Ratio of two quantities a and b is the fraction ba and we write it as a:b. a is called as the first term or antecedent. b the second term or consequent. Example: i) The ratio 4:7 has antecedent =4 and consequent =7.
Calculate ratios of two given quantities.
To find the ratio of two quantities, remember the following points:
The quantities should be of the same type.
Their units should be same.
Represent the ratio as a fraction.
Reduce the fraction to its simplest form.
Example: Find the ratio of 54 minutes to 2 hours in its simplest form Solution: Both the quantities represent time, hence they are of the same type. We first convert both the quantities in same units i.e. minutes. 2 hours =2×60=120min
∴, the ratio is 9:20
Comparison of Ratios
Consider two ratios ba and dc ....where b>0andd>0 Use the following conditions to compare the two ratios.
If a×b>b×d then ba>dc
If a×b<b×d then ba<dc
If a×b=b×d then ba=dc
Solved Example on Comparison of Two Ratios
1)Compare 56, 115138 Solution: For ratios 56,115138 We have 6×115=690 and 5×138=690 ∴6×115=5×138 ∴56=115138
2) Compare 2875,1235 Solution: For ratios 2875,1235 We have, 75×12=75×12=900 and 28×35=28×35=980 But 900<980 ∴75×12<28×35 ∴2875<1235