Question
Do the ratios 7:5 and 9:7 form a proportion?
Answers
GPT-4o mini
To determine whether the ratios \(7:5\) and \(9:7\) form a proportion, we can set up a proportion based on the two ratios. A proportion states that two ratios are equal to each other, mathematically represented as:
\[
\frac{7}{5} = \frac{9}{7}
\]
To check if they are equal, we can cross-multiply:
\[
7 \times 7 = 49
\]
\[
5 \times 9 = 45
\]
Now compare the two products:
\[
49 \neq 45
\]
Since \(49\) is not equal to \(45\), the ratios \(7:5\) and \(9:7\) do not form a proportion.
\[
\frac{7}{5} = \frac{9}{7}
\]
To check if they are equal, we can cross-multiply:
\[
7 \times 7 = 49
\]
\[
5 \times 9 = 45
\]
Now compare the two products:
\[
49 \neq 45
\]
Since \(49\) is not equal to \(45\), the ratios \(7:5\) and \(9:7\) do not form a proportion.