The problem asks to select all ratios that are equivalent to the ratio $7:8$. The given options are $2:28$, $16:14$, and $63:72$.

1. Problem Description

The problem asks to select all ratios that are equivalent to the ratio $7:8$. The given options are $2:28$, $16:14$, and $63:72$.

2. Solution Steps

We need to check if any of the given ratios are equivalent to $7:8$. Two ratios $a:b$ and $c:d$ are equivalent if $\frac{a}{b} = \frac{c}{d}$.

Option 1: $2:28$.

We have the ratio $2:28$, which can be written as the fraction $\frac{2}{28}$. Simplifying this fraction gives $\frac{2}{28} = \frac{1}{14}$.

Since $\frac{1}{14} \neq \frac{7}{8}$, the ratio $2:28$ is not equivalent to $7:8$.

Option 2: $16:14$.

We have the ratio $16:14$, which can be written as the fraction $\frac{16}{14}$. Simplifying this fraction gives $\frac{16}{14} = \frac{8}{7}$. Note that $\frac{8}{7}$ is the reciprocal of $\frac{7}{8}$.

Since $\frac{8}{7} \neq \frac{7}{8}$, the ratio $16:14$ is not equivalent to $7:8$.

Option 3: $63:72$.

We have the ratio $63:72$, which can be written as the fraction $\frac{63}{72}$. We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is

9. $\frac{63}{72} = \frac{63 \div 9}{72 \div 9} = \frac{7}{8}$.

Since $\frac{7}{8} = \frac{7}{8}$, the ratio $63:72$ is equivalent to $7:8$.

3. Final Answer

The ratio equivalent to $7:8$ is $63:72$.