Ratios and Rates

Front

What is a ratio?

Back

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

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common divisor (GCD).

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 the same fraction.

Front

What is a rate?

Back

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

Front

How do you find the unit rate?

Back

To find the unit rate, divide the quantity by the number of units to express the amount per one unit.

Front

If a car travels 120 miles in 2 hours, what is its speed in miles per hour?

Back

60 miles per hour.

Front

What is the formula to find the total number of items based on a ratio?

Back

If the ratio is a:b and the total is T, then a = (a/(a+b)) * T and b = (b/(a+b)) * T.

Front

How can you express the ratio 16:2 as a fraction?

Back

16:2 can be expressed as 16/2, which simplifies to 8/1.

Front

If a recipe calls for a ratio of 3:2 of flour to sugar, how much sugar is needed for 6 cups of flour?

Back

4 cups of sugar are needed.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, and equivalent ratios will simplify to the same fraction.