Solving Linear Proportions

Front

What is a linear proportion?

Back

A linear proportion is a relationship between two quantities where the ratio of the two quantities remains constant.

Front

How do you solve for a variable in a linear proportion?

Back

To solve for a variable in a linear proportion, set up the equation based on the given ratios and cross-multiply to isolate the variable.

Front

What does cross-multiplication mean in solving proportions?

Back

Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio to create an equation.

Front

If a/b = c/d, what is the cross-multiplication result?

Back

The result is ad = bc.

Front

What is the first step in solving the proportion 3/4 = x/12?

Back

The first step is to cross-multiply: 3 * 12 = 4 * x.

Front

What is the solution for x in the proportion 3/4 = x/12?

Back

x = 9.

Front

How do you check if two ratios are proportional?

Back

To check if two ratios are proportional, cross-multiply and see if the products are equal.

Front

What is the value of b in the proportion 5/b = 10/20?

Back

b = 10.

Front

What is the relationship between direct variation and linear proportions?

Back

Direct variation is a specific case of linear proportions where one variable is a constant multiple of another.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.