After putting the appropriate signs, we have \(\frac { 3 }{ 7 } \boxed { < } \frac { 5 }{ 7 } \)

We have \(\frac { 6 }{ 10 } ,\frac { 7 }{ 10 } \)
Here, denominators of both fractions are same and 7 > 6.
So, \(\frac { 7 }{ 10 } >\frac { 6 }{ 10 } \)

7

We know that, total minutes in an hour = 60 min
∴   Required field fraction = \(\frac { 40\quad min }{ 60\quad min } =\frac { 40 }{ 60 } =\frac { 2 }{ 3 } \)

Here, fraction \(\frac { 1 }{ 3 } \) shows that out of 3 equal parts, 1 part is shaded. So, the required figure is shown alongside.

Total number of equal parts = 7; Shaded parts = 3
 ∴ Fraction representing the shaded portion = \(\frac { 3 }{ 7 } \)

Total number of equal parts = 4; Shared parts = 2
∴ Fraction representing the shaded portion
 = \(\frac { Number\ of\ shaded\ parts }{ Total\ number\ of\ equal\ parts } =\frac { 2 }{ 4 } \)

Here, the given figure is divided into 4 equal parts and 3 parts out of 4 parts are shaded.
∴ The required fraction = \(\frac { 3 }{ 4 } \)

We have \(\Box{ } -\frac { 5 }{ 8 } =\frac { 1 }{ 4 } \)
Here\(\frac { 5 }{ 8 } \) is subtracted from missing fraction to get\(\frac { 1 }{ 4 } .\) This means addition of \(\frac { 5 }{ 8 } \) and \(\frac { 1 }{ 4 } \) gives the missing fraction.
∴ Missing fraction = \(\frac { 1 }{ 4 } +\frac { 5 }{ 8 } \)
⇒ \(\frac { 1 }{ 4 } =\frac { 1\times 2 }{ 4\times 2 } =\frac { 2 }{ 8 } \)
Now, \(\frac { 1 }{ 4 } +\frac { 5 }{ 8 } =\frac { 2 }{ 8 } +\frac { 5 }{ 8 } =\frac { 2+5 }{ 8 } =\frac { 7 }{ 8 } \)
Hence  \(\boxed { \frac { 7 }{ 8 } } -\frac { 5 }{ 8 } =\frac { 1 }{ 4 } \)

\(\frac { 3 }{ 5 } =\frac { \boxed { 12 } }{ 20 } \)

We have \(\frac { 16 }{ 72 } \)
Now, factors of 16 = 2\(\times\)2\(\times\)2\(\times\)2 and factor of 72 = 2\(\times\)2\(\times\)2\(\times\)2\(\times\)3
Common factors = 2,2 and 2
∴ HCF of 16 and 72 = 2\(\times\) 2\(\times\)2 = 8
Then, \(\frac { 16 }{ 72 } =\frac { 16\div 8 }{ 16\div 8 } =\frac { 2 }{ 9 } \)
Hence ,fraction \(\frac { 2 }{ 9 } \)is the simplest form of given fraction.

Here, fractions are \(\frac { 1 }{ 8 } ,\frac { 2 }{ 8 } ,\frac { 3 }{ 8 } and\frac { 7 }{ 8 } \)
Now, draw a number line, mark two points 0 and Ion it. Divide the gap between 0 and 1 into eight equal parts because denominator is 8, then each part will show.\(\frac { 1 }{ 8 } \)Also 2 parts show\(\frac { 2 }{ 8 } \), 3 parts show\(\frac { 3 }{ 8 } \) and 7 parts show \(\frac { 7 }{ 8 } \)

Hence, A, B, C and D represent \(\frac { 1 }{ 8 } ,\frac { 2 }{ 8 } ,\frac { 3 }{ 8 } and\frac { 7 }{ 8 } \) respectively.

Let a rectangle be divided into x equal parts.
Now, 16 of the parts represent =\(\frac{1}{4}\)
\(\therefore \frac { 16 }{ x } =\frac { 1 }{ 4 } \Rightarrow x=16\times 4\Rightarrow \) x = 64 parts
Hence, rectangle is divided into 64 equal parts.

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 = 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.