Select all ratios equivalent to 12:4.
Understand the Problem
The question asks to identify which of the given ratios (10:2, 9:3, 2:1) are equivalent to the ratio 12:4. This involves simplifying the ratios or finding a common multiplier.
Answer
The equivalent ratio to $12:4$ is $9:3$.
Answer for screen readers
The equivalent ratio to $12:4$ is $9:3$.
Steps to Solve
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Simplify the given ratio 12:4
To find equivalent ratios, we will start by simplifying the ratio $12:4$. This involves dividing both parts by their greatest common divisor (GCD).
The GCD of 12 and 4 is 4.
$$ \frac{12}{4} : \frac{4}{4} = 3 : 1 $$ -
Simplify the first ratio 10:2
Next, we simplify the ratio $10:2$. Again, we find the GCD, which is 2.
$$ \frac{10}{2} : \frac{2}{2} = 5 : 1 $$
Since $3:1 \neq 5:1$, this ratio is not equivalent. -
Simplify the second ratio 9:3
Now, we simplify the ratio $9:3$. The GCD here is 3.
$$ \frac{9}{3} : \frac{3}{3} = 3 : 1 $$
Since $3:1 = 3:1$, this ratio is equivalent. -
Simplify the third ratio 2:1
Finally, we simplify the ratio $2:1$. Since it is already in simplest form, we compare it directly with $3:1$.
Since $2:1 \neq 3:1$, this ratio is not equivalent.
The equivalent ratio to $12:4$ is $9:3$.
More Information
The ratio $12:4$ simplifies to $3:1$, which shows the relationship between two quantities—12 and 4. Understanding equivalent ratios is useful in various real-life applications, such as cooking or scaling projects.
Tips
- Confusing equivalent ratios with simplified ratios. It’s essential to simplify first before comparing.
- Not finding the GCD accurately, which leads to incorrect simplifications.
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