Question

How do you factor each ratio $50:30$?

Answer 1

Hint: In this question we have to simplify the given ratio and write it in the simplified manner, to do that we will factorize both the parts of the ratio and cancel the similar terms to simplify it to get the required solution.

Complete step-by-step solution:
We have the given ratio as:
$ \Rightarrow 50:30$
Now we have to factor the given ratio therefore, we will factorize each term.
We have the term on the left-hand side of the ratio as:
$ \Rightarrow 50$
Now the number $50$, can be written as a multiplication of prime numbers as:
$ \Rightarrow 50 = 5 \times 5 \times 2$
And, we have the term on the right-hand side of the ratio as:
$ \Rightarrow 30$
Now the number $30$, can be written as a multiplication of prime numbers as:
$ \Rightarrow 30 = 3 \times 5 \times 2$
Therefore, the ration can be written as:
$ \Rightarrow 5 \times 5 \times 2:3 \times 5 \times 2$
Therefore, we get:
$ \Rightarrow 5:3$, which is the required solution.

5:3 is the required answer.

Note: 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.