# The ratio of 92:115 in its simplest form is

(a).23:25

(b).18:25

(c).3:5

(d).4:5

Answer

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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.

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.

Last updated date: 16th Sep 2023

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