Question

1. para dois números naturais A e B, vale a relação: A ×B= mmc (a, b). mdc (a, b)

verifique essa relação para os pares de números a seguir, efetuando os cálculos necessários.
A )▪15×20 = _______▪mmc (15, 20)× mdc (15, 20)=_______


b)▪9×11=__________ ▪mmc (9, 11)×mdc
(9, 11)=_________


C)▪110×120=____▪mmc(110,120)×mdc
(110, 120)=_______

a relação apresentada foi satisfeita em todos os itens? justifique sua resposta.


por favor me ajudem e pra hoje esse trabalho tem que ser com cálculo por favor​

Answer 1

a)

$15~,~20~~|~~2\\15~,~10~~|~~2\\15~,~~\,5~~|~~3\\~~\,5~,~~\,5~~|~~\boxed{5}\\~~\,1~,~~\,1~~|~~\boxed{1}\\\\\\MMC(15,20)~=~2~.~2~.~3~.~5~.~1\\\\MMC(15,20)~=~60\\\\\\MDC(15,20)~=~5~.~1\\\\MDC(15,20)~=~5$

--> 15 x 20 = 300

--> MMC(15,20) x MDC(15,20) = 300

b)

$9~,~11~~|~~3\\3~,~11~~|~~3\\1~,~11~~|~~11\\1~,~~\,1~~|~~\boxed{1}\\\\\\MMC(9,11)~=~3~.~3~.~11~.~1\\\\MMC(9,11)~=~99\\\\\\MDC(9,11)~=~1$

--> 9 x 11 = 99

--> MMC(9,11) x MDC(9,11) = 99

c)

$110~,~120~~|~~\boxed{2}\\~~\,55~,~~\,60~~|~~2\\~~\,55~,~~\,30~~|~~2\\~~\,55~,~~\,15~~|~~3\\~~\,55~,~~~~5~~|~~\boxed{5}\\~~\,11~,~~~~1~~|~~11\\~~~~1~,~~~~1~~|~~\boxed{1}\\\\\\MMC(110,120)~=~2~.~2~.~2~.~3~.~5~.~11~.~1\\\\MMC(110,120)~=~1320\\\\\\MDC(110,120)~=~2~.~5~.~1\\\\MDC(110,120)~=~10$

--> 110 x 120 = 13200

--> MMC(110,120) x MDC(110,120) = 13200

Resposta: Sim, a relação foi satisfeita em todos os casos.

Answer 2

Resposta:

Olha em cima ajuda

Explicação passo-a-passo: