Rates and Unit Rates

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a quantity of one. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

Front

How do you calculate the cost per item?

Back

To calculate the cost per item, divide the total cost by the number of items. For example, if 4 pounds of bananas cost $6, the cost per pound is $6 ÷ 4 = $1.50.

Front

What is a ratio?

Back

A ratio is a relationship between two quantities, showing how many times one value contains or is contained within the other. For example, the ratio of dimes to nickels in 10 dimes and 5 nickels is 2 to 1.

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms of the ratio by their greatest common divisor (GCD). For example, the ratio 8:4 can be simplified to 2:1.

Front

What is the formula for finding the price per ticket?

Back

The price per ticket can be found by dividing the total cost by the number of tickets purchased. For example, if 4 tickets cost $252, the price per ticket is $252 ÷ 4 = $63.

Front

What is the relationship between rates and unit rates?

Back

Rates are comparisons of two quantities with different units, while unit rates are rates that have been simplified to a quantity of one. For example, a rate could be 70 boxes per 5 minutes, while the unit rate would be 14 boxes per minute.

Front

How do you solve for a variable in an equation?

Back

To solve for a variable, isolate the variable on one side of the equation using inverse operations. For example, in the equation x + 3 = 12, subtract 3 from both sides to find x = 9.

Front

What is the concept of proportionality in rates?

Back

Proportionality in rates means that two quantities increase or decrease at the same rate. For example, if a machine packs boxes at a constant rate, the number of boxes packed is proportional to the time spent packing.

Front

How do you find the total output based on a rate?

Back

To find the total output based on a rate, multiply the rate by the time. For example, if a machine packs 70 boxes in 5 minutes, in 8 minutes it can pack 70/5 * 8 = 112 boxes.

Front

What is the significance of unit rates in real-life applications?

Back

Unit rates help compare prices, speeds, and efficiencies in real-life situations, making it easier to make informed decisions, such as choosing the best deal or understanding travel times.