Comparing and scaling

Front

What is comparing and scaling?

Back

Comparing and scaling involves analyzing relationships between quantities and understanding how one quantity changes in relation to another.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities, often represented as 'k' in the equation y = kx.

Front

How do you find the unit rate?

Back

To find the unit rate, divide the total quantity by the number of units. For example, if 12 donuts cost $7.56, the unit rate is $7.56 ÷ 12.

Front

What is a rate?

Back

A rate is a ratio that compares two different quantities, such as speed (miles per hour) or price per item.

Front

What is a unit rate?

Back

A unit rate is a rate in which the second quantity is one unit. For example, if a car travels 90 miles in 2 hours, the unit rate is 45 miles per hour.

Front

How do you calculate commission?

Back

To calculate commission, multiply the selling price by the commission rate. For example, if the selling price is $362 and the commission is 5%, the commission is $362 × 0.05.

Front

What is the formula for finding the total cost when given a unit price?

Back

Total Cost = Unit Price × Quantity. For example, if a donut costs $1.59 and you buy 12, the total cost is $1.59 × 12.

Front

What does it mean for two quantities to be proportional?

Back

Two quantities are proportional if they maintain a constant ratio or rate. For example, if you double one quantity, the other quantity also doubles.

Front

What is the difference between a rate and a unit rate?

Back

A rate compares two quantities, while a unit rate compares a quantity to one unit of another quantity.

Front

How can you represent a proportional relationship with an equation?

Back

A proportional relationship can be represented by the equation y = kx, where k is the constant of proportionality.