1. Find Compare ratios of `2:3,3:4,4:5`
Solution:
Step-1 : Find the LCD of denominators
Here, LCD of 3, 4, 5 = 60
Step-2 : Convert each fraction into its equivalent with the LCD in the denominator
For `2/3`, multiply numerator and denominator by 20 to have LCD = 60 in the denominator.
`2/3 = 2/3 xx 20/20 = 40/60`
For `3/4`, multiply numerator and denominator by 15 to have LCD = 60 in the denominator.
`3/4 = 3/4 xx 15/15 = 45/60`
For `4/5`, multiply numerator and denominator by 12 to have LCD = 60 in the denominator.
`4/5 = 4/5 xx 12/12 = 48/60`
Step-3 : Arrange fractions: If denominators are the same, then we can arrange the numerators.
Here 40 < 45 < 48
`:. 40/60 < 45/60 < 48/60 `
So, we conclude `2/3< 3/4< 4/5`
2. Find Compare ratios of `2:3,4:5,5:6`
Solution:
Step-1 : Find the LCD of denominators
Here, LCD of 3, 5, 6 = 30
Step-2 : Convert each fraction into its equivalent with the LCD in the denominator
For `2/3`, multiply numerator and denominator by 10 to have LCD = 30 in the denominator.
`2/3 = 2/3 xx 10/10 = 20/30`
For `4/5`, multiply numerator and denominator by 6 to have LCD = 30 in the denominator.
`4/5 = 4/5 xx 6/6 = 24/30`
For `5/6`, multiply numerator and denominator by 5 to have LCD = 30 in the denominator.
`5/6 = 5/6 xx 5/5 = 25/30`
Step-3 : Arrange fractions: If denominators are the same, then we can arrange the numerators.
Here 20 < 24 < 25
`:. 20/30 < 24/30 < 25/30 `
So, we conclude `2/3< 4/5< 5/6`
This material is intended as a summary. Use your textbook for detail explanation.
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