How to write a ratio in simplest form?
Understand the Problem
The question is asking for the method to simplify a ratio to its most basic form. This will involve dividing both parts of the ratio by their greatest common factor.
Answer
$2:3$
Answer for screen readers
The simplified ratio of $8:12$ is $2:3$.
Steps to Solve
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Identify the Ratio Start by clearly writing down the ratio you need to simplify. For example, if you have the ratio $8:12$, it needs to be simplified.
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Find the Greatest Common Factor (GCF) Determine the GCF of the two numbers in the ratio. In the example, the factors of $8$ are $1, 2, 4, 8$ and the factors of $12$ are $1, 2, 3, 4, 6, 12$. The GCF is $4$.
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Divide Both Parts of the Ratio Now, divide both parts of the ratio by the GCF you found. For the example ratio:
$$ \frac{8}{4} : \frac{12}{4} $$
This results in:
$$ 2 : 3 $$
- Write the Simplified Ratio Finally, write the simplified ratio. In the example, the simplified ratio of $8:12$ is $2:3$.
The simplified ratio of $8:12$ is $2:3$.
More Information
When simplifying ratios, finding the GCF is crucial as it ensures both parts of the ratio are evenly reduced. This process can be applied to any ratio, regardless of the numbers involved.
Tips
- Forgetting to find the GCF and dividing incorrectly.
To avoid this, always list the factors of both numbers to ensure you find the correct GCF. - Not reducing both parts of the ratio equally.
Make sure to divide each part of the ratio by the same GCF.
