{"id":28102,"date":"2022-01-29T16:16:18","date_gmt":"2022-01-29T10:46:18","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=28102"},"modified":"2022-01-29T16:16:18","modified_gmt":"2022-01-29T10:46:18","slug":"algebra-class-6-notes-maths-chapter-11","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material-notes\/maths\/class-6\/algebra-class-6-notes-maths-chapter-11\/","title":{"rendered":"Algebra Class 6 Notes Maths Chapter 11"},"content":{"rendered":"<h2>CBSE Class 6 Maths Notes Chapter 11 Algebra<\/h2>\n<p>The branch of mathematics in which we study numbers is called arithmetic. The branch of mathematics in which we study shapes is called geometry. Another branch of mathematics is Algebra.<\/p>\n<p>In algebra, we use letters. Use of letters helps us in numerous ways as follows:<\/p>\n<ul>\n<li>Using letters we can write rules and formulae in a general way.<\/li>\n<li>Using letters we can talk about any number and not just a particular number.<\/li>\n<li>The letters may stand for unknown quantities. By learning methods of determining unknowns, we develop powerful tools for solving puzzles and many problems from daily life.<\/li>\n<li>Since letters stand for numbers, operations can be performed on them as on numbers. This leads to the study of algebraic expressions and their properties.<\/li>\n<\/ul>\n<p>Matchstick Patterns<br \/>\nWe can make letters and other shapes using matchsticks. We can write a general relation between the number of matchsticks required for repeating a given shape. The number of times a given shape is repeated varies; it takes on values 1, 2, 3,\u2026 . It is a variable, denoted by some letter n.<\/p>\n<p>The Idea of a Variable<br \/>\nVariable means something that can vary (or change). The value of a variable is not fixed. It can take different values. The length of a square can have any value. It is a variable. But the number of angles of a triangle has a fixed value 3. It is not a variable. We may use any letter n, l, m, p, x, y, z, etc. to show a variable.<\/p>\n<p>More Matchstick Patterns<br \/>\nWe can make many letters of the alphabet and other shapes from matchsticks. For example U, V, triangle, Square, etc. In matchstick patterns, we use the variable n to give us the general rule for die number of matchsticks required to make a pattern. This is an important use of variables in Mathematics.<\/p>\n<p>More Examples of Variables<br \/>\nTo show a variable, we may use any letter as n, m, l, p, x,y, z, etc. Recall that a variable is a number, which does not have a fixed value. It can take on various values. For example, the number 10, or the number 100 or any other given number is not a variable. They have fixed values. Similarly, the number of comers of a quadrilateral (4) is fixed; it is also not a variable.<\/p>\n<p>Use of Variables in Common Rules<br \/>\nRules from geometry<br \/>\nPerimeter of a square (p) = 4l, where l is the length of the side of the square<br \/>\nPerimeter of a rectangle (p) = 2l + 2b, where l is the length and b is the breadth of the rectangle.<\/p>\n<p><strong>Rules from Arithmetic<\/strong><br \/>\nCommutativity of Addition<br \/>\nLet a and b be two variables, which can take any numerical value.<br \/>\nThen, a + b = b + a<br \/>\nCommutativity of Multiplication<br \/>\nLet a and b be two variables.<br \/>\nThen, a \u00d7 b = b \u00d7 a<br \/>\nDistributivity of multiplication over addition<br \/>\nLet a, b and c be three variables.<br \/>\nThen a \u00d7 (b + c) = a \u00d7 b + a \u00d7 c<br \/>\nAssociativity of addition<br \/>\nLet a, b and c be three variables.<br \/>\nThen, (a + b) + c = a + (b + c).<\/p>\n<p><strong>Expressions With Variables<\/strong><br \/>\nWe know that variables can take different values; they have no fixed value. But they are numbers. That is why as in the case of numbers, operations of addition, subtraction, multiplication, and division can be performed on them. Using different operations, we can form expressions with variables like x \u2013 2, x + 1, 3n, 2m, \\(\\frac { p }{ 4 }\\), 2y + 5, 3l \u2013 7, etc.<\/p>\n<p>Note: A number of expressions can be immediately evaluated.<br \/>\nFor example: 3 \u00d7 4 + 6 = 12 + 6 = 18<br \/>\nBut an expression containing the variable x cannot be evaluated until x is assigned same value.<br \/>\nFor example,<br \/>\nWhen x = 1, 4x + 3 = 4 \u00d7 1 + 3 = 4 + 3 = 7.<\/p>\n<p><strong>Using Expressions Practically<\/strong><br \/>\nMany statements described in ordinary language can be changed to statements using expressions with variables.<\/p>\n<p>What is the Equation?<br \/>\nAn equation is a condition on a variable. It is expressed by saying that expression with a variable is equal to a fixed number.<br \/>\nFor example, x \u2013 3 = 2.<br \/>\nAn equation has two sides, LHS and RHS and between them, is file sign of equality (=).<br \/>\nThe equation states that the value of the left-hand side (LHS) is equal to the value of the right-hand side (RHS).<br \/>\nIf the LHS is not equal to the RHS, we do not get an equation.<br \/>\nFor example, the statement 2n &gt; 10 or 2n &lt; 10 is not an equation.<br \/>\nNote: An equation like 10 \u2013 1 = 9 is called a numerical equation as neither of its two sides contains a variable. Usually, the word equation is used only for equations involving one or more variables.<\/p>\n<p><strong>Solution of an Equation<\/strong><br \/>\nThe value of the variable in an equation for which LHS of the equation becomes equal to RHS of the equation is said to satisfy the equation and itself is called a solution of the equation. For example, n = 2 is a solution to the equation 2n = 4, where n = 3 is not a solution of the equation 3n = 13.<\/p>\n<p><strong>Getting a Solution to the Equation<\/strong><br \/>\nFor getting the solution of an equation, one method is trial and error method. In this method, we assign some value to the variable and check whether it satisfies the equation. We go on assigning this way different values to the variable until we find the right value which satisfies the equation.<\/p>\n<p>But this is not a direct and practical way of finding a solution. We need a more systematic way of getting a solution of the equation than the trial and error method. In case of very simple equations, the variable is replaced by a place holder I and its value is determined by usual methods. Thus the value of the variable obtained is the solution of the equation.<\/p>\n<p><strong>Using an Equation<\/strong><br \/>\nOriginally, we are given an equation in a variable whose value is unknown to us. To solve the equation means to find the unknown value. Thus a variable in an equation is looked upon as unknown and starting from the unknown, we can see up the equation. Solving the equation is thus a method of finding the unknown. It is, therefore, a powerful method of solving puzzles and problems.<\/p>\n<h5><\/h5>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Class 6 Maths Notes Chapter 11 Algebra The branch of mathematics in which we study numbers is called arithmetic. [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\"Get Algebra Class 6 Notes Maths Chapter 11 on Infinity Learn.\"","custom_permalink":"study-material-notes\/maths\/class-6\/algebra-class-6-notes-maths-chapter-11\/"},"categories":[92,13,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Algebra Class 6 Notes Maths Chapter 11 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"&quot;Get Algebra Class 6 Notes Maths Chapter 11 on Infinity Learn.&quot;\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-material-notes\/maths\/class-6\/algebra-class-6-notes-maths-chapter-11\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Algebra Class 6 Notes Maths Chapter 11 - 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