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CBSE Class 8 Answered

cannot understand commutative and distributive property in rational numbers
 
Asked by ajayrath7 | 24 Mar, 2017, 10:01: AM
answered-by-expert 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 | 24 Mar, 2017, 10:19: AM

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