants, and arithmetic operations:<br>(i) 6 more than thrice a number x.<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>3x + 6<\/p>\n\n\n\n<p><strong><br>(ii) 5 times x is subtracted from 13.<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>13 \u2013 5x<\/p>\n\n\n\n<p><strong><br>(iii) The numbers x and y both squared and added.<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>x<sup>2<\/sup>&nbsp;+ y<sup>2<\/sup><\/p>\n\n\n\n<p><strong><br>(iv) Number 7 is added to 3 times the product of p and q.<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>3pq + 7<\/p>\n\n\n\n<p><strong><br>(v) Three times of x is subtracted from the product of x with itself.<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>x<sup>2<\/sup>&nbsp;\u2013 3x<\/p>\n\n\n\n<p><strong><br>(vi) Sum of the numbers m and n is subtracted from their product.<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>mn \u2013 (m + n)<\/p>\n\n\n\n<p><strong>2. A taxi charges \u20b9 9 per km and a fixed charge of \u20b9 50. If the taxi is hired for x km, write an algebraic expression for this situation.<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>From the question it is given that,<\/p>\n\n\n\n<p>A taxi charges \u20b9 9 per km<\/p>\n\n\n\n<p>A fixed charge of \u20b9 50<\/p>\n\n\n\n<p>If the taxi is hired for x km = \u20b9 (9x + 50)<\/p>\n\n\n\n<p><strong>3. Write down the algebraic expression whose terms are:<br>(i) 5a, -3b, c<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expressions is defined as, numbers, symbols and operators (such as +. \u2013 , \u00d7 and \u00f7) grouped together that show the value of something.<\/p>\n\n\n\n<p>So, Expressions = 5a \u2013 3b + c<\/p>\n\n\n\n<p><strong><br>(ii) x<sup>2<\/sup>, -5x, 6<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expressions is defined as, numbers, symbols and operators (such as +. \u2013 , \u00d7 and \u00f7) grouped together that show the value of something.<\/p>\n\n\n\n<p>So, Expressions = x<sup>2<\/sup>&nbsp;\u2013 5x + 6<\/p>\n\n\n\n<p><strong><br>(iii) x<sup>2<\/sup>y, xy, -xy<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expressions is defined as, numbers, symbols and operators (such as +. \u2013 , \u00d7 and \u00f7) grouped together that show the value of something.<\/p>\n\n\n\n<p>So, Expressions = x<sup>2<\/sup>y + xy \u2013 xy<sup>2<\/sup><\/p>\n\n\n\n<p><strong>4. Write all the terms of each of the following algebraic expressions:<\/strong><\/p>\n\n\n\n<p><strong>(i) 3 \u2013 7x<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or \u2013 signs or sometimes by division.<\/p>\n\n\n\n<p>Terms = 3, -7x<\/p>\n\n\n\n<p><strong>(ii) 2 \u2013 5a + \u00bdb<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or \u2013 signs or sometimes by division.<\/p>\n\n\n\n<p>Terms = 2, -5a, \u00bdb<\/p>\n\n\n\n<p><strong>(iii) 3x<sup>5<\/sup>&nbsp;+ 4y<sup>3<\/sup>&nbsp;\u2013 7xy<sup>2<\/sup>&nbsp;+ 3<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or \u2013 signs or sometimes by division.<\/p>\n\n\n\n<p>Terms = 3x<sup>5<\/sup>, 4y<sup>3<\/sup>, -7xy<sup>2<\/sup>, 3<\/p>\n\n\n\n<p><strong>5. Identify the terms and their factors in the algebraic expressions given below:<br>(i) -4x + 5y<br>(ii) xy + 2x<sup>2<\/sup>y<sup>2<\/sup><br>(iii) 1.2ab \u2013 2.4b + 3.6a<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expressions is defined as, numbers, symbols and operators (such as +. \u2013 , \u00d7 and \u00f7) grouped together that show the value of something.<\/p>\n\n\n\n<p>In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or \u2013 signs or sometimes by division.<\/p>\n\n\n\n<p>Factors is defined as, numbers we can multiply together to get another number.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Sl.No.<\/strong><\/td><td><strong>Expression<\/strong><\/td><td><strong>Terms<\/strong><\/td><td><strong>Factors<\/strong><\/td><\/tr><tr><td><strong>(i)<\/strong><\/td><td>\u2013 4x + 5y<\/td><td>-4x5y<\/td><td>-4, x5, y<\/td><\/tr><tr><td><strong>(ii)<\/strong><\/td><td>Xy + 2x<sup>2<\/sup>y<sup>2<\/sup><\/td><td>xy2x<sup>2<\/sup>y<sup>2<\/sup><\/td><td>x, y2, x, x, y, y<\/td><\/tr><tr><td><strong>(iii)<\/strong><\/td><td>1.2ab \u2013 2.4b + 3.6a<\/td><td>1.2ab-2.4b3.6a<\/td><td>1.2, a, b-2.4, b3.6, a<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>6. Show the terms and their factors by tree diagrams of the following algebraic expressions:<br>(i) 8x + 3y<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expression: 8x \u2013 3y<sup>2<\/sup><\/p>\n\n\n\n<p>Terms: 8x, -3y<sup>2<\/sup><\/p>\n\n\n\n<p>Factors: 8, x; 3, y, y<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2022\/05\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-image-1.png\" alt=\"ML Aggarwal Solutions for Class 7 Maths Chapter 8 Image 1\" title=\"ML Aggarwal Solutions for Class 7 Chapter 8 Image 1\"\/><\/figure>\n\n\n\n<p><strong><br>(ii) y \u2013 y<sup>3<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expression: y \u2013 y<sup>3<\/sup><\/p>\n\n\n\n<p>Terms: y, -y<sup>3<\/sup><\/p>\n\n\n\n<p>Factors: y; -y, -y, -y<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2022\/05\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-image-2.png\" alt=\"ML Aggarwal Solutions for Class 7 Maths Chapter 8 Image 2\" title=\"ML Aggarwal Solutions for Class 7 Chapter 8 Image 2\"\/><\/figure>\n\n\n\n<p><strong><br>(iii) 5xy<sup>2<\/sup>&nbsp;+ 7x<sup>2<\/sup>y<\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expression: 5xy<sup>2<\/sup>&nbsp;+ 7x<sup>2<\/sup>y<\/p>\n\n\n\n<p>Terms: 5xy<sup>2<\/sup>, 7x<sup>2<\/sup>y<\/p>\n\n\n\n<p>Factors: 5, x, y, y; 7, x, x, y<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2022\/05\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-image-3.png\" alt=\"ML Aggarwal Solutions for Class 7 Maths Chapter 8 Image 3\" title=\"ML Aggarwal Solutions for Class 7 Chapter 8 Image 3\"\/><\/figure>\n\n\n\n<p><strong><br>(iv) -ab + 2b<sup>2<\/sup>&nbsp;\u2013 3a<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>Expression: -ab + 2b<sup>2<\/sup>&nbsp;\u2013 3a<sup>2<\/sup><\/p>\n\n\n\n<p>Terms: -ab, 2b<sup>2<\/sup>, -3a<sup>2<\/sup><\/p>\n\n\n\n<p>Factors: -a, b; 2, b, b; -3, a, a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2022\/05\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-image-4.png\" alt=\"ML Aggarwal Solutions for Class 7 Maths Chapter 8 Image 4\" title=\"ML Aggarwal Solutions for Class 7 Chapter 8 Image 4\"\/><\/figure>\n\n\n\n<p><strong>7. Write down the numerical coefficient of each of the following:<br>(i) -7x<br>(ii) -2x<sup>3<\/sup>y<sup>2<\/sup><br>(iii) 6abcd<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(iv) (2\/3)pq<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:-<\/strong><\/p>\n\n\n\n<p>A coefficient is a number used to multiply a variable (3x&nbsp;means&nbsp;3 times x, so 3 is a&nbsp;coefficient) Variables on their own (without a number next to them) actually have a&nbsp;coefficient&nbsp;of 1 (x is really 1x)<\/p>\n\n\n\n<p>Then,<\/p>\n\n\n\n<p>(i) -7x numerical co-efficient is -7<br><br>(ii) -2x<sup>3<\/sup>y<sup>2<\/sup>&nbsp;numerical co-efficient is -2<br><br>(iii) 6abcd<sup>2<\/sup>&nbsp;numerical co-efficient is 6<\/p>\n\n\n\n<p>(iv) (2\/3)pq<sup>2<\/sup>&nbsp;numerical co-efficient is 2\/3<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-download-pdf\"><strong>Download PDF<\/strong><\/h2>\n\n\n\n<p>ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions<\/p>\n\n\n\n<p><a href=\"https:\/\/www.indcareer.com\/docs\/780589fc-bc9b-4310-9ee6-701ade4f0ff7\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download PDF<\/strong>: ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions PDF<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"block-5e63e5e5-c292-421b-9798-a655bf73262a\"><strong>Chapterwise ML Aggarwal Solutions for Class 7 Maths :<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\" id=\"block-75833e5e-83a3-4621-bc6d-6e42697f265f\"><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-1-integers\/\">Chapter 1- Integers<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-2-fractions-and-decimals\/\">Chapter 2- Fractions and Decimals<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-3-rational-numbers\/\">Chapter 3- Rational Numbers<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-4-exponents-and-powers\/\">Chapter 4- Exponents and Powers<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-5-sets\/\">Chapter 5- Sets<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-6-ratio-and-proportion\/\">Chapter 6- Ratio and Proportion<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-7-percentage-and-its-applications\/\">Chapter 7- Percentage and Its Applications<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/\">Chapter 8- Algebraic Expressions<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-9-linear-equations-and-inequalities\/\">Chapter 9- Linear Equations and Inequalitie<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-10-lines-and-angles\/\">Chapter 10- Lines and Angles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-11-triangles-and-its-properties\/\">Chapter 11- Triangles and its Properties<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-12-congruence-of-triangles\/\">Chapter 12- Congruence of Triangles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-13-practical-geometry\/\">Chapter 13- Practical Geometry<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-14-symmetry\/\">Chapter 14- Symmetry<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-15-visualising-solid-shapes\/\">Chapter 15- Visualising Solid Shapes<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-16-perimeter-and-area\/\">Chapter 16- Perimeter and Area<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-17-data-handling\/\">Chapter 17- Data Handling<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">About ML Aggarwal<\/h2>\n\n\n\n<p>M. L. Aggarwal, is an Indian mechanical engineer, educator. His achievements include research in solutions of industrial problems related to fatigue design. Recipient Best Paper award, Manipal Institute of Technology, 2004. Member of TSTE.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Class 7: Maths Chapter 8 solutions. Complete Class 7 Maths Chapter 8 Notes. ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions ML Aggarwal 7th Maths Chapter 8, Class 7 Maths Chapter 8 solutions 1. From the algebraic expressions using variables, constants, and arithmetic operations:(i) 6 more than thrice a number x. Solution:- [&hellip;]<\/p>\n","protected":false},"author":302,"featured_media":602464,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[1411,907],"tags":[2265],"boards":[],"class_list":["post-602463","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book-solutions","category-class-7","tag-ml-aggarwal-solutions","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.1.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>ML Aggarwal Solutions for Class 7, maths Chapter 8 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions | Browse all Class 7 Maths - IndCareer Schools\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions\" \/>\n<meta property=\"og:description\" content=\"Class 7: Maths Chapter 8 solutions. 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ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions ML\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2022-05-14T08:42:49+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-17T04:27:28+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2022\/05\/NCERT-Solutions-7-9.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1080\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"ML Aggarwal Solutions for Class 7 Maths Chapter 8- Algebraic Expressions\",\"datePublished\":\"2022-05-14T08:42:49+00:00\",\"dateModified\":\"2022-05-17T04:27:28+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/\"},\"wordCount\":866,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2022\/05\/NCERT-Solutions-7-9.jpg\",\"keywords\":[\"ML Aggarwal Solutions\"],\"articleSection\":[\"Book Solutions\",\"Class 7\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/ml-aggarwal-solutions-for-class-7-maths-chapter-8-algebraic-expressions\/\",\"name\":\"ML Aggarwal Solutions for Class 7, maths Chapter 8 - 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