Ratios and Rates

A ratio is a comparison of two quantities expressed as a fraction, indicating how many times one value contains or is contained within the other.

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

A unit rate is a rate in which the denominator is 1, allowing for easy comparison of quantities.

Ratios can be expressed in three ways: as a fraction (3/5), with a colon (3:5), or with the word 'to' (3 to 5).

Two ratios are equivalent if they represent the same relationship between quantities, meaning they can be simplified to the same fraction.

6:10 is equivalent to 3:5 because both can be simplified to the same fraction (3/5).

The first step is to identify the quantities being compared and express them in ratio form.

Divide the total number of items by the number of groups to find the number of items per group.

The order matters because it indicates which quantity is being compared to which; reversing the order changes the meaning of the ratio.

Yes, ratios can be simplified by dividing both terms by their greatest common divisor.