(i) \(\frac { 3 }{ 4 } \)
\(\frac { 3 }{ 4 } \)means 3 parts out of 4 equal parts. So, we  divide the gap between 0 and 1 into 4 equal parts and  show 3 parts as \(\frac { 3 }{ 4 } \) .

(ii) \(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ 2 } \)means 1 part out of 2 equal parts. So, we divide the gap between 0 and 1 into 2 equal parts and show 1 part as \(\frac { 1 }{ 2 } \) .

(iii) \(\frac { 9 }{ 10 } \)
\(\frac { 9 }{ 10 } \) means a part out of 10 equal parts. So, we divide the gap between 0 and 1 into 10 equal parts and show 9 parts as \(\frac { 9 }{ 10 } \) .

(iv) \(\frac { 0 }{ 3 } \)
\(\frac { 0 }{ 3 } \)is the point zero.

(v) \(\frac { 5 }{ 8 } \)
\(\frac { 5 }{ 8 } \) means 5 parts out of 8 equal parts. So, we  divide the gap between 0 and I into 8 equal parts and  show 5 parts as  \(\frac { 5 }{ 8 } \) .

\(3\frac{8}{28}\)

Unlike fractions: Fractions having different denominators

In the given table, we see that the minimum value is 3.0 J and maximum value is 5.3 J.
∴ Least energy provide by food = 3.0 J i.e. Milk
Food which provide the maximum energy = 5.3 J i.e. Rice
∴ Required fraction = \(\frac { Least\ energy }{ Maximum\ energy } =\frac { 3.0 }{ 5.3 } =\frac { 30 }{ 53 } \) 

Number of pieces the cake cut = 8
Number of pieces each cut piece divided into = 3
∴ Total number of pieces =\(8\times3=24\)
Hence, each piece is represented by the fraction\(\frac{1}{24}.\) 

Given, Rajan's age on the joining = 24 yr
and retirement age = 60 yr
The number of years, he did the job
= Retirement age - Joining age
= 60 - 24 = 36 yr
∴ The fraction of his age till retirement, when he was in the job
\(=\frac { Total\ years\ he\ did\ the\ job }{ Retirement\ age } =\frac { 36 }{ 60 } \) [ \(\because\) HCF of 36 and 60 = 12 ]
\(=\frac { 36\div 12 }{ 60\div 12 } =\frac { 3 }{ 5 } \)
Hence, the required fraction is = \(\frac { 3 }{ 5 } .\) 

Here, a watermelon is divided into 16 parts.
∴ Each part =\(\frac { 1 }{ 16 } \)
I ate 7 parts out of 16 parts i.e. \(\frac { 7 }{ 16 } \) part
My friend ate 4 parts out of 16 parts i.e\(\frac { 4 }{ 16 } \) part
Now, the part which we eat together
=\(\frac { 7 }{ 16 } +\frac { 4 }{ 16 } =\frac { 7+4 }{ 16 } =\frac { 11 }{ 16 } \)  part
Now, difference between our parts = \(\frac { 7 }{ 16 } -\frac { 4 }{ 16 } =\frac { 7-4 }{ 16 } =\frac { 3 }{ 16 } \)
So, I ate\(\frac { 3 }{ 16 } \) part of watermelon more than my friend. Now, remaining part of the watermelon = 1- \(\frac { 11 }{ 16 } -\frac { 16 }{ 16 } -\frac { 11 }{ 16 } \)
 [∵ \(\frac { 16 }{ 16 } \)and 1 are equivalent fractions]
= \(\frac { 16-11 }{ 16 } =\frac { 5 }{ 16 } \)

We have,
Pictorially, it can be shown as

By folding paper, it can be shown in the following way Take a square piece of paper say ABCD [figure (i)].

Fold it by overlapping its edge AB and CD to get figure (ii).

Again, refold it by taking EF over C(A) D(B) to get figure (iii).

Now,reopen it, then we get the following figure (iv)

Now,fold it vertically at two places to obtain three equal vertical portion as shown in figure (v)

Shaded \(\frac { 1 }{ 12 } \)portion twice,
We see that, \(\frac { 1 }{ 12 } +\frac { 1 }{ 12 } =\frac { 1+1 }{ 12 } =\frac { 2 }{ 12 } =\frac { 1 }{ 6 } \)

(i) Total number of equal parts = 12;
Number of shaded parts = 4
 ∴  Fraction of shaded portion = \(\frac { 4 }{ 12 } \)
(ii) Total number of equal parts = 9;
Number of shaded parts = 3
 ∴ Fraction of shaded portion = 3/9
(iii) Total number of equal parts = 6;
Number of shaded parts = 2
 ∴ Fraction of shaded portion = 2/6
(iv) Total number of equal parts = 3;
Number of shaded parts = 1
 ∴ Fraction of shaded portion =1/3
(v) Total number of equal parts = 15;
Number of shaded parts = 6
 ∴ Fraction of shaded portion = \(\frac { 6 }{ 15 } \)
Now,   \(\frac { 4 }{ 12 } =\frac { 4\div 4 }{ 12\div 4 } =\frac { 1 }{ 3 } \)    [∵HCF of 4 and 12 is 4]
\(\frac { 3 }{ 9 } =\frac { 3\div 3 }{ 9\div 3 } =\frac { 1 }{ 3 } \)  [∵HCF of 3 and 9 is 3]
\(\frac { 2 }{ 6 } =\frac { 2\div 2 }{ 6\div 2 } =\frac { 1 }{ 3 } \) [∵HCF of 2 and 6 is 2]
\(\frac { 6 }{ 15 } =\frac { 6\div 3 }{ 15\div 3 } =\frac { 2 }{ 5 } \)  [∵HCF of 6 and 15 is 3]
Here, except \(\frac { 6 }{ 15 } \)all the fractions in simplest form are same.
So, \(\frac { 4 }{ 12 } =\frac { 3 }{ 9 } =\frac { 2 }{ 6 } =\frac { 1 }{ 3 } \neq \frac { 2 }{ 5 } \)
Hence, these fractions are not equivalent.

(i) Total number of equal parts = 2;
Number of shaded parts = 1
∴ Fraction of shaded portion = \(\frac { Number\ of\ shaded\ parts\ }{ Total\ number\ of\ equal\ parts } =\frac { 1 }{ 2 } \)
(ii) Total number of equal parts = 4;
Number of shaded parts = 2
∴ Fraction of shaded portion = 2/4
(iii) Total number of equal parts = 6;
Number of shaded parts = 3
∴ Fraction of shaded portion = 3/6
(iv) Total number of equal parts = 8;
Number of shaded parts = 4
∴ Fraction of shaded portion = 4/8
Now, \(\frac { 2 }{ 4 } =\frac { 2\div 2 }{ 4\div 2 } =\frac { 1 }{ 2 } \)  [∵ HCF of 2 and 4 is 2]
\(\frac { 3 }{ 6 } =\frac { 3\div 3 }{ 6\div 3 } =\frac { 1 }{ 2 } \)  [∵ HCF of 3 and 6 is 3]
\(\frac { 4 }{ 8 } =\frac { 4\div 4 }{ 8\div 4 } =\frac { 1 }{ 2 } \) [∵ HCF of 4 and 8 is 4]
Since all fraction in simple form are same.
∴ \(\frac { 1 }{ 2 } =\frac { 2 }{ 4 } =\frac { 3 }{ 6 } =\frac { 4 }{ 8 } \) i.e the fractions are equivalent.