\(\Rightarrow\)18 x 4 = 24 x \(\Box\)
\(\Rightarrow\) \(\Box\) = \(\frac { 18\times 4 }{ 24 } \)
\(\Rightarrow\) \(\Box\) = 3
\(\therefore\) \(\frac { 18 }{ 24 } =\frac { \boxed { 3 } }{ 4 } \)

\({18\over 24}={\boxed{3}\over 4}\)

9

\(\frac{7}{9}\)is greater by \(\frac{20}{153}\)

Quantity of juice Nazima has = 5\(\frac{1}{2}\) L
She gave 2\(\frac{3}{4}\) L out of this to her friends.
Now, juice left with her =  5\(\frac{1}{2}\) -  2\(\frac{3}{4}\) 
= \(\frac{11}{2}-\frac{11}{4}=\frac{22-11}{4}=\frac{11}{4}=2\frac{3}{4}\) L
So, \(2\frac{3}{4}\) of juice is left with her.

The size of grip of tennis racket = 12 \(\frac{3}{20}\) cm
= 12 + \(\frac{3}{20}=\frac{12\times20+3}{20}\)
= \(\frac{240+3}{20}=\frac{243}{20}\)cm

we have, 

⇒ 5 x 12= 9 x 7
60 ≠ 63
So,\(\frac{7}{5},\frac{21}{5}\)are not equivalent fractions.

We have, Improper fraction = \(\frac{15}{4}\)
∴ \(\frac{15}{4}=3\frac{3}{4}\)

We have \(2\frac { 2 }{ 5 } \) and \(3\frac { 5 }{ 6 } \)
To add mixed fractions, first convert both mixed fractions into improper fractions.
Now, \(2\frac { 2 }{ 5 } =\frac { 12 }{ 5 } \) and  \(3\frac { 5 }{ 6 } =\frac { 23 }{ 6 } \) ⇒ \(2\frac { 2 }{ 5 } +3\frac { 5 }{ 6 } =\frac { 12 }{ 5 } +\frac { 23 }{ 6 } \)
Now, converting them into equivalent fractions with the same denominator
\(\frac { 12 }{ 5 } =\frac { 12\times 6 }{ 5\times 6 } =\frac { 72 }{ 30 } ,\)    we have \(\frac { 23 }{ 6 } =\frac { 23\times 5 }{ 6\times 5 } =\frac { 115 }{ 30 } \)   [∵ LCM of 5 and 6 is 30]
∴  \(2\frac { 2 }{ 5 } +3\frac { 5 }{ 6 } =\frac { 72 }{ 30 } +\frac { 115 }{ 30 } =\frac { 187 }{ 30 } =6\frac { 7 }{ 30 } \)

The given fractions are unlike, we should first get their equivalent fractions with a denominator, which is common multiple of 6 and 15 i.e 30.
now \(\frac { 5\times 5 }{ 6\times 5 } =\frac { 25 }{ 30 } ,\frac { 13\times 2 }{ 15\times 2 } =\frac { 26 }{ 30 } \)
Since\(\frac { 26 }{ 30 } >\frac { 25 }{ 30 } \)so \(\frac { 13 }{ 15 } >\frac { 5 }{ 6 } \)

We have 
Now, factors of 48 = 2\(\times\)2\(\times\)3\(\times\)2\(\times\)2 and factors of 60 = 2\(\times\)2\(\times\)3\(\times\)5
Common factors = 2, 2 and 3 HCF of 48 and 60 = 2\(\times\)2\(\times\)3= 12
∴ \(\frac { 48 }{ 60 } =\frac { 48\div 12 }{ 60\div 12 } =\frac { 4 }{ 5 } \)
Hence, simplest form of the fraction \(\frac { 48 }{ 60 } \)is \(\frac { 4 }{ 5 } .\)

We have, \(\frac { 2 }{ 7 } ={{8}\over{\Box}}\)
∴ \(2\times \Box =7\times 8\)
So, \(2\times \Box =7\times 2\times 4=28\times 2\)   [∵ 8 = 2\(\times\)4]
On comparing we get \(\Box =28\)
Hence \(\frac { 2 }{ 7 } =\frac { 8 }{ \boxed { 28 } } \)

We have \(\frac { 15 }{ 75 } \)
Now,  factors of 15 = 3\(\times\)5
and factors of 75 = 3\(\times\)5\(\times\)5
Common factors = 3 and 5
∴ HCF of 15 and 75 = 3\(\times\)5 = 15
Then, \(\frac { 15 }{ 75 } =\frac { 15\div 15 }{ 75\div 15 } =\frac { 1 }{ 5 } \)
Hence, fraction 1/5 is the simplest form of given fraction.

Given fraction is \(\frac { 16 }{ 72 } \)

Firstly, we find the HCF of 16 and 72.
HCF of 16 and 72 is 8.
Now, to change into simplest form, divide numerator and denominator by HCF.
 ∴  \(\frac { 16 }{ 72 } =\frac { 16\div 8 }{ 72\div 8 } =\frac { 2 }{ 9 } \)

Given fraction is \(\frac { 15 }{ 75 } \)

now first of all we find the HCF of 15 and 75.
So, the HCF of 15 and 75 is 15.
Now, to change into simplest form, divide numerator and denominator by HCF.
\(\frac { 15 }{ 75 } =\frac { 15\div 15 }{ 75\div 15 } =\frac { 1 }{ 5 } \)