Unit Rates and COP

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. It is often used to describe how much of one item is present for every one unit of another item.

Front

How do you calculate the constant of proportionality from a graph?

Back

The constant of proportionality can be found by determining the ratio of the dependent variable (y) to the independent variable (x) at any point on the line. It is the slope of the line in a proportional relationship.

Front

What is the formula for finding the unit rate?

Back

The unit rate can be calculated by dividing the total quantity of one item by the total quantity of another item, typically expressed as 'quantity of item A per 1 unit of item B'.

Front

If a truck travels 7/8 of a mile in 3/4 of a minute, how do you find the unit rate in miles per minute?

Back

To find the unit rate, divide the distance traveled (7/8 miles) by the time taken (3/4 minutes). This results in (7/8) ÷ (3/4) = (7/8) * (4/3) = 7/6 miles per minute.

Front

What is the relationship between weight and cost in the equation y = 4x?

Back

In the equation y = 4x, y represents the cost and x represents the weight. The constant 4 indicates that for every unit of weight, the cost increases by 4 units.

Front

How do you convert a fraction to a unit rate?

Back

To convert a fraction to a unit rate, divide the numerator by the denominator to find the value per one unit of the denominator.

Front

What is the unit rate of Ben drinking tea if he drinks 1/2 liter every 2/3 of an hour?

Back

To find the unit rate, divide 1/2 liter by 2/3 hour, which equals (1/2) ÷ (2/3) = (1/2) * (3/2) = 3/4 liter per hour.

Front

How do you find the number of pages written per hour if Henry writes 5 ¼ pages in 3 hours?

Back

To find the pages per hour, divide the total pages (5 ¼ or 5.25) by the total hours (3). This results in 5.25 ÷ 3 = 1.75 pages per hour.

Front

What does it mean if a relationship is proportional?

Back

A relationship is proportional if there is a constant ratio between two quantities, meaning that as one quantity increases, the other quantity increases at a consistent rate.

Front

How can you express a constant of proportionality in a real-world context?

Back

In a real-world context, the constant of proportionality can be expressed as a price per unit, such as cost per pound of fruit or miles per hour of travel.