1. Comparing Fractions with like / unlike denominators examples
1. Find Comparing fractions `1/2` and `2/3`
Solution:
Comparing Fractions with unlike denominators
`1/2` ? `2/3`
Step-1 : Find the LCM of denominators
Here, LCM of 2 and 3 = 6
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 `6/2=3`. So multiply numerator and denominator by 3.
`1/2 = 1/2 xx 3/3 = 3/6`
For `2/3`, ratio of LCM and denominator is `6/3=2`. So multiply numerator and denominator by 2.
`2/3 = 2/3 xx 2/2 = 4/6`
Step-3 : Compare fractions: If denominators are the same, then we can compare the numerators.
Here 3 < 4,
`:. 3/6 < 4/6`
So, we conclude `1/2 < 2/3`
2. Find Comparing fractions `2/3` and `4/5`
Solution:
Comparing Fractions with unlike denominators
`2/3` ? `4/5`
Step-1 : Find the LCM of denominators
Here, LCM of 3 and 5 = 15
Step-2 : Convert each fractions into like fractions, So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
For `2/3`, ratio of LCM and denominator is `15/3=5`. So multiply numerator and denominator by 5.
`2/3 = 2/3 xx 5/5 = 10/15`
For `4/5`, ratio of LCM and denominator is `15/5=3`. So multiply numerator and denominator by 3.
`4/5 = 4/5 xx 3/3 = 12/15`
Step-3 : Compare fractions: If denominators are the same, then we can compare the numerators.
Here 10 < 12,
`:. 10/15 < 12/15`
So, we conclude `2/3 < 4/5`
3. Find Comparing fractions `3/4` and `2/5`
Solution:
Comparing Fractions with unlike denominators
`3/4` ? `2/5`
Step-1 : Find the LCM of denominators
Here, LCM of 4 and 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 `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 : Compare fractions: If denominators are the same, then we can compare the numerators.
Here 15 > 8,
`:. 15/20 > 8/20`
So, we conclude `3/4 > 2/5`
4. Find Comparing fractions `2/3` and `4/5`
Solution:
Comparing Fractions with unlike denominators
`2/3` ? `4/5`
Step-1 : Find the LCM of denominators
Here, LCM of 3 and 5 = 15
Step-2 : Convert each fractions into like fractions, So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
For `2/3`, ratio of LCM and denominator is `15/3=5`. So multiply numerator and denominator by 5.
`2/3 = 2/3 xx 5/5 = 10/15`
For `4/5`, ratio of LCM and denominator is `15/5=3`. So multiply numerator and denominator by 3.
`4/5 = 4/5 xx 3/3 = 12/15`
Step-3 : Compare fractions: If denominators are the same, then we can compare the numerators.
Here 10 < 12,
`:. 10/15 < 12/15`
So, we conclude `2/3 < 4/5`
This material is intended as a summary. Use your textbook for detail explanation.
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