1. Arrange the fractions `1/2,3/4,5/6` in Ascending order

Solution:
Step-1 : Find the LCM of denominators
Here, LCM of 2, 4, 6 = 12

Step-2 : Convert each fractions into like fractions, So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
For `1/2`, ratio of LCM and denominator is `12/2=6`. So multiply numerator and denominator by 6.

`1/2=1/2 xx 6/6=6/12`

For `3/4`, ratio of LCM and denominator is `12/4=3`. So multiply numerator and denominator by 3.

`3/4=3/4 xx 3/3=9/12`

For `5/6`, ratio of LCM and denominator is `12/6=2`. So multiply numerator and denominator by 2.

`5/6=5/6 xx 2/2=10/12`


Step-3 : Arrange fractions: If denominators are the same, then we can arrange the numerators.
Here 6 < 9 < 10
`:. 6/12 < 9/12 < 10/12 `

So, we conclude `1/2< 3/4< 5/6`

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2. Arrange the fractions `3/4,1/2,2/5` in Ascending order

Solution:
Step-1 : Find the LCM of denominators
Here, LCM of 4, 2, 5 = 20

Step-2 : Convert each fractions into like fractions, So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
For `3/4`, ratio of LCM and denominator is `20/4=5`. So multiply numerator and denominator by 5.

`3/4=3/4 xx 5/5=15/20`

For `1/2`, ratio of LCM and denominator is `20/2=10`. So multiply numerator and denominator by 10.

`1/2=1/2 xx 10/10=10/20`

For `2/5`, ratio of LCM and denominator is `20/5=4`. So multiply numerator and denominator by 4.

`2/5=2/5 xx 4/4=8/20`


Step-3 : Arrange fractions: If denominators are the same, then we can arrange the numerators.
Here 8 < 10 < 15
`:. 8/20 < 10/20 < 15/20 `

So, we conclude `2/5< 1/2< 3/4`

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3. Arrange the fractions `3/4,1/2,1/4,2/5` in Ascending order

Solution:
Step-1 : Find the LCM of denominators
Here, LCM of 4, 2, 4, 5 = 20

Step-2 : Convert each fractions into like fractions, So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
For `3/4`, ratio of LCM and denominator is `20/4=5`. So multiply numerator and denominator by 5.

`3/4=3/4 xx 5/5=15/20`

For `1/2`, ratio of LCM and denominator is `20/2=10`. So multiply numerator and denominator by 10.

`1/2=1/2 xx 10/10=10/20`

For `1/4`, ratio of LCM and denominator is `20/4=5`. So multiply numerator and denominator by 5.

`1/4=1/4 xx 5/5=5/20`

For `2/5`, ratio of LCM and denominator is `20/5=4`. So multiply numerator and denominator by 4.

`2/5=2/5 xx 4/4=8/20`


Step-3 : Arrange fractions: If denominators are the same, then we can arrange the numerators.
Here 5 < 8 < 10 < 15
`:. 5/20 < 8/20 < 10/20 < 15/20 `

So, we conclude `1/4< 2/5< 1/2< 3/4`

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4. Arrange the fractions `1/4,1/2,3/5,4/7` in Ascending order

Solution:
Step-1 : Find the LCM of denominators
Here, LCM of 4, 2, 5, 7 = 140

Step-2 : Convert each fractions into like fractions, So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
For `1/4`, ratio of LCM and denominator is `140/4=35`. So multiply numerator and denominator by 35.

`1/4=1/4 xx 35/35=35/140`

For `1/2`, ratio of LCM and denominator is `140/2=70`. So multiply numerator and denominator by 70.

`1/2=1/2 xx 70/70=70/140`

For `3/5`, ratio of LCM and denominator is `140/5=28`. So multiply numerator and denominator by 28.

`3/5=3/5 xx 28/28=84/140`

For `4/7`, ratio of LCM and denominator is `140/7=20`. So multiply numerator and denominator by 20.

`4/7=4/7 xx 20/20=80/140`


Step-3 : Arrange fractions: If denominators are the same, then we can arrange the numerators.
Here 35 < 70 < 80 < 84
`:. 35/140 < 70/140 < 80/140 < 84/140 `

So, we conclude `1/4< 1/2< 4/7< 3/5`

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