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 (i.e., a/b = c/d implies 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, meaning they have no common factors other than 1.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, and vice versa; both represent a comparison of two quantities.

Front

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

Back

To solve for a missing value in a proportion, use cross-multiplication and then isolate the variable.

Front

What is the GCD and how is it used in simplifying ratios?

Back

The GCD (Greatest Common Divisor) is the largest number that divides two or more numbers without leaving a remainder, used to simplify ratios.

Front

If a ratio is 4:8, what is its simplest form?

Back

The simplest form of the ratio 4:8 is 1:2.

Front

How do you express a ratio of 10 to 15 in simplest form?

Back

The simplest form of the ratio 10 to 15 is 2:3.