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Home > Pre-Algebra calculators > Ascending and descending order of fractions example
17. Ascending and descending order of fractions example ( Enter your problem )
( Enter your problem )
  1. Example-1
 		Other related methods
  1. Numerator and Denominator
  2. Proper and Improper Fractions
  3. Like and Unlike fractions
  4. Model Fractions (Visual Fractions)
  5. Simplify Fraction
  6. Equivalent Fractions
  7. How many eighths are equivalent to 1/2
  8. Fraction to Decimal (Mixed Number to Decimal)
  9. Decimal to Fraction (Decimal to Mixed Number)
  10. Fraction to Percentage (Mixed Number to Percentage)
  11. Improper fraction to Mixed number
  12. Mixed Number to Improper Fraction
  13. Reciprocal of a fraction
  14. LCD of fractions
  15. Convert unlike fraction to like fraction
  16. Comparing fractions
  17. Ascending and descending order of fractions
  18. Add, subtract, multiply and divide of Fractions
  19. Add, subtract, multiply and divide of Mixed numbers
  20. Visual Model for Adding, Subtracting of Fractions
  21. Simplify fraction expression
16. Comparing fractions
(Previous method)		18. Add, subtract, multiply and divide of Fractions
(Next method)

1. Example-1


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`
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`
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`
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`

This material is intended as a summary. Use your textbook for detail explanation.
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16. Comparing fractions
(Previous method)		18. Add, subtract, multiply and divide of Fractions
(Next method)


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