Two ratios are equivalent if each of the numbers in the first ratio can be multiplied by the same factor to get the numbers in the second ratio. For example, \(8:6\) is equivalent to \(4:3\), because \(8\boldcdot\frac12 = 4\) and \(6\boldcdot\frac12 = 3\).

The word per means “for each.”

For example, the price is \$5 per ticket. This means \$5 must be paid for each ticket. Buying 4 tickets costs $20, because \(4 \boldcdot 5 = 20\).

A ratio is a way to relate 2 or more quantities.

For example, the ratio \(3:2\) could describe:

• A recipe that uses 3 cups of flour for every 2 eggs.
• A boat that moves 3 meters every 2 seconds.
• A diagram that has 3 blue squares for every 2 green squares.

The phrase same rate is used to describe two situations that have equivalent ratios.

For example, a sink is filled at a rate of 2 gallons per minute. A tub is also filled at a rate of 2 gallons per minute. So, the sink and the tub are filled at the same rate.

A tape diagram is a group of rectangles put together to represent a relationship between quantities.

This tape diagram shows a ratio of 30 gallons of yellow paint to 50 gallons of blue paint.

This tape diagram represents the equivalent ratio of 15 gallons of yellow paint to 25 gallons of blue paint.

The unit price is the cost for 1 item or for 1 unit of measure.

For example, 10 feet of fencing costs \$150. The unit price is \(150 \div 10\), or \$15 per foot.