Question

do the ratios 6:3 and 14:7 form a proportion

Answer 1

To determine if the ratios \(6:3\) and \(14:7\) form a proportion, we can compare their cross products.

A proportion exists when the ratios are equal, i.e., when:

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

This can also be checked using cross-multiplication:

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

For the ratios \(6:3\) and \(14:7\):

- \(a = 6\)
- \(b = 3\)
- \(c = 14\)
- \(d = 7\)

Now, calculate the cross products:

1. \(a \cdot d = 6 \cdot 7 = 42\)
2. \(b \cdot c = 3 \cdot 14 = 42\)

Since \(42 = 42\), the cross products are equal, and thus the ratios \(6:3\) and \(14:7\) do form a proportion.

Additionally, you can simplify both ratios:

- \(6:3\) simplifies to \(2:1\)
- \(14:7\) simplifies to \(2:1\)

Both simplified ratios are equal, confirming that \(6:3\) and \(14:7\) do indeed form a proportion.