Proportion:

A proportion is a statement that two ratios or rates are equal.

If \(\displaystyle{\frac{{{a}}}{{{b}}}}\) and \(\displaystyle{\frac{{{c}}}{{{d}}}}\) are two ratios or rates, then \(\displaystyle{\frac{{{a}}}{{{b}}}}={\frac{{{c}}}{{{d}}}}\) is a proportion.

It can be read as "a is to b as c is to d"

\(\displaystyle{a}\cdot{d}={b}\cdot{c}\) is the set of cross products.

Given proportions,

\(\displaystyle{\frac{{{\frac{{{1}}}{{{3}}}}}}{{{25}}}}={\frac{{{x}}}{{{30}}}}\)

\(\displaystyle{\frac{{{1}}}{{{3}\cdot{25}}}}={\frac{{{x}}}{{{30}}}}\)

\(\displaystyle{x}\cdot{3}\cdot{25}={1}\cdot{30}\)

\(\displaystyle{x}={\frac{{{30}}}{{{3}\cdot{25}}}}\)

Cancel the common factor 3

\(\displaystyle{x}={\frac{{{10}}}{{{25}}}}\)

Cancel the common factor 5

\(\displaystyle{x}={\frac{{{2}}}{{{5}}}}\)

Therefore, the value of \(\displaystyle{x}={\frac{{{2}}}{{{5}}}}\)

Answer:\(\displaystyle{x}={\frac{{{2}}}{{{5}}}}\)

A proportion is a statement that two ratios or rates are equal.

If \(\displaystyle{\frac{{{a}}}{{{b}}}}\) and \(\displaystyle{\frac{{{c}}}{{{d}}}}\) are two ratios or rates, then \(\displaystyle{\frac{{{a}}}{{{b}}}}={\frac{{{c}}}{{{d}}}}\) is a proportion.

It can be read as "a is to b as c is to d"

\(\displaystyle{a}\cdot{d}={b}\cdot{c}\) is the set of cross products.

Given proportions,

\(\displaystyle{\frac{{{\frac{{{1}}}{{{3}}}}}}{{{25}}}}={\frac{{{x}}}{{{30}}}}\)

\(\displaystyle{\frac{{{1}}}{{{3}\cdot{25}}}}={\frac{{{x}}}{{{30}}}}\)

\(\displaystyle{x}\cdot{3}\cdot{25}={1}\cdot{30}\)

\(\displaystyle{x}={\frac{{{30}}}{{{3}\cdot{25}}}}\)

Cancel the common factor 3

\(\displaystyle{x}={\frac{{{10}}}{{{25}}}}\)

Cancel the common factor 5

\(\displaystyle{x}={\frac{{{2}}}{{{5}}}}\)

Therefore, the value of \(\displaystyle{x}={\frac{{{2}}}{{{5}}}}\)

Answer:\(\displaystyle{x}={\frac{{{2}}}{{{5}}}}\)