Proportions

Front

What is a proportion?

Back

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

Front

How do you determine if two ratios form a proportion?

Back

Two ratios form a proportion if the cross products are equal.

Front

What is the cross product of the ratios \( \frac{a}{b} \) and \( \frac{c}{d} \)?

Back

The cross product is \( a \cdot d \) and \( b \cdot c \). If \( a \cdot d = b \cdot c \), then the ratios form a proportion.

Front

If \( \frac{3}{x} = \frac{12}{16} \), what is the value of x?

Back

x = 4.

Front

What is a scale drawing?

Back

A scale drawing is a representation of an object with accurate ratios between the dimensions of the drawing and the actual object.

Front

If two rectangles are similar, what can be said about their corresponding sides?

Back

The ratios of their corresponding sides are equal.

Front

What is the formula for solving proportions?

Back

To solve a proportion, use the cross-multiplication method: if \( \frac{a}{b} = \frac{c}{d} \), then \( a \cdot d = b \cdot c \).

Front

If \( \frac{5}{x} = \frac{10}{20} \), what is the value of x?

Back

x = 10.

Front

What does it mean if two ratios do not form a proportion?

Back

It means that the cross products of the ratios are not equal.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, where the first quantity is the numerator and the second quantity is the denominator.