Select all ratios equivalent to 16:12.

Steps to Solve

1. Simplify the original ratio

First, simplify the ratio $16:12$. To do this, find the greatest common divisor (GCD) of 16 and 12. The GCD is 4.

Now, divide both numbers by 4:

$$ \frac{16}{4} : \frac{12}{4} = 4:3 $$

So, the simplified form of $16:12$ is $4:3$.

2. Compare each given ratio to the simplified form

Now, let's simplify each of the given ratios to check for equivalence to $4:3$.

• For $12:9$, divide both by their GCD, which is 3:

$$ \frac{12}{3} : \frac{9}{3} = 4:3 $$

• For $18:24$, divide both by their GCD, which is 6:

$$ \frac{18}{6} : \frac{24}{6} = 3:4 $$

• For $10:18$, divide both by their GCD, which is 2:

$$ \frac{10}{2} : \frac{18}{2} = 5:9 $$

3. Determine equivalence

Now compare each simplified ratio to $4:3$:

• $12:9$ simplifies to $4:3$, which is equivalent.
• $18:24$ simplifies to $3:4$, which is not equivalent.
• $10:18$ simplifies to $5:9$, which is also not equivalent.