actividad 2 grado octavo

Activity in class :  solve the following operations   -120 + (-30) + [ -80 + (-120 / 4) ( -3) ]=  ·         -24 – 30 [-20 + (-40) + (-10+ (-3) ) (-4)]= ·         -40 -  (-20) (-5) + 8 – ( -7)= ·         -40 - 8-(-20 )/ (-10) + 4 = ·         -100  + (-120) [(-8 + 9 ) ( -20 – ( -4 ) ) ] Numbers sets: 1.       Rational Numbers A Rational Number is a real number that can be written as a simple fraction (i.e. as a ratio). Most numbers we use in everyday life are Rational Numbers. Example: 1,5 is a rational number because 1,5 = 3/2 (it can be written as a fraction) 2.       Irrational Numbers An Irrational Number is a real number that cannot be written as a simple fraction. Irrational means not Rational Examples: Rational Numbers  Rational Number can be written as a Ratio of two integers (is a simple fraction). Example: 1,5 is rational, because it can be written as the ratio 3/2 Example: 7 is rational, because it can be written as the ratio 7/1 Example 0,333... (3 repeating) is also rational, because it can be written as the ratio1/3 Irrational Numbers But some numbers cannot be written as a ratio of two integers ... ...they are called Irrational Numbers. 3.       Real Numbers Real Numbers are just numbers like: 1 12,38 −0,8625 3/4 √2 198 In fact: Nearly any number you can think of is a Real Number Real Numbers include: Whole Numbers (like 0, 1, 2, 3, 4, etc) Rational Numbers (like 3/4, 0,125, 0,333..., 1,1, etc ) Irrational Numbers (like π, √3, etc ) Real Numbers can also be positive, negative or zero. So ... what is NOT a Real Number? Imaginary Numbers like √−1 (the square root of minus 1) are not Real Numbers Infinity is not a Real Number Real Number Properties Example: Multiplying by zero When we multiply a real number by zero we get zero: ·         5 × 0 = 0 ·         −7 × 0 = 0 ·         0 × 0,0001 = 0 It is called the "Zero Product Property", and is listed below. Properties: the main are Real Numbers are Commutative, Associative and Distributive: Commutative Example a + b = b + a 2 + 6 = 6 + 2 ab = ba 4 × 2 = 2 × 4 Associative Example (a + b) + c = a + ( b + c ) (1 + 6) + 3 = 1 + (6 + 3) (ab)c = a(bc) (4 × 2) × 5 = 4 × (2 × 5) Distributive Example a × (b + c) = ab + ac 3 × (6+2) = 3 × 6 + 3 × 2 (b+c) × a = ba + ca (6+2) × 3 = 6 × 3 + 2 × 3 Real Numbers are closed (the result is also a real number) under addition and multiplication: Closure Example a+b is real 2 + 3 = 5 is real a×b is real 6 × 2 = 12 is real Adding zero leaves the real number unchanged, likewise for multiplying by 1: Identity Example a + 0 = a 6 + 0 = 6 a × 1 = a 6 × 1 = 6 For addition the inverse of a real number is its negative, and for multiplication the inverse is itsreciprocal: Additive Inverse Example a + (−a ) = 0 6 + (−6) = 0 Multiplicative Inverse Example a × (1/a) = 1 6 × (1/6) = 1 But not for 0 as 1/0 is undefined Multiplying by zero gives zero (the Zero Product Property): Zero Product Example If ab = 0 then a=0 or b=0, or both a × 0 = 0 × a = 0 5 × 0 = 0 × 5 = 0 Multiplying two negatives make a positive, and multiplying a negative and a positive makes a negative: Negation Example −1 × (−a) = −(−a) = a −1 × (−5) = −(−5) = 5 (−a)(−b) = ab (−3)(−6) = 3 × 6 = 18 (−a)(b) = (a)(−b) = −(ab) −3 × 6 = 3 × −6 = −18 Study the properties