When an object moves at a constant speed, it moves at the same speed at all times. It does not move faster or slower at any time. So, the ratios of distance traveled to elapsed time are always equivalent.

For example, a car moves at a constant speed of 50 miles per hour. This means it travels 50 miles in 1 hour, 100 miles in 2 hours, and 150 miles in 3 hours. The ratios of distance in miles to time in hours are equivalent.

A double number line diagram uses a pair of parallel number lines to represent equivalent ratios. There is one number line for each quantity in the ratio. The tick marks for equivalent ratios line up.

This double number line diagram shows that and are equivalent ratios.

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, is equivalent to , because and .

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 .

The word percent means “for each 100.” The symbol for percent is %.

For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. A quarter is worth 25% of a dollar.

A diagram of two bars with different lengths. The top bar is labeled 1 Quarter and 25 cents is labeled inside the bar. The bottom bar is labeled 1 Dollar. It is 4 times longer than the top bar and 100 cents is labeled inside the bar.

A percentage is a rate per 100.

For example, a fish tank can hold 36 liters. There are 27 liters of water in the tank. The percentage of the tank that is full is 75%.

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

For example, the ratio 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 , or $15 per foot.

A unit rate is a rate per 1.

For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because  . The other unit rate is  of a pie per person, because .