Reduction of fractions-Definition and principles Reduction of fractions to lowest terms Reduction of mixed quantities to improper fractions. Reduction of fractions to similar forms Addition and subtraction of fractions Multiplication and division of fractions. Multiplication and division by fractions-Definitions and prin- Transformation of equations-Definition and principles Simple equations of one unknown quantity-Solution of numeri- Simple equations of three unknown quantities-Solution of ab- stract equations. Concrete examples 146 . 147 152 155 157 Involution of polynomials-Principles and applications . 163 Affected quadratics-Definitions and principles Solution of numerical affected quadratics EXPONENTS, RADICALS, AND INEQUALITIES. Fractional and negative exponents-Principles and applications NUMBERS SYMBOLIZED. INTRODUCTION. LITERAL QUANTITIES-IDEAS AND EXPRESSION. EXERCISE 1. 1. What is the sum of 2 units, 3 units, and 4 units? 2 tens, 3 tens, and 4 tens? 2 fives, 3 fives, and 4 fives? What, then, is the sum of 2 times any number, 3 times that number, and 4 times that number? 2. If we let a stand for any number, what will be the sum of 2 times a, 3 times a, and 4 times a? 3 times a, 4 times a, and 6 times a? Two times a is written 2a, and is read two a; three times a is written 3a; etc. 3. What is the sum of 4a, 5a, and 6a? 8a, 4a, and 7a? 4. If we let b stand for any number, what will be the sum of 4b, 3b, and 2b? 5b, 4b, and 6b? In algebra, any letter may stand for any number. 5. What is the sum of 3b, 4b, and 2b, if b stands for 3? Ifb stands for 4? The symbol of addition is +, read plus. 6. What is the sum of 2 m +3m+5m? What when m equals 2? When m equals 5? The symbol = is read equals. |