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Matematica


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» OPERATII CU FRACTII


OPERATII CU FRACTII



OPERATII CU FRACTII

MULTIMEA NUMERELOR RATIONALE POZITIVE


            Q=   a   aI½N, bI½N*              

                     b                                                                                                                                                                                                                                                                                                   

·        Un numar rational este o multime de fractii echivalente

1.- Fractii echivalente a = c Û a x d= b x c

2.- Procedee de obtinere a fractiilor echivalente

            a.- AMPLIFICAREA: a= a x m

                                               b   b x m

            b.- SIMPLIFICAREA:

                                                a= a : m

                                                       b   b : m

·        Fractia care nu se simplifica se numeste fractie ireductibila

3.- Clasificarea fractiilor: fractii: - supraunitare

-         echiunitare

-         subunitare

4.- Scoaterea intregilor din fractie:

            Scoaterea intregilor din fractie se face impartind numaratorul laa numitor.

5.- Introducerea intregilor in fractie: a m = a x n + m

                                                              n           n

6.- Operatii: a.- Adunarea si scaderea:

                                    I.- a ± b  = a+b

                                    k   k       k

                                    II.- a ± a  = ap+ak

                                    k     k       k x p

                      b.- Inmultirea: - a  x  b  = a x b

                                                 k      p     k x p

                      c.- Impartirea: - a  :   b  = a  x  p = ap

                                                 k      p     k     b    kb

                          d.- I.- Operatii cu puteri

                                                            a  x  a ..aÞ   a   n

                                                    b      b              b

                       

                                                            n factori

                                    II.- Operatii cu puteri:

                                                           a   x   a  =   a   

                                                    b        b       b

                                                             a    =   a   

                                                    b         b

                                                            a   x   a  =   a   

                                                    b        b       b

                                                            a   x   c  =   a   x   c

                                                    b       d       b       d

7.- Ordinea operatiilor si folosirea parantezelor:

R1: Daca intr-un exercitiu avem operatii de acelasi ordin ele se efectueaza in ordinea in care sunt scrise.

R2: Daca intr-un exercitiu avem operatii de ordinul I, II, III, ele se efectueaza in ordinea III, II, I.

R3: Daca intr-un exercitiu avem paranteze , [], ()       , se efectueaza in ordinea (), [], , respectand R1 si R2.

8.- Operatii cu numere rationale pozitive


Q+ =     1, 1, ., n, .  

            a.- Adunarea:  a  +  c  = a+c

                                  b      b        b

                       

                                       a  +  d  = ap + dk (kI  x p) = 1

                                  k      p         kp

            b.- Scaderea: :  a  -  b  = a-b     a ³ b

                                   c      c        c

                       

                                       a  -  b  = ap - bk (kI  x p) = 1

                                  k     p         kp

            c.- Inmultirea:

                                  a  x  c  = a x c

                                  b      d    b x d

            d.- Impartirea:

                       

                                       a  :  c  = a  x d  =  ad

                                  b     d     b     c       bc

            e.- Puteri:



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