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Find an equivalent ratio in simplest terms:

110:36
:

Find an equivalent ratio in simplest terms: $\newline$ $110: 36$ $\newline$ $\square$ : $\square$

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Write an equivalent ratio

Full solution

Q. Find an equivalent ratio in simplest terms:

\newline

110: 36

\newline

\square

:

\square

Find GCD Factors: To find the simplest form of the ratio, we need to find the greatest common divisor (GCD) of $110$ and $36$ , which can be used to divide both numbers to simplify the ratio.
Identify Largest Common Factor: First, we list the factors of $110$ and $36$ to find the GCD. The factors of $110$ are $1$ , $2$ , $5$ , $10$ , $11$ , $22$ , $55$ , $110$ . The factors of $36$ are $1$ , $2$ , $36$ $4$ , $36$ $5$ , $36$ $6$ , $36$ $7$ , $36$ $8$ , $36$ $9$ , $36$ .
Apply Euclidean Algorithm: Looking at the factors of both numbers, we see that the largest common factor is $2$ . However, we need to check if there's a larger common factor that can be used to simplify the ratio further.
Apply Euclidean Algorithm: Looking at the factors of both numbers, we see that the largest common factor is $2$ . However, we need to check if there's a larger common factor that can be used to simplify the ratio further.We can use the Euclidean algorithm to find the GCD of $110$ and $36$ . We divide $110$ by $36$ and get a remainder. $110 \div 36 = 3$ with a remainder of $2$ .

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