+9665 \(\dfrac{21}{57}\)
This fraction is not beautiful, why? Because it is not the simplest form :(
Then we will try to make both numerator and denominator smaller and at the same time keep its value the same.
But how??
We will divide it by a fraction which denominator and numerator is the same because if the denominator and numerator is the same, the fraction is equal to 1!
\(\dfrac{21}{57}\div \dfrac{3}{3}\)
Then we will distribute the division sign......
\(\dfrac{21\div 3}{57\div 3}\)
Then divide........
\(\dfrac{7}{19}\)
Yay that fraction is beautiful now because that we cannot do the same process to the fraction. It is because 7 and 19 have no common factors except 1.
What if we have this?
\(\dfrac{42}{126}\)
Repeat the progress with 2 over 2 as they are both divisible by 2!
\(\dfrac{42}{126}\div \dfrac{2}{2}\)
Distribute the division sign:
\(\dfrac{42\div 2}{126\div 2}\)
Divide them:
\(\dfrac{21}{63}\)
This is still not beautiful enough! We have to make it more beautiful!! :(
We can see that they are both divisible by 7, therefore we will repeat the process using 7 over 7.
\(\dfrac{21}{63}\div\dfrac{7}{7}\)
Distribute the division sign:
\(\dfrac{21\div 7}{63\div 7}\)
Divide them:
\(\dfrac{3}{9}\)
NO!! That's not beautiful enough :(
Repeat the process with 3 over 3.
\(\dfrac{3}{9}\div \dfrac{3}{3}\)
Distribute the division sign:
\(\dfrac{3\div 3}{9\div 3}\)
Divide them:
\(\dfrac{1}{3}\)
Yay that's beautified by me again :D 1 and 3 have no common factors except 1!!
