Describe what makes a proportion and give an example of a proportion

Answer 1

A proportion is a mathematical statement that indicates two ratios are equivalent. In simpler terms, it's an equation that says two fractions are equal. A proportion can be written in the form of \(\frac{a}{b} = \frac{c}{d}\), where \(a\), \(b\), \(c\), and \(d\) are numbers, and \(b\) and \(d\) are not zero.

To check if two ratios form a proportion, you can use cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa. If the cross-products are equal, then the ratios form a proportion.

Here’s an example of a proportion:

Consider the ratios \(\frac{2}{3}\) and \(\frac{4}{6}\).

To verify if these ratios form a proportion, we use cross-multiplication:
\(2 \times 6 = 12\)
\(3 \times 4 = 12\)

Since \(12 = 12\), the two ratios \(\frac{2}{3}\) and \(\frac{4}{6}\) form a proportion. Therefore, we can say that \(\frac{2}{3} = \frac{4}{6}\) is a proportion.