Ratios and Rates

Front

What is a ratio?

Back

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.

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

What is a unit rate?

Back

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

Front

How can ratios be expressed?

Back

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).

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 simplified to the same fraction.

Front

If a ratio is 3:5, what is the equivalent ratio for 6:10?

Back

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

Front

What is the first step to solving a problem involving ratios?

Back

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

Front

How do you find the number of items per group when given a total and number of groups?

Back

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

Front

What is the significance of the order in which quantities are placed in a ratio?

Back

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

Front

Can ratios be simplified?

Back

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