Question

# To write: The two other true proportions for \frac{6}{18}=\frac{1}{3}.

Ratios, rates, proportions
To write:
The two other true proportions for $$\displaystyle{\frac{{{6}}}{{{18}}}}={\frac{{{1}}}{{{3}}}}$$.

2021-08-11
Approach:
A proportion is true, if its ratios are equal. As ratios are fractions, one way to determine whether the given proportion is true or false by writting both the ratios in simplest form. Another way is by comparing their cross product.
If the cross product are equal, then the proportion is said to be true. If cross product are not equal, then the proportion is false.
Calculation:
If two ratios are equal in a proportion, then it is called a true proportion.
If it is a true proportion, their cross product are equal.
$$\displaystyle{\frac{{{6}}}{{{18}}}}={\frac{{{1}}}{{{3}}}}$$
$$\displaystyle{6}\times{3}={18}\times{1}$$
Therefore, the two other true proportions will be
$$\displaystyle{\frac{{{6}}}{{{1}}}}={\frac{{{18}}}{{{3}}}}$$ and $$\displaystyle{\frac{{{18}}}{{{6}}}}={\frac{{{3}}}{{{1}}}}$$
Final statement:
The two other true proportion are $$\displaystyle{\frac{{{6}}}{{{1}}}}={\frac{{{18}}}{{{6}}}}$$ and $$\displaystyle{\frac{{{18}}}{{{6}}}}={\frac{{{3}}}{{{1}}}}$$