# Find the greatest number and the smallest number among the following 3/7,-2/3,0,-7/9,-2/5.

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2015-04-16T01:28:28+05:30

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Let us first put the positive and negative numbers on either side of 0.

-2/3  , -2/5,  -7/9,    0 ,  3/7

Since only one number 3/7 is positive,  and more than 0, it is the greatest number among the given numbers.  So now we need to find the smallest number.  It will be the most negative number.

2/3  and  2/5  have same numerator.
Since 5 > 3,      So    2/5  <  2/3 ,  as 5 and 3 are in the denominators.
Hence,    -2/5  >  - 2/3              as we add - sign.
So  -2/3 is smaller of the two.

-2/3  and -7/9  are to be compared.
-2/3 = -6/9      and  -7/9  are to be compared.
Since    6  <  7 ,      - 6 >  - 7      as  we  add the - sign.
Hence,  -6/9    >  - 7/9            as we divide by a positive number 9.

So -7/9  is the smallest number.
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we use the subtraction operation to decide the smallest number.
(-2/3)  -  (-2/5)
=  - 2/3  + 2/5
=  ( -2*5 + 2*3 ) /15
= -4/15      is negative.  the first number is smaller.

(-2/3)  -  (-7/9)
=  -2/3 + 7/9
=  (-2*3 + 7) / 9
=  1 / 9
result is positive, so the first number is larger.

Thus  the smallest number is  -7/9