Ratio

A ratio is simply a fraction. The following notations all express the ratio of x to y: x: y , x Ã· y , or $\frac{x}{y}$. Writing two numbers as a ratio provides a convenient way to compare their sizes. For example, since $\frac{3}{\mathrm{Ï€}}<1$ , we know that 3 is less than Ï€. A ratio compares two numbers. Just as you cannot compare apples and oranges, so to must the numbers you are comparing have the same units. For example, you cannot form the ratio of 2 feet to 4 yards because the two numbers are expressed in different unitsâ€”feet vs. yards. It is quite common for the GRE to ask for the ratio of two numbers with different units. Before you form any ratio, make sure the two numbers are expressed in the same units.

Example 1:

Column A
The ratio of 2 miles to 4 miles

Column B
The ratio of 2 feet to 4 yards

Forming the ratio in Column A yields

= $\frac{1}{2}$ or 1: 2

The ratio in Column B cannot be formed until the numbers are expressed in the same units. LetÂ’â€™s turn the yards into feet. Since there are 3 feet in a yard, 4 yards = 4 Ã— 3 feet = 12 feet . Forming the ratio yields

or 1: 6
Hence, Column A is larger.

Note, taking the reciprocal of a fraction usually changes its size. For example, . So order is important in a ratio: 3:4 â‰  4:3.