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Find an equivalent ratio in simplest terms:

16:28
:

Find an equivalent ratio in simplest terms: $\newline$ $16: 28$ $\newline$ $\square$ : $\square$

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Write an equivalent ratio

Full solution

Q. Find an equivalent ratio in simplest terms:

\newline

16: 28

\newline

\square

:

\square

Identify GCD: Identify the greatest common divisor (GCD) of the two numbers in the ratio. The numbers in the ratio are $16$ and $28$ . To simplify the ratio, we need to find the GCD of these two numbers. The factors of $16$ are $1$ , $2$ , $4$ , $8$ , $16$ and the factors of $28$ are $1$ , $2$ , $4$ , $28$ $2$ , $28$ $3$ , $28$ . The greatest common factor they share is $4$ .
Divide by GCD: Divide both terms of the ratio by the GCD to find the simplest form. Divide $16$ by $4$ to get $4$ . Divide $28$ by $4$ to get $7$ . So, the simplest form of the ratio $16:28$ is $4:7$ .
Check Calculation: Check the calculation to ensure no math error has been made. $16$ divided by $4$ is indeed $4$ , and $28$ divided by $4$ is indeed $7$ . There are no smaller common divisors than $4$ for both $16$ and $28$ , so the ratio cannot be simplified further. This confirms that the ratio $4:7$ is in its simplest form.

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