Ratios, Rates, 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 find the unit rate?

Back

To find the unit rate, divide the total quantity by the number of units. For example, if you have 624 calories in 3 servings, the unit rate is 624 ÷ 3 = 208 calories per serving.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

What does constant of proportionality (COP) mean?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, expressed as y = kx.

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if the ratio between the two quantities remains constant. You can check this by calculating the ratios for different pairs of values.

Front

What is the ratio of cats to dogs if there are 3 cats for every 5 dogs?

Back

The ratio of cats to dogs is 3:5.

Front

If there are 25 dogs in a shelter with a cat-to-dog ratio of 3:5, how many cats are there?

Back

If the ratio is 3:5, then for every 5 dogs, there are 3 cats. With 25 dogs, there are (3/5) * 25 = 15 cats.

Front

What is a unit rate in the context of speed?

Back

A unit rate in speed is the distance traveled per unit of time, such as miles per hour (mph). For example, if you travel 150 miles in 5 hours, the unit rate is 150 ÷ 5 = 30 mph.

Front

How do you express a ratio in simplest form?

Back

To express a ratio in simplest form, divide both terms of the ratio by their greatest common divisor (GCD). For example, the ratio 6:8 simplifies to 3:4.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions. For example, the ratio 3:4 can be written as the fraction 3/4.