How to write ratios in simplest form?
Understand the Problem
The question is asking for guidance on how to reduce ratios to their simplest form. This involves dividing both terms of the ratio by their greatest common divisor (GCD) to simplify it.
Answer
The simplified form of the ratio $12:16$ is $3:4$.
Answer for screen readers
The simplified form of the ratio $12:16$ is $3:4$.
Steps to Solve
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Identify the Ratio Begin by clearly writing down the ratio you want to simplify. For example, consider the ratio $12:16$.
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Find the Greatest Common Divisor (GCD) Next, find the GCD of the two numbers in the ratio. The GCD is the largest number that divides both numbers evenly. For example, the GCD of $12$ and $16$ is $4$.
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Divide Both Terms by the GCD Now, divide each term of the ratio by the GCD you found. Using our example: $$ \text{First term: } \frac{12}{4} = 3 $$ $$ \text{Second term: } \frac{16}{4} = 4 $$
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Write the Simplified Ratio Finally, write the simplified ratio using the results from the division. For our example, the simplified ratio is $3:4$.
The simplified form of the ratio $12:16$ is $3:4$.
More Information
Understanding how to reduce ratios to their simplest form is useful in many areas of math, including fractions and proportions. It ensures clarity and simplicity when working with ratios in equations or real-life applications.
Tips
- Not finding the GCD correctly: Ensure you check all divisors and find the largest one.
- Forgetting to divide both terms: Always apply the GCD to both parts of the ratio.
- Miswriting the ratio: Make sure the order of the numbers remains the same after simplification.
