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Arithmetic : Ratio and Proportion

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A ratio is a number (like a fraction) that compares two numbers by division.
The ratio of a to b may be written in different ways such as a to b, or a : b, or a ÷ b, or a / b.
The numbers a and b are called the terms of the ratio.


Since a ratio a : b is a fraction a / b, the term b cannot be zero.
Ratios can be treated just like fractions.
Since the fraction a / b is different from the fraction b / a, the order of the terms in a ratio is important.
For example, the ratio of the number of sides in a pentagon to the number of sides in an octagon is 5 : 8 and not 8 : 5.


To find the ratio of two quantities, they must be expressed in the same unit of measure.


What is the ratio of 5 feet to 9 inches?
Solution. 5 feet = 5 × 12 inches = 60 inches since 1 foot = 12 inches.
So, the ratio is 60 inches / 9 inches = 20/3 or 20 : 3
Note that the units cancel out in the fraction above to give the ratio as a pure number without any units.


Note that a division of two distinct quantities with different units is usually a rate and not a ratio.
For example, 100 miles / 2 hours is a rate of speed of 50 miles per hour.



GMAT Math Review - Arithmetic : Index for Ratio & Proportion

GMAT Math Review - Arithmetic : Practice Exercise for Ratio & Proportion


10 more pages in GMAT Math Review

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