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</html>";s:4:"text";s:6643:">> endobj 44 0 obj endobj rgq"Hq�nR�cg�;��Gڗ\jN@����I�������;�؇��+�� �N����?h۹)�z�4lx�@3�IF��P�d���"Q���j�yz��g��xO|��9B�d�Ӂ�5vG,�5���7���{s0/��%�`s��(�zJ��6�g�.�lP �Yw!��O��x�E2��5Y��٣F)(/f�q�Y�]������Y��t��$74���Yz���7�cY0z��uX�ӓB���v��J] /A << /S /GoTo /D (section.9) >> /Rect [71.004 565.079 217.34 577.699] /Border[0 0 1]/H/I/C[1 0 0] The inverse of a matrix is denoted by the superscript “-1”. /Type /Annot /Rect [71.004 419.875 273.512 432.494] Each part in an algebraic expression is called a term. 5 0 obj Here we will briefly review reducing, multiplying, dividing, adding, and subtracting fractions. endobj >> 33 0 obj 72 0 obj << << /S /GoTo /D (section.9) >> 63 0 obj << Ȉ�	O:����6�F�����' �_���6j�Ѥ�}ο.E�g���|n��e��]�)����_�t�t��J^{��[O� �v]����S����wW����}Q�T��4ptt00t400 @� In matrix algebra, the inverse of a matrix is that matrix which, when multiplied by the original matrix, gives an identity matrix. /ProcSet [ /PDF /Text ] endobj endobj /Border[0 0 1]/H/I/C[1 0 0] /Border[0 0 1]/H/I/C[1 0 0] /Type /Annot It is used by the pure mathematician and by the mathematically trained scien-tists of all disciplines. (The Quadratic Formula and Applications \(outlined\)) 20 0 obj If you were told that +4=10, you can probably see straight away that =6. Basic Algebra Algebra is about using letters in place of numbers. 41 0 obj endobj Algebra permeates all of our mathematical intuitions. (Linear Equations in One Variable) >> endobj Basic Algebra is very basic level of algebra where student learns to find the value of a single variable. << /S /GoTo /D [50 0 R  /Fit ] >> 40 0 obj >> endobj e{`[9����p$�$X�jHAc�QJ�$��������˗t\���N�0���b�1t�fK��K�F�jp�@���c:��&,���OAb�yD3h�x7t^d۰82����vQ���Q�t0N�����l:��YB$�Fr��&�ٜ|��;��i�b:���9�fޜ���1���O���&����Kq4/���0�z�����L2JV{�%�}Hs�E��/Ӆه46�ج1'fu�yhdL���`nl_ڂN�ͱ�V�q�����a�r��a��I�J�|�9��؍�:�Q�ۛ�֋4�/YQlM��d�kC/Oޞ�M^��'v00Ex[� Algebraic expressions with an equals sign ‘=’ are called equations. >> If you were told that −7=5, you can probably see straight away that =12. >> endobj >> endobj Y�e@�$��('��x��{��P(�gѦH3zU�Y�5b�"_y��r05K>��*���\�G���`C��҃K��#_�@�zɀ2�`\�! /Border[0 0 1]/H/I/C[1 0 0] endobj endobj 12 0 obj stream /A << /S /GoTo /D (section.8) >> >> endobj /D [50 0 R /XYZ 72 683.138 null] xڕT���0��+r��G@�h�J�����M��R;8���g\���Y�\b;�y���o�ūk�ʂc%�v�I�UJ���&� endobj endobj /Length 506        (Linear Equations in Two Variables and Their Graphs) endobj Look at the algebraic expression 4 – a 47+=x Constant term (Can't change) 36 0 obj (Linear functions and proportional reasoning) /Subtype /Link What is Algebra Algebraic thinking spans all areas of mathematics. >> endobj As this is a review, concepts will not be explained in detail as other lessons are. << /S /GoTo /D (section.4) >> This book is directed more at the former audience than the latter, but it is hoped that the writing is sufficiently clear with /Border[0 0 1]/H/I/C[1 0 0] 32 0 obj Basic Algebra Algebra is about using letters in place of numbers. /Rect [71.004 451.24 218.788 461.535] 67 0 obj << 69 0 obj << /Font << /F17 55 0 R /F18 56 0 R /F29 57 0 R /F30 58 0 R >> /MediaBox [0 0 612 792] /A << /S /GoTo /D (section.10) >> /D [73 0 R /XYZ 110.851 721 null] endobj endobj /A << /S /GoTo /D (section.6) >> endobj In fact the first mathematical concepts we ever encounter are the foundation of the subject. (Exponents) These worksheets contain pre-algebra & Algebra exercises suitable for preschool, kindergarten, first grade to eigth graders levels . �q��4DX�a�(r�2@�
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 /A << /S /GoTo /D (section.3) >> Glossary 3. /A << /S /GoTo /D (section.4) >> /Rect [71.004 361.793 349.72 374.412]  >> endobj Pre-Algebra - Fractions Objective: Reduce, add, subtract, multiply, and divide with fractions. Hence, AA−1 = A−1A = I A matrix must be square to have an inverse, but not all square matrices have an inverse. 51 0 obj << >> endobj /A << /S /GoTo /D (section.1) >> Answer key is at the end of each worksheet so even parents can check the answers after student has solved the algebric equations. 37 0 obj endobj 17 0 obj In some cases, the inverse does not exist. %PDF-1.4 If you were told that −7=5, you can probably see straight away that =12. /Rect [71.004 390.834 257.254 403.453] 1 0 obj /Annots [ 60 0 R 61 0 R 62 0 R 63 0 R 64 0 R 65 0 R 66 0 R 67 0 R 68 0 R 69 0 R 70 0 R 71 0 R ] /Subtype /Link ↓ Linear algebra is one of the most applicable areas of mathematics. Answers 9. /Border[0 0 1]/H/I/C[1 0 0] 0
 (Symbolic Expressions) Let me summarize the first six to seven years of your mathematical education: The concept of Unity. /Filter /FlateDecode (Transcription of Verbal Information into Symbolic Language) 76 0 obj << 8 0 obj 70 0 obj << 1015 0 obj
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