Rates, Ratios, and Proportions

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 simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common factor (GCF).

Front

What does it mean for two ratios to be equivalent?

Back

Two ratios are equivalent if they represent the same relationship between quantities, meaning they can be expressed as a fraction that simplifies to the same value.

Front

How can you determine if two ratios are equivalent?

Back

Cross-multiply the ratios. If the products are equal, the ratios are equivalent.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you write a ratio in simplest form?

Back

To write a ratio in simplest form, divide both parts of the ratio by their greatest common factor.

Front

What is the ratio of 32 to 4 in simplest form?

Back

The simplest form of the ratio 32 to 4 is 8 to 1.

Front

If 8 feet are covered in 15 seconds, how many feet are covered in 40 seconds?

Back

In 40 seconds, 16 feet are covered, but this does not form a proportion with 8 feet in 15 seconds.

Front

What is the simplest form of the ratio 120:5?

Back

The simplest form of the ratio 120:5 is 24:1.

Front

What is the relationship between rates and ratios?

Back

Rates are a specific type of ratio that compares two quantities with different units, such as speed (miles per hour).