Ratios and Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities expressed as a fraction, indicating 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) until no further simplification is possible.

Front

What is a proportion?

Back

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

Front

How can you determine if two ratios form a proportion?

Back

Two ratios form a proportion if the cross products are equal. For example, for a/b = c/d, then a*d = b*c.

Front

What is the cross-multiplication method?

Back

The cross-multiplication method involves multiplying the numerator of one ratio by the denominator of the other ratio to check for equality.

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 simplified to the same fraction.

Front

How do you convert a ratio to a fraction?

Back

To convert a ratio to a fraction, write the first quantity as the numerator and the second quantity as the denominator.

Front

What is the simplest form of a ratio?

Back

The simplest form of a ratio is when the two quantities are expressed in their lowest terms, with no common factors other than 1.

Front

How do you solve for a missing value in a proportion?

Back

To solve for a missing value in a proportion, set up the equation based on the proportion and cross-multiply to find the unknown.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, and both represent a part-to-part or part-to-whole relationship.