Ratios and Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as 'a:b' or 'a/b'.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, expressed as 'a/b = c/d'.

Front

How do you determine if two ratios form a proportion?

Back

Two ratios form a proportion if the cross products are equal, i.e., a*d = b*c.

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 simplify a ratio?

Back

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

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 to check for equality.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, and vice versa; a ratio of a:b can be written as a/b.

Front

How do you solve for a variable in a proportion?

Back

To solve for a variable in a proportion, cross-multiply and then isolate the variable.

Front

What is an example of an equivalent ratio?

Back

An example of an equivalent ratio is 2:3 and 4:6; both ratios represent the same relationship.

Front

What does it mean for two ratios to be unequal?

Back

Two ratios are unequal if their cross products do not equal each other.