Question

The ratio of 92:115 in its simplest form is
(a).23:25
(b).18:25
(c).3:5
(d).4:5

Answer 1

Hint:Take the common factors of 92 and 115 by prime factorization method. Cancel out the same terms in both the numbers. And you will get their simplified ratio.


Complete step-by-step answer:
A ratio is the quantitative relation between 2 amounts showing the number of times one value contains or is contained within the other i.e. a ratio indicates how many times one number contains another.
For example there are 4 boxes of 3 that are shaded and 1 is not shaded so their ratio 3 shaded box to 1 non-shaded box is 3:1, it can be also used the word “to” = 3 to 1.
It can be also written as a fraction\[\dfrac{3}{1}\].
Given is the ratio 92:115, we need to simplify it.
Taking 92 let us find the common factors by using the prime factorization method.

Similarly, let us find the common factors of 115.
\[\begin{align}
  & \therefore 92=2\times 2\times 23 \\
 & 115=5\times 23 \\
\end{align}\]
We said that 92:115 can also be written in fraction \[\dfrac{92}{115}\].
\[\therefore \dfrac{92}{115}=\dfrac{2\times 2\times 23}{5\times 23}\]
Cancel 23 from the numerator and the denominator.
\[\therefore \dfrac{92}{115}=\dfrac{4}{5}\]
\[\therefore \] The simplified ratio of 92:115 is 4:5.
So, option (d) is correct.
Note:
We can always simplify or expand it.
4:5 ratio is similar to\[4\times 2:5\times 2=8:10\].
8:10 ratio is similar to\[8\times 3:10\times 3=24:30\].
If we are multiplying 23 on 4:5 \[\Rightarrow 4\times 23:5\times 23\] we get 92:115.