Ratios, Rates and Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressing how much of one quantity exists in relation to another.

Front

How do you write a ratio?

Back

A ratio can be written in three ways: using a colon (e.g., 3:2), as a fraction (e.g., 3/2), or in words (e.g., '3 to 2').

Front

What is a rate?

Back

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

Front

What is a proportion?

Back

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

Front

How do you determine if two ratios are equivalent?

Back

Two ratios are equivalent if their cross products are equal, meaning a/b = c/d if and only if a*d = b*c.

Front

If 5 candy bars cost $3.00, what is the cost of 1 candy bar?

Back

The cost of 1 candy bar is $0.60, calculated by dividing the total cost by the number of candy bars (3.00/5).

Front

What is the ratio of music apps to all apps if Kelly has 10 apps in total?

Back

The ratio of music apps (2) to all apps (10) is 1 to 5.

Front

How do you express the ratio of girls to boys if there are 7 girls and 5 boys?

Back

The ratio of girls to boys is expressed as 7 to 5.

Front

In a fruit bowl with 4 apples, 2 bananas, and 5 pears, how do you find the ratio of pears to all fruit?

Back

To find the ratio of pears (5) to all fruit (4+2+5=11), express it as 5:11.

Front

What is the first step in solving a ratio problem?

Back

The first step is to identify the quantities being compared and ensure they are in the same units if necessary.