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by what number should -28 multiplied to get the multiplicative inverse of -5
                     

Asked by satish01 14th May 2016, 1:35 PM
Answered by Expert
Answer:
W h a t space i s space a space m u l t i p l i c a t i v e space i n v e r s e ?
M u l t i p l i c a t i v e space i n v e r s e space o f space a space n u m b e r space i s space a space n u m b e r space w h i c h space w h e n space m u l t i p l i e d space w i t h space t h e space g i v e n space n u m b e r comma space g i v e s space
t h e space p r o d u c t space 1.


M u l t i p l i c a t i v e space i n v e r s e space o f space minus 5 colon
L e t space t h e space M u l t i p l i c a t i v e space i n v e r s e space o f space minus 5 space b e space x.
T h e r e f o r e comma space b y space t h e space d e f i n i t i o n comma space w e space h a v e space x cross times open parentheses negative 5 close parentheses equals 1
rightwards double arrow x space i s space t h e space r e c i p r o c a l space o f space minus 5
rightwards double arrow x equals fraction numerator 1 over denominator negative 5 end fraction
therefore M u l t i p l i c a t i v e space i n v e r s e space o f space minus 5 space i s space fraction numerator negative 1 over denominator 5 end fraction


L e t space y space b e space t h e space n u m b e r space m u l t i p l i e d space t o space minus 28 space t o space g e t space fraction numerator negative 1 over denominator 5 end fraction.
T h e r e f o r e comma space w e space h a v e space y cross times open parentheses negative 28 close parentheses equals fraction numerator negative 1 over denominator 5 end fraction
rightwards double arrow y equals fraction numerator 1 over denominator open parentheses negative 5 close parentheses cross times open parentheses negative 28 close parentheses end fraction
therefore space t h e space n u m b e r space m u l t i p l i e d space t o space minus 28 space t o space g e t space fraction numerator negative 1 over denominator 5 end fraction space i s space 1 over 140
Answered by Expert 14th May 2016, 3:24 PM
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