Geometry Flashcard Ratios and Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities, showing the relative size of one quantity to another, often expressed in the form 'a:b'.

Front

How can a ratio be expressed?

Back

A ratio can be expressed in several ways, including as a fraction (a/b), with a colon (a:b), or in words (a to b). However, it cannot be expressed as an equation like 3=4.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, typically written as a/b = c/d.

Front

What is the Cross Products Property?

Back

The Cross Products Property states that in a proportion a/b = c/d, the cross products are equal, meaning a*d = b*c.

Front

How do you solve a proportion?

Back

To solve a proportion, you can use cross multiplication or find a common ratio to isolate the variable.

Front

If the ratio of dogs to cats in an animal shelter is 5:3 and there are 25 dogs, how many cats are there?

Back

To find the number of cats, set up the proportion 5/3 = 25/c. Cross-multiply to get 5c = 75, so c = 15.

Front

What is the value of k in the proportion 2/3 = k/15?

Back

To solve for k, cross-multiply: 2*15 = 3*k, which gives k = 10.

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 proportion.

Front

How can you check if two ratios are equivalent?

Back

You can check if two ratios are equivalent by cross-multiplying and seeing if the products are equal.

Front

What is an example of a real-world application of ratios and proportions?

Back

An example is in cooking, where recipes may require ingredients in specific ratios, and you can scale the recipe up or down using proportions.