Representing Ratios with Equations

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as a fraction or with a colon (e.g., 3:2).

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

How can ratios be represented using equations?

Back

Ratios can be represented using equations by expressing one quantity in terms of another, such as y = kx, where k is a constant that represents the ratio.

Tags

CCSS.7.RP.A.2C

Front

What does the equation y = 5x represent in a real-world context?

Back

This equation indicates that for every car washed (x), $5 is earned (y). It shows a direct proportional relationship between the number of cars washed and the total money earned.

Tags

CCSS.8.EE.B.5

Front

If t = 10d, what does this equation mean?

Back

This equation means that for every unit of d (e.g., distance), t (e.g., time) is 10 times that amount, indicating a direct proportional relationship.

Tags

CCSS.HSF-LE.A.1B

Front

What is the significance of the slope in the equation y = mx?

Back

The slope (m) represents the rate of change between the two variables, indicating how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

How do you find the total money earned if the equation is m = 6h?

Back

To find the total money earned (m), multiply the number of hours worked (h) by the hourly rate (6). For example, if h = 9, then m = 6 * 9 = $54.

Tags

CCSS.HSF.LE.B.5

Front

What does the equation y = 400x represent?

Back

This equation indicates that for every unit of x, y increases by 400, showing a direct proportional relationship.

Tags

CCSS.HSF.LE.B.5

Front

What is the formula to convert a ratio into a fraction?

Back

To convert a ratio a:b into a fraction, you can write it as a/b.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

What is a constant of proportionality?

Back

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

Tags

CCSS.7.RP.A.2B

Front

How can you determine if two quantities are proportional?

Back

Two quantities are proportional if their ratio remains constant as the quantities change.

Tags

CCSS.7.RP.A.2A