Rates, Ratios, 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 simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common factor (GCF).

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 fraction that simplifies to the same value.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you determine if two ratios form a proportion?

Back

Cross-multiply the ratios. If the products are equal, the ratios form a proportion.

Front

What is the cost per pound?

Back

Cost per pound is calculated by dividing the total cost of an item by its weight in pounds.

Front

How do you find the simplest form of a ratio?

Back

To find the simplest form of a ratio, divide both parts of the ratio by their greatest common divisor.

Front

What is the relationship between rates and ratios?

Back

Rates are a specific type of ratio that compares two quantities with different units, such as miles per hour or cost per item.

Front

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

Back

To find the amount of sugar needed, set up the proportion: 2/3 = x/6. Solving gives x = 4 cups of sugar.

Front

What is the formula for calculating a unit rate?

Back

Unit rate = total quantity / total cost or total time, expressed as a quantity per one unit.