By Lynette Long Ph.D.
For college kids who're intimidated by way of all sorts of math, here's a set of simple steps that bring about an knowing of ordinary algebra. the writer defines all phrases, issues out strength pitfalls in algebraic calculation, and makes challenge fixing a enjoyable job. New during this variation are painless ways to figuring out and graphing linear equations, fixing structures of linear inequalities, and graphing quadratic equations. BarronГўВЂВ™s well known Painless sequence of research publications for heart institution and highschool scholars provide a lighthearted, usually funny method of their topics, remodeling info that will as soon as have appeared dull or tricky right into a sequence of attention-grabbing and mentally hard principles. so much titles within the sequence characteristic many fun-to-solve ГўВЂВњBrain TicklerГўВЂВќ issues of solutions on the finish of every bankruptcy.
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Extra resources for Painless Algebra
Example: (ϩ3) ϩ (ϩ5) Case 2: Both numbers are negative. Example: (Ϫ2) ϩ (Ϫ4) Case 3: One of the two numbers is positive and one is negative. Example: (ϩ3) ϩ (Ϫ8) Case 4: One of the two numbers is zero. Example: 0 ϩ (ϩ2) Now let’s see how to solve each of these types of problems. Case 1: Both numbers are positive. Painless Solution: Add the numbers just as you would add any two numbers. The answer is always positive. Take this Painless Solution and call me in the morning. 45 algebra_ch2 5/4/06 9:30 AM Page 46 THE INTEGERS EXAMPLES: (ϩ3) ϩ (ϩ8) ϭ ϩ11 2 ϩ (ϩ4) ϭ ϩ6 3ϩ2ϭ5 Case 2: Both numbers are negative.
All of the irrational numbers are real numbers. All of the rational numbers are real numbers. All of the integers are real numbers. All of the whole numbers are real numbers. All of the natural numbers are real numbers. EXAMPLES: 7 ᎏ1ᎏ 1 Ϫ53, Ϫᎏ13ᎏ , 4 2 , Ϫ 2 , Ϫᎏ53ᎏ, 0, ᎏ61ᎏ, 3 , 4, ᎏ47ᎏ and 1,247 are all real numbers. 30 algebra_ch1 5/4/06 9:27 AM Page 31 NUMBER SYSTEMS The Real Number System Rational Numbers Integers Irrational Numbers Whole Numbers Natural Numbers Caution—Major Mistake Territory!
You could continue counting until you reached Ϫ100 or Ϫ1,000, or you could continue counting forever. After every negative number there is another negative number that is one less than the number before it. When you place all these positive numbers, negative numbers, and zero together, you have what mathematicians call the integers. WHAT ARE THE INTEGERS? The integers are made up of three groups of numbers: • the positive integers • the negative integers • zero 37 algebra_ch2 5/4/06 9:30 AM Page 38 THE INTEGERS The positive integers are 1, 2, 3, 4, .