7th Grade Unit 3(Ratios, Rates, Constant of Proportionality

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, showing how many times one value contains or is contained within the other.

Front

How do you write a ratio?

Back

Ratios can be written in three ways: using a colon (e.g., 2:3), as a fraction (e.g., 2/3), or with the word 'to' (e.g., 2 to 3).

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, expressed in the equation y = kx.

Front

How do you find the constant of proportionality?

Back

To find the constant of proportionality (k), use the formula k = y/x, where y is the dependent variable and x is the independent variable.

Front

What does the point (0, 0) represent in a coordinate plane?

Back

The point (0, 0) is called the origin, where the x-axis and y-axis intersect.

Front

If a line passes through the point (3, 9), what is the slope if it is in the form y = kx?

Back

The slope (k) is 3, so the equation is y = 3x.

Front

What is a rate?

Back

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

Front

How do you calculate the rate from a total cost and quantity?

Back

To calculate the rate, divide the total cost by the quantity. For example, if 4 tickets cost $124, the rate per ticket is $124/4 = $31.

Front

What is the difference between a ratio and a rate?

Back

A ratio compares two quantities of the same kind, while a rate compares two quantities of different kinds.

Front

If there are 10 dimes and 5 nickels, what is the ratio of dimes to nickels?

Back

The ratio of dimes to nickels is 2 to 1.