Verify the property, x x (y+z)=(x x y)+(x x y).     x=-8/3,y=5/6,and z=-7/12
Find five rational numbers between -2/3 and 5/3.
Find any three rational numbers between 1/2 and 1/5
Arrange the following rational numbers in ascending order   1/2 , 2/3 ,-1/4 ,-3/5
The cost of 1 m of cloth is ₹25(1/4) . find the cost of 5(3/4) of cloth.
A cyclist covers 14(2/5)km in 2(1/4) hours .Find the distance covered in  1 hour.
 

Asked by Krishna | 24th Aug, 2015, 12:42: PM

Expert Answer:

1. space C o n s i d e r space t h e space g i v e n space p r o p e r t y colon x cross times open parentheses y plus z close parentheses equals open parentheses x cross times y close parentheses plus open parentheses x cross times z close parentheses S u b s t i t u t i n g comma space x equals 8 over 3 comma space y equals 5 over 6 comma space z equals fraction numerator negative 7 over denominator 12 end fraction T h u s comma L H S equals x cross times open parentheses y plus z close parentheses equals 8 over 3 cross times open parentheses 5 over 6 plus open parentheses fraction numerator negative 7 over denominator 12 end fraction close parentheses close parentheses equals 8 over 3 cross times open parentheses 10 over 12 minus 7 over 12 close parentheses equals 8 over 3 cross times 3 over 12 equals 2 over 3 N o w space c o n s i d e r space t h e space R H S colon open parentheses x cross times y close parentheses plus open parentheses x cross times z close parentheses equals 8 over 3 cross times 5 over 6 plus 8 over 3 cross times open parentheses fraction numerator negative 7 over denominator 12 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals 40 over 18 plus open parentheses fraction numerator negative 56 over denominator 36 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 40 cross times 2 over denominator 18 cross times 2 end fraction plus open parentheses fraction numerator negative 56 over denominator 36 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals 80 over 36 plus open parentheses fraction numerator negative 56 over denominator 36 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 80 minus 56 over denominator 36 end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals 24 over 36 space space space space space space space space space space space space space space space space space space space space space space space space equals 2 over 3 T h u s comma space L H S equals R H S  2. W e space h a v e space t w o space r a t i o n a l space n u m b e r s space fraction numerator negative 2 over denominator 3 end fraction space a n d space 5 over 3 fraction numerator negative 2 over denominator 3 end fraction less than 5 over 3 fraction numerator negative 2 over denominator 3 end fraction less than fraction numerator negative 1 over denominator 3 end fraction less than 0 less than 1 third less than 2 over 3 less than 3 over 3 less than 4 over 3 less than 5 over 3 T h u s comma space r a t i o n a l space n u m b e r s space i n space b e t w e e n space fraction numerator negative 2 over denominator 3 end fraction space a n d space 5 over 3 space a r e colon fraction numerator negative 1 over denominator 3 end fraction comma 0 comma 1 third comma space 2 over 3 comma 1 comma 4 over 3 3. W e space h a v e space t w o space r a t i o n a l space n u m b e r s space 1 half space a n d space 1 fifth 1 half greater than 1 fifth rightwards double arrow 1 half cross times 5 over 5 greater than 1 fifth cross times 2 over 2 rightwards double arrow 5 over 10 greater than 2 over 10 rightwards double arrow 2 over 10 less than 3 over 10 less than 4 over 10 less than 5 over 10 T o space f i n d space a space r a t i o ln a l space n u m b e r space b e t w e e n comma space 3 over 10 space a n d space 4 over 10 colon fraction numerator 3 over 10 plus 4 over 10 over denominator 2 end fraction equals fraction numerator begin display style 7 over 10 end style over denominator 2 end fraction equals 7 over 20 T h u s comma space r a t i o n a l space n u m b e r s space i n space b e t w e e n space 1 half space a n d space 1 fifth space a r e colon 3 over 10 comma space 7 over 20 space a n d space 4 over 10

Answered by Vimala Ramamurthy | 25th Aug, 2015, 10:19: AM

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