Question

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make up a true proportion out of each set of four numbers. is it possible to make another proportion using the same set of numbers?

\\(\frac{1}{7}; 0.2; \frac{5}{7}; 1\\)

answer

the proportion is: .

it v possible to make another proportion using the same set of numbers.

Explanation:

Convert numbers to fractions

$$ 0.2 = \frac{1}{5} $$

The set of numbers is:

$$ \frac{1}{7}, \frac{1}{5}, \frac{5}{7}, 1 $$

Find a true proportion

$$ \frac{1}{7} \cdot 1 = \frac{1}{7} $$

$$ \frac{1}{5} \cdot \frac{5}{7} = \frac{1}{7} $$

Since the products of the extremes and means are equal:

$$ \frac{1/7}{1/5} = \frac{5/7}{1} \implies \frac{1}{7} : 0.2 = \frac{5}{7} : 1 $$

Determine if other proportions are possible

Using the same product relation \(ad = bc\), we can rearrange the terms:

$$ \frac{1}{7} : \frac{5}{7} = 0.2 : 1 $$

Thus, it is possible to make another proportion.

Answer:

Make up a true proportion out of each set of four numbers. Is it possible to make another proportion using the same set of numbers?

\(\frac{1}{7}; 0.2; \frac{5}{7}; 1\)

The proportion is: <blank>\(\frac{1}{7} : 0.2 = \frac{5}{7} : 1\)</blank>.

It <blank>is</blank> possible to make another proportion using the same set of numbers.