5.1: Ratios
A ratio is a comparison of two numerical quantities in the same units that is usually expressed as a fraction.
Examples:
- The ratio of 2 meters to 7 meters is \(\frac{2m}{7m}=\frac{2}{7}\).
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There are 200,000 gallons of water in a rectangular basin and 400,000 gallons of water in a cylindrical basin.
- What is the ratio of the number of gallons of water in the rectangular basin to the cylindrical basin?\[\frac{200,000\,\, gallons}{400,000\,\, gallons}=\frac{2}{4}=\frac{1}{2}\nonumber \]
- What is the ratio of the number of gallons of water in the cylindrical basin to the rectangular basin?\[\frac{400,000\,\, gallons}{200,000\,\, gallons}=\frac{4}{2}=\frac{2}{1}=2\nonumber \]
- The price of (some chemical) recently increased from $10.80/case to $13.50/case. Find the ratio of the increase in price to the original price.
The increase in price is determined by subtracting the original price from the ending price:increase in price = $13.50-$10.80 = $2.70.
The ratio of the increase in price to the original price = \(\frac{\$2.70}{\$10.80}=0.25\, \, \text{or}\, \, \frac{1}{4}\)