1. The problem is to determine which ratios are equivalent to $2:7$. 2. Two ratios $a:b$ and $c:d$ are equivalent if their cross products are equal, i.e., if $a \times d = b \times c$. 3. Check each ratio: - For $4:14$, check if $4 \times 7 = 2 \times 14$: $$4 \times 7 = 28$$ $$2 \times 14 = 28$$ Since both products are equal, $4:14$ is equivalent to $2:7$. - For $8:28$, check if $8 \times 7 = 2 \times 28$: $$8 \times 7 = 56$$ $$2 \times 28 = 56$$ Since both products are equal, $8:28$ is equivalent to $2:7$. - For $6:21$, check if $6 \times 7 = 2 \times 21$: $$6 \times 7 = 42$$ $$2 \times 21 = 42$$ Since both products are equal, $6:21$ is equivalent to $2:7$. 4. Therefore, all the given ratios $4:14$, $8:28$, and $6:21$ are equivalent to $2:7$. Final answer: $4:14$, $8:28$, and $6:21$ are all equivalent to $2:7$.