Resumo - Modulo III - Parte I
Autor: Prof. Edson Santos | Publicado: 2011-09-16T09:10:00-07:00

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MÓDULO IIINúmeros Inteiros e Racionais Negativos
Vamos relembrar
• Sabemos que os números 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,... são chamadosNúmeros Naturais e a sequência de números naturais não tem fim.
• Os números naturais 1, 2, 3, 4, 5,... são números inteiros e positivos.
• Mas em algumas situações estes números não são suficientes para expressar a solução de determinadas situações-problema e utilizamos os números inteiros negativos como - 1, - 2, - 3, - 4 etc, que lemos menos um, menos dois, menos três, menos quatro;
• Podemos visualizar na reta numérica os números inteiros:Vamos relembrar
• O oposto de um número positivo é um número negativo simétrico a ele em relação ao zero. Por exemplo: o oposto de + 2 é - 2; o oposto de - 3 é + 3.
• A soma de um número com seu oposto é sempre zero. Por exemplo, (+ 4) + (- 4) = 0
• A reta numérica nos ajuda na comparação de números inteiros. Assim por exemplo, podemos observar que 3 &gt; 2, mas que - 3 &lt; - 2.
• Quando representamos um número inteiro positivo podemos usar o sinal de + à sua frente ou não: 3 e + 3 são escritas do mesmo número.
Deslocamentos na reta numérica, perdas e ganhos
“Complete com as palavras “sucessor” ou antecessor”, conforme o casoa) 3 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de 2 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e) 0 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de 1b) 2 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de 3 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f) 1 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de 0c) - 5 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de - 4  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; g) - 1 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de - 2d) - 4 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de - 5  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; h) - 2 é &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de - 1
Observando a tabela que conclusões você pode tirar a respeito do antecessor e do sucessor dos números inteiros negativos ou positivos? Registre o que pensou.________________________________________________________________________________________________________________________________________________________________________________________________
A professora de Mauro combinou com sua turma algumas regras de deslocamento na reta numérica: deslocamentos para a direita são positivos e deslocamentos para a esquerda são negativos. Desse modo:
O deslocamento do ponto + 1 para o ponto + 3 é positivo e corresponde a 2 unidades (u) : + 1 + 2 = + 3
O deslocamento do ponto - 1 para o ponto - 3 é negativo e corresponde a 2 unidades (u) : - 1 ____ = - 3
O deslocamento do ponto + 1 para o ponto - 3 é negativo e corresponde a 4 unidades (u) : + 1 ____ = - 3
O deslocamento do ponto - 1 para o ponto + 3 é positivo e corresponde a 4 unidades (u) : - 1 ____ = + 3
Observando a reta numérica e essas regras de deslocamento, complete:+ 3 + 6 = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - 8 + 5 = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + 3 - 3 =&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  - 2 - 3 =+ 1 + 5 = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - 2 + 7 = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + 5 - 9 = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - 5 - 7 =+ 11 + 10 = &nbsp;&nbsp; -12 + 15 = &nbsp;&nbsp;&nbsp;&nbsp; + 20 - 9 = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - 4 - 5 =
Usando a idéia de oposto de números inteiros
A escrita - (+ 2) representa o oposto de dois positivo, ou seja, dois negativo. Já a escrita - (- 2) representa o oposto de dois negativo, ou seja, dois positivo. Com base nessa informação, Joana completou a segunda coluna da tabela abaixo. Explique o que ela fez e comente se concorda com os resultados registrados.(+ 3) - (+ 4) &nbsp;&nbsp; /&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + 3 - 4 = -1(+ 3) - (- 4) &nbsp;&nbsp;&nbsp; /&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + 3 + 4 = + 7(- 3) - (- 4) &nbsp;&nbsp;&nbsp;&nbsp; /&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - 3 + 4 = +1(- 3) - (+ 4) &nbsp;&nbsp;&nbsp; /&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - 3 - 4 = - 7