How do you write ratios in simplest form?
Understand the Problem
The question asks for the procedure to simplify ratios. To write ratios in simplest form, you divide both parts of the ratio by their greatest common divisor (GCD).
Answer
The simplified ratio is $3:4$.
Answer for screen readers
The simplified ratio of 12:16 is $3:4$.
Steps to Solve
- Identify the ratio components
First, identify the two numbers in the ratio. For example, if the ratio is 12:16, the two components are 12 and 16.
- Find the GCD
Next, calculate the greatest common divisor (GCD) of the two numbers. You can list the factors or use the Euclidean algorithm. For 12 and 16, the factors are:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 16: 1, 2, 4, 8, 16
The GCD is 4.
- Divide both numbers by the GCD
Now, divide each component of the ratio by the GCD to simplify it. For our example: $$ \frac{12}{4} : \frac{16}{4} = 3 : 4 $$
- Write the simplified ratio
Finally, write the simplified ratio in its lowest terms. The simplified form of the ratio 12:16 is 3:4.
The simplified ratio of 12:16 is $3:4$.
More Information
Simplifying ratios helps in making comparisons easier. Ratios can represent various real-world relationships, such as mixing ingredients or comparing quantities.
Tips
- Failing to find the correct GCD can lead to incorrect simplification. Double-check the factors of each number.
- Sometimes, people reduce ratios incorrectly by dividing only one part. Make sure to divide both parts by the GCD.
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