cannot understand commutative and distributive property in rational numbers
 

Asked by ajayrath7 | 24th Mar, 2017, 10:01: AM

Expert Answer:

begin mathsize 16px style bold Commutative bold space bold Law bold colon
Two space rational space numbers space can space be space added space in space any space order.
If space straight p over straight q space and space straight r over straight s space are space two space rational space numbers comma space then space we space have
open parentheses space straight p over straight q plus straight r over straight s close parentheses equals open parentheses straight r over straight s plus straight p over straight q close parentheses
bold Example bold colon
open parentheses space 1 half plus 4 over 5 close parentheses equals fraction numerator 5 plus 8 over denominator 10 end fraction equals 13 over 10
open parentheses 4 over 5 plus 1 half close parentheses equals fraction numerator 8 plus 5 over denominator 10 end fraction equals 13 over 10
So comma space open parentheses space 1 half plus 4 over 5 close parentheses equals open parentheses 4 over 5 plus 1 half close parentheses

bold Distributive bold space bold Property bold space bold of bold space bold Multiplication bold space bold over bold space bold Addition bold colon
For space any space three space rational space numbers comma space straight a over straight b comma space straight c over straight d comma space and space straight e over straight f comma space we space have colon
straight a over straight b cross times open parentheses straight c over straight d plus space straight e over straight f close parentheses equals open parentheses straight a over straight b cross times straight c over straight d close parentheses plus open parentheses straight a over straight b cross times space straight e over straight f close parentheses
bold Example bold colon
Consider space the space rational space numbers comma space fraction numerator negative 1 over denominator 2 end fraction comma space 2 over 3 space and space fraction numerator negative 3 over denominator 5 end fraction
fraction numerator negative 1 over denominator 2 end fraction cross times open parentheses 2 over 3 plus space fraction numerator left parenthesis negative 3 right parenthesis over denominator 5 end fraction close parentheses equals fraction numerator negative 1 over denominator 2 end fraction cross times open parentheses fraction numerator 10 minus 9 over denominator 15 end fraction close parentheses equals fraction numerator negative 1 over denominator 2 end fraction cross times open parentheses 1 over 15 close parentheses equals fraction numerator negative 1 over denominator 30 end fraction
open parentheses fraction numerator negative 1 over denominator 2 end fraction cross times 2 over 3 close parentheses plus open parentheses fraction numerator negative 1 over denominator 2 end fraction cross times fraction numerator negative 3 over denominator 5 end fraction close parentheses equals fraction numerator negative 2 over denominator 6 end fraction plus 3 over 10 equals fraction numerator negative 10 plus 9 over denominator 30 end fraction equals fraction numerator negative 1 over denominator 30 end fraction
So comma space fraction numerator negative 1 over denominator 2 end fraction cross times open parentheses 2 over 3 plus space fraction numerator left parenthesis negative 3 right parenthesis over denominator 5 end fraction close parentheses equals open parentheses fraction numerator negative 1 over denominator 2 end fraction cross times 2 over 3 close parentheses plus open parentheses fraction numerator negative 1 over denominator 2 end fraction cross times fraction numerator negative 3 over denominator 5 end fraction close parentheses
This space means space that space multiplication space can space be space distributed space over space addition. end style

Answered by Rebecca Fernandes | 24th Mar, 2017, 10:19: AM