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Find an equivalent ratio in simplest terms:

110:42
:

Find an equivalent ratio in simplest terms: $\newline$ $110: 42$ $\newline$ $\square$ : $\square$

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Write an equivalent ratio

Full solution

Q. Find an equivalent ratio in simplest terms:

\newline

110: 42

\newline

\square

:

\square

Find GCD: To find an equivalent ratio in simplest terms, we need to find the greatest common divisor (GCD) of $110$ and $42$ . This will allow us to divide both numbers by the GCD to simplify the ratio.
List Factors: First, we list the factors of $110$ and $42$ to find the GCD. The factors of $110$ are $1$ , $2$ , $5$ , $10$ , $11$ , $22$ , $55$ , $110$ . The factors of $42$ are $1$ , $2$ , $42$ $4$ , $42$ $5$ , $42$ $6$ , $42$ $7$ , $42$ $8$ , $42$ .
Identify GCD: Looking at the factors of both numbers, we see that the largest common factor is $2$ . Therefore, the GCD of $110$ and $42$ is $2$ .
Divide by GCD: Now, we divide both terms of the ratio by the GCD. So, we divide $110$ by $2$ and $42$ by $2$ . $\newline$ $110 \div 2 = 55$ $\newline$ $42 \div 2 = 21$
Simplify Ratio: After dividing both numbers by the GCD, we get the simplified ratio of $55:21$ .

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