Module 1 Ratios and Proportional Relationships

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

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) in the equation y = kx, representing the ratio between y and x.

Front

How do you find the unit rate?

Back

To find the unit rate, divide the quantity by the number of units. For example, if you travel 150 miles on 5 gallons, the unit rate is 150 miles ÷ 5 gallons = 30 miles per gallon.

Front

What is the formula for a proportional relationship?

Back

The formula for a proportional relationship is y = kx, where k is the constant of proportionality.

Front

If a map scale is 1 cm = 5 km, how do you calculate the actual distance?

Back

To calculate the actual distance, multiply the distance on the map by the scale factor. For example, if two cities are 3 cm apart, the actual distance is 3 cm × 5 km/cm = 15 km.

Front

What does it mean if a graph is proportional?

Back

A graph is proportional if it passes through the origin (0,0) and has a constant slope, indicating a constant ratio between the two variables.

Front

What is an example of a non-proportional relationship?

Back

An example of a non-proportional relationship is y = 5x + 2, as it does not pass through the origin.

Front

How can you determine if two ratios are equivalent?

Back

Two ratios are equivalent if their cross products are equal. For example, for ratios a/b and c/d, they are equivalent if a*d = b*c.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, where the first quantity is the numerator and the second quantity is the denominator.