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Find an equivalent ratio in simplest terms:

99:42
:

Find an equivalent ratio in simplest terms: $\newline$ $99: 42$ $\newline$ $\square$ : $\square$

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Write an equivalent ratio

Full solution

Q. Find an equivalent ratio in simplest terms:

\newline

99: 42

\newline

\square

:

\square

Find GCD of $99$ and $42$ : To find the simplest form of the ratio, we need to find the greatest common divisor (GCD) of $99$ and $42$ . This will allow us to divide both numbers by the GCD to simplify the ratio.
List Factors of $99$ and $42$ : First, we list the factors of $99$ and $42$ to find the GCD. $\newline$ Factors of $99$ : $1$ , $3$ , $9$ , $11$ , $33$ , $99$ $\newline$ Factors of $42$ : $1$ , $42$ $1$ , $3$ , $42$ $3$ , $42$ $4$ , $42$ $5$ , $42$ $6$ , $42$ $\newline$ The greatest common factor that appears in both lists is $3$ .
Identify GCD as $21$ : However, we need to check if there is a larger common factor. We can see that both $99$ and $42$ are divisible by $3$ , but they are also divisible by a larger number, which is $21$ . So, we will use $21$ as the GCD.
Divide Numbers by GCD: Now, we divide both numbers by the GCD, which is $21$ . $\newline$ $99 \div 21 = 4.714285714285714$ (This is incorrect, we need to redo the division)

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