Question

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

Ratios, rates, proportions
ANSWERED
asked 2021-08-11
To find: The value of x in \(\displaystyle{\frac{{{\frac{{{1}}}{{{3}}}}}}{{{25}}}}={\frac{{{x}}}{{{30}}}}\)

Answers (1)

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