1. Standard form of rational number of `12/20`

Solution:
`12/20`


Step-1: Find factors of numerator and denominator

Factors of 12 and 20 using division method
2 12 2 6 3 3   1	2 20 2 10 5 5   1
Or Factors of 12 and 20 using factor tree method
12     2 6     2 3	20     2 10     2 5

Step-2: Rewrite the numerator and denominator as the product of the primes
`12/20=(2 xx 2 xx 3)/(2 xx 2 xx 5)`

Step-3: Remove the common factors `2,2`

`=(cancel{(2)} xx cancel{(2)} xx 3)/(cancel{(2)} xx cancel{(2)} xx 5)`

`=3/5`

Standard form of `12/20` is `3/5`

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2. Standard form of rational number of `25/30`

Solution:
`25/30`


Step-1: Find factors of numerator and denominator

Factors of 25 and 30 using division method
5 25 5 5   1	2 30 3 15 5 5   1
Or Factors of 25 and 30 using factor tree method
25     5 5	30     2 15     3 5

Step-2: Rewrite the numerator and denominator as the product of the primes
`25/30=(5 xx 5)/(2 xx 3 xx 5)`

Step-3: Remove the common factors `5`

`=(cancel{(5)} xx 5)/(2 xx 3 xx cancel{(5)})`

`=(5)/(2 xx 3)`

`=5/6`

Standard form of `25/30` is `5/6`

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3. Standard form of rational number of `35/100`

Solution:
`35/100`


Step-1: Find factors of numerator and denominator

Factors of 35 and 100 using division method
5 35 7 7   1	2 100 2 50 5 25 5 5   1
Or Factors of 35 and 100 using factor tree method
35     5 7	100     2 50     2 25     5 5

Step-2: Rewrite the numerator and denominator as the product of the primes
`35/100=(5 xx 7)/(2 xx 2 xx 5 xx 5)`

Step-3: Remove the common factors `5`

`=(cancel{(5)} xx 7)/(2 xx 2 xx cancel{(5)} xx 5)`

`=(7)/(2 xx 2 xx 5)`

`=7/20`

Standard form of `35/100` is `7/20`