Question

The given proportion is thue or false. Given: \frac{19}{8}=\frac{14}{6}

Ratios, rates, proportions
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asked 2021-08-14
The given proportion is thue or false. Given: \(\displaystyle{\frac{{{19}}}{{{8}}}}={\frac{{{14}}}{{{6}}}}\)

Answers (1)

2021-08-15
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.
If the cross products are equal, then the proportion is true.
If the cross products are not equal, then the proportion is false.
Given proportions,
\(\displaystyle{\frac{{{19}}}{{{8}}}}={\frac{{{14}}}{{{6}}}}\)
\(\displaystyle{19}\cdot{6}={14}\cdot{8}\)
\(\displaystyle{114}\ne{q}{112}\)
Here, the cross products are not equal.
Therefore, the given proportion is false.
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