Question

Check whether the given ratios are equal, that is, they are in proportion. If yes, then write them in proper form.
$2:9$ and $18:81$

Answer 1

Hint: A ratio or a proportion is a quantity that indicates how many times one number contains another. Ratios or proportions are something used to compare the values of two different things. In this case, the first ratio is $2:9$ which is also known as two is to nine or the ratio of $2$ to $9$ . For a ratio to be equal, it needs to be in its lowest form.

Complete step-by-step solution:
To reduce a ratio to its simplest forms, you divide both numerator and denominator by the same quantity that is also known as their greatest common factor. Once the ratio is in its simplest form, you can equate it and confirm whether ratios or proportions are real or not.
For the first ratio, $2:9$ , the greatest common factor possible is $1$ and since division by 1 gives the same quantity therefore this particular ratio or proportion is already in its simplest form.
For the second ratio, $18:81$ multiple factors are available but the greatest common factor appears to be$9$ . Dividing both numerator and denominator by the greatest common factor, $9$ we get the final simplest ratio as:
$2:9$ .
This is the same ratio as the first given ratio hence, it can be proved that the given ratios are, in fact, equal and in proper form.
$2:9 = \dfrac{2}{9}$

The given two ratios are equal.

Note: Note that ratios can always exist in multiples and doesn’t necessarily need to be readily available in the simplest form. Ratios are comparisons of two things, two comparisons can be equal only when they are both in their simplest forms.