# Algebra: Pure and Applied by Aigli Papantonopoulou

By Aigli Papantonopoulou

This ebook offers thorough insurance of the most issues of summary algebra whereas delivering approximately a hundred pages of functions. A repetition and examples first procedure introduces rookies to mathematical rigor and abstraction whereas educating them the elemental notions and result of smooth algebra. bankruptcy issues comprise staff idea, direct items and Abelian teams, earrings and fields, geometric structures, historic notes, symmetries, and coding conception. For destiny academics of algebra and geometry on the highschool point.

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Algebra_ch2 5/4/06 9:30 AM Page 55 DIVIDING INTEGERS DIVIDING INTEGERS When you divide two integers, there are five possible cases. Case 1: Both numbers are positive. Example: 21 Ϭ 7 Case 2: Both numbers are negative. Example: (Ϫ15) Ϭ (Ϫ3) Case 3: One number is negative and one number is positive. Example: (ϩ8) Ϭ (Ϫ4) Case 4: The dividend is zero. Example: 0 Ϭ (Ϫ2) Case 5: The divisor is zero. Example: 6 Ϭ 0 Here is how you solve each of these cases. Case 1: Both numbers are positive. Painless Solution: Divide the numbers.

6 Ϫ (4) C. Ϫ6 ϩ (4) ____ 4. (Ϫ6) Ϫ (Ϫ4) R. Ϫ6 ϩ (Ϫ4) ____ 5. 0 Ϫ (Ϫ4) Y. 0 ϩ (Ϫ4) ____ 6. 0 Ϫ (ϩ4) K. ) 51 algebra_ch2 5/4/06 9:30 AM Page 52 THE INTEGERS BRAIN TICKLERS Set # 10 Now solve these same subtraction problems. Use the addition problems in Brain Ticklers #3 for help. 1. 6 Ϫ (Ϫ4) 4. Ϫ6 Ϫ (Ϫ4) 2. Ϫ6 Ϫ (4) 5. 0 Ϫ (Ϫ4) 3. 6 Ϫ (4) 6. ) Remember . . Just change the subtraction problem into an addition problem, and take the opposite of the number being subtracted. Then solve the new addition problem.

The whole numbers are not irrational numbers. The natural numbers are not irrational numbers. EXAMPLES: Ϫ 2 , 2 , and 3 are irrational numbers. 1 , and 1,247 are not irrational Ϫ41, Ϫ17ᎏ21ᎏ, Ϫᎏ83ᎏ, ᎏ51ᎏ, 4, ᎏ47ᎏ numbers. The real numbers The real numbers are a combination of all the number systems. The real numbers are the natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Every point on the number line is a real number. All of the irrational numbers are real numbers.