Question

A proportion is a statement that two ratios are equal. It expresses the relationship between two sets of numbers or quantities. In a proportion, the two ratios are written as fractions and are set equal to each other using an equals sign.

Answer 1

That's correct! A proportion is indeed a statement that shows two ratios are equal. In mathematical terms, if you have two ratios, \( \frac{a}{b} \) and \( \frac{c}{d} \), then the proportion can be written as:

\[
\frac{a}{b} = \frac{c}{d}
\]

In this statement:

- \( a \) and \( c \) are the numerators of the fractions.
- \( b \) and \( d \) are the denominators.

This means that the relationship between \( a \) and \( b \) is the same as the relationship between \( c \) and \( d \). Proportions can be used to solve problems involving ratios, such as in scaling, recipes, and comparing quantities. To find unknown values in proportions, you can use cross-multiplication, which states that:

\[
a \cdot d = b \cdot c
\]

This property helps in solving for variables present in the proportion. Proportions are widely used in various fields, including mathematics, science, and finance.