Solving Proportions

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms. For example, if a/b = c/d, then ad = bc.

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 find an unknown value.

Front

If 3/4 = x/16, what is x?

Back

x = 12, because 3 * 16 = 4 * x leads to 48 = 4x, thus x = 12.

Front

What is the scale factor in proportions?

Back

The scale factor is the ratio of any two corresponding lengths in similar geometric figures.

Front

If 5/8 = 15/x, how do you find x?

Back

Cross-multiply to get 5x = 120, then x = 24.

Front

What does it mean if two ratios are equivalent?

Back

Two ratios are equivalent if they represent the same relationship or proportion between quantities.

Front

How can proportions be used in real life?

Back

Proportions can be used in various real-life situations, such as cooking, map reading, and financial calculations.

Front

What is a direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx.

Front

If y varies directly with x and y = 10 when x = 2, what is the constant of variation k?

Back

k = 5, because y = kx leads to 10 = k(2), thus k = 5.