Getallestelsels: RGMD#1

Vereenvoudig die volgende breuke.

a) $3 over 4 cross times 2 over 3$

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 5 over 24 close parentheses divided by end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 over 3 close parentheses end cell end table

c) $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 over 4 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 cross times 2 squared over denominator 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank divided by end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 cross times 2 over denominator 2 cross times open parentheses negative 4 close parentheses end fraction end cell end table$

a)
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 4 cross times 2 over 3 end cell row blank equals cell up diagonal strike 3 to the power of 1 over up diagonal strike 4 squared cross times up diagonal strike 2 to the power of 1 over up diagonal strike 3 to the power of 1 end cell row blank equals cell fraction numerator 1 cross times 1 over denominator 2 cross times 1 end fraction end cell row blank equals cell 1 half end cell row blank blank cell O F end cell row blank blank cell 3 over 4 cross times 2 over 3 end cell row blank equals cell fraction numerator 3 cross times 2 over denominator 4 cross times 3 end fraction end cell row blank equals cell fraction numerator 6 divided by 6 over denominator 12 divided by 6 end fraction end cell row blank equals cell 1 half end cell end table$

b)
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 5 over 24 close parentheses divided by open parentheses 2 over 3 close parentheses end cell row blank equals cell open parentheses negative 5 over 24 close parentheses cross times open parentheses 3 over 2 close parentheses end cell row blank equals cell open parentheses negative 5 over up diagonal strike 24 to the power of 8 close parentheses cross times open parentheses up diagonal strike 3 to the power of 1 over 2 close parentheses end cell row blank equals cell fraction numerator negative 5 cross times 1 over denominator 8 cross times 2 end fraction end cell row blank equals cell fraction numerator negative 5 over denominator 16 end fraction end cell row blank blank cell O F end cell row blank blank cell open parentheses negative 5 over 24 close parentheses divided by open parentheses 2 over 3 close parentheses end cell row blank equals cell open parentheses negative 5 over 24 close parentheses cross times open parentheses 3 over 2 close parentheses end cell row blank equals cell fraction numerator negative 5 cross times 3 over denominator 24 cross times 2 end fraction end cell row blank equals cell fraction numerator negative 15 divided by 3 over denominator 48 divided by 3 end fraction end cell row blank equals cell fraction numerator negative 5 over denominator 16 end fraction end cell end table$

c)
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 over 4 cross times fraction numerator 3 cross times 2 squared over denominator 6 end fraction divided by fraction numerator 3 cross times 2 over denominator 2 cross times open parentheses negative 4 close parentheses end fraction end cell row blank equals cell 6 over 4 cross times fraction numerator 3 cross times 2 squared over denominator 6 end fraction divided by fraction numerator 3 cross times 2 over denominator 2 cross times open parentheses negative 4 close parentheses end fraction end cell row blank equals cell 6 over 4 cross times 12 over 6 divided by fraction numerator 6 over denominator open parentheses negative 8 close parentheses end fraction end cell row blank equals cell up diagonal strike 6 to the power of 1 over up diagonal strike 4 to the power of 1 cross times up diagonal strike 12 squared over up diagonal strike 6 to the power of 1 cross times fraction numerator open parentheses negative up diagonal strike 8 squared close parentheses over denominator up diagonal strike 6 to the power of 1 end fraction end cell row blank equals cell fraction numerator 1 cross times 2 cross times open parentheses negative 2 close parentheses over denominator 1 cross times 1 cross times 1 end fraction end cell row blank equals cell fraction numerator negative 4 over denominator 1 end fraction end cell row blank equals cell negative 4 end cell end table$

d)
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 8 begin display style 2 over 3 end style over denominator 2 begin display style 2 over 5 end style end fraction end cell row blank equals cell 8 2 over 3 divided by 2 2 over 5 end cell row blank equals cell 26 over 3 divided by 12 over 5 end cell row blank equals cell up diagonal strike 26 to the power of 13 over 3 cross times 5 over up diagonal strike 12 to the power of 6 end cell row blank equals cell fraction numerator 13 cross times 5 over denominator 3 cross times 6 end fraction end cell row blank equals cell 65 over 18 end cell row blank equals cell 3 11 over 18 end cell end table$