Question # To find: The value of x in \frac{\frac{1}{3}}{25}=\frac{x}{30}

Ratios, rates, proportions
ANSWERED To find: The value of x in $$\displaystyle{\frac{{{\frac{{{1}}}{{{3}}}}}}{{{25}}}}={\frac{{{x}}}{{{30}}}}$$ 2021-08-12
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:$$\displaystyle{x}={\frac{{{2}}}{{{5}}}}$$