Rational numbers between \(\frac { 1 }{ 2 } \) and \(\frac { 1 }{ 5 } \)
= \(\left( \frac { 1 }{ 2 } +\frac { 1 }{ 5 } \right) \div 2\frac { 7 }{ 10 } \times \frac { 1 }{ 2 } =\frac { 7 }{ 20 } \)

Rational number between \(\frac { 1 }{ 5 } \) and \(\frac { 7 }{ 10 } \)
= \(\left( \frac { 1 }{ 5 } +\frac { 7 }{ 20 } \right) \div 2=\frac { 11 }{ 20 } \times \frac { 1 }{ 2 } =\frac { 11 }{ 40 } \)

Rational number between \(\frac { 7 }{ 20 } \) and \(\frac { 1 }{ 2 } \)
= \(\left( \frac { 7 }{ 20 } +\frac { 1 }{ 2 } \right) \div 2=\frac { 17 }{ 20 } \times \frac { 1 }{ 2 } =\frac { 17 }{ 40 } \)

Thus, the three rational numbers \(\frac { 11 }{ 40 } ,\frac { 7 }{ 20 } ,\frac { 17 }{ 40 } \) lie between \(\frac { 1 }{ 5 } \) and \(\frac { 1 }{ 2 } \)

Given, sugar required for one fruit salad =\({1\over2}\) cup
Sugar required for another salad = 2\(\times{1\over16}={2\over16}cup\)
\(\therefore\) Required sugar =\({1\over2}-{2\over16}={18-2\over16}={6\over16}={3\over8}cup\)

Given, sugar required for one fruit salad =\({1\over2}\) cup
Sugar required for another salad = 2\(\times{1\over16}={2\over16}cup\)
\(\therefore\) Required sugar =\({1\over2}-{2\over16}={18-2\over16}={6\over16}={3\over8}cup\)

Now, we have, \({1\over25},{1\over32},{1\over40},{1\over20}\)
Now, making same denominator, we get
\({1\over25}={32\over800},{1\over32}={25\over800},{1\over40}={20\over800},{1\over20}={40\over800}\)
(a) Soni hop more than Nancy with distance  
\(={40\over800}-{25\over800}={15\over800}={3\over160}Km\)
(b) Total distance covered by Seema and Megha  
\(={32\over800}+{20\over800}={52\over800}={13\over200}Km\)
(c) Clearly, Nancy walked farther than Megha.
(d) By competition, we make ourself relate with the surrounding in terms of compatibility of our quality. It helps to enrich our strength.

\({-3\over5}\times\{{3\over7}+({-5\over6})\}={-3\over5}\times{3\over7}+({-3\over5})\times ({-5\over6})\)
[using distributive property]
\(={-9\over35}+{15\over30}={-54+105\over210}={51\over210}={17\over70}\)

We know that, rational numbers are closed under addition, subtraction and multiplication. We can understand this from the following examples:
Rational numbers are closed under
Addition
\(eg.{4\over7}+{1\over2}={8+7\over14}={15\over14}\)
which is a rational number.
Subtraction
\(eg.{4\over7}-{1\over2}={8-7\over14}={1\over14}\)
which is a rational number.
Multiplication
\(eg.{4\over7}\times{1\over2}={4\over14}={2\over7}\)
which is a rational number.
But rational numbers are not closed under division. If zero is excluded from the collection of rational numbers, then we can say that rational numbers are closed under division.
Now, we see the examples given below:
\({4\over7}\div{1\over2}={4\over7}\times2={8\over7}{}\)
which is a rational number.
Also, \({1\over2}\div0={1\over2}\times{1\over0}\)
which is not defined and so, it is not a rational number.
Also, \({1\over2}\div0={1\over2}\times{1\over0}\)
which is not defined and also not a rational number.

9

\(23\over21\)

\(22\over7\)

\({29\over30}\)