Question

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

Ratios, rates, proportions
The given proportion is thue or false. Given: $$\displaystyle{\frac{{{19}}}{{{8}}}}={\frac{{{14}}}{{{6}}}}$$

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.