proportions

Front

What is a proportion?

Back

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

Front

How do you solve a proportion?

Back

To solve a proportion, you can use cross-multiplication, where you multiply the numerator of one ratio by the denominator of the other ratio.

Front

What is cross-multiplication?

Back

Cross-multiplication is a method used to solve proportions by multiplying the numerator of one fraction by the denominator of the other fraction.

Front

If \( \frac{a}{b} = \frac{c}{d} \), what is the cross-multiplication result?

Back

The result of cross-multiplication is \( a \cdot d = b \cdot c \).

Front

What is the first step in solving the proportion \( \frac{3}{4} = \frac{x}{20} \)?

Back

The first step is to cross-multiply: \( 3 \cdot 20 = 4 \cdot x \).

Front

What is the value of \( x \) in the proportion \( \frac{3}{4} = \frac{x}{20} \)?

Back

The value of \( x \) is 15.

Front

How do you determine if two ratios are in proportion?

Back

Two ratios are in proportion if their cross-products are equal.

Front

What is the cross-product of the ratios \( \frac{6}{10} \) and \( \frac{2}{5} \)?

Back

The cross-product is \( 6 \cdot 5 = 30 \) and \( 10 \cdot 2 = 20 \), which are not equal, so they are not in proportion.

Front

What is the solution to the proportion \( \frac{9}{10} = \frac{m}{100} \)?

Back

The solution is \( m = 90 \).

Front

If \( \frac{x}{10} = \frac{1}{4} \), how do you solve for \( x \)?

Back

Cross-multiply to get \( 4x = 10 \), then divide by 4 to find \( x = 2.5 \).