Question

How do you simplify to tell whether the ratios $\dfrac{3}{{10}},\dfrac{9}{{20}}$ form a proportion?

Answer 1

Hint: We will try to simply both the ratios to their respective simplest forms and check whether they form a proportion. Finally we get the required answer.

Complete step-by-step solution:
We know that for two ratios to be in proportion, they have to be the same value in their simplest form.
Let’s consider the first ratio $\dfrac{3}{{10}}$ , now since it cannot be further simplified because there are no common factors, it is already in the simplest form.
Now consider the second ratio $\dfrac{9}{{20}}$, even this fraction cannot be simplified further because there are no common factors therefore, it is already the simplest form.
Now because both the values are not same, the numbers $\dfrac{3}{{10}}$ and $\dfrac{9}{{20}}$ are not in a proportion because $\dfrac{3}{{10}} \ne \dfrac{9}{{20}}$

Therefore, the ratios $\dfrac{3}{{10}},\dfrac{9}{{20}}$ are not in a proportion, which is the required solution.

Note: In the given question if the second ratio was $\dfrac{6}{{20}}$, then we could have simplified it further as $\dfrac{3}{{10}}$ and then both the ratios would have been in proportion.
It is to be remembered that ratio is based on the concept of fractions, a ratio is basically a fraction in the form of $\dfrac{a}{b}$ represented as $a:b$ . It is used to represent a value in terms of another value.
Proportion is a concept in ratio and it represents when two ratios are the same.
A ratio of two fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$ can be represented as: $a:b::c:d$
A ratio has to be with similar quantities for comparison, while comparison of two quantities the units of both the quantities should be the same.
Ratios and proportions are used mostly when 2 quantities are in terms of a fraction for example distance upon time or rupees per meter etc.