How to write a ratio in simplest form?
Understand the Problem
The question is asking how to simplify a ratio to its simplest form. This involves finding the greatest common factor of the numbers in the ratio and dividing both by that factor to reduce it.
Answer
The simplified ratio is $3:4$.
Answer for screen readers
The simplified ratio is $3:4$.
Steps to Solve
- Identify the ratio
Start with the given ratio. For example, if the ratio is $12:16$, we will use these numbers to simplify it.
- Find the greatest common factor (GCF)
Determine the GCF of the two numbers in the ratio.
For $12$, its factors are $1, 2, 3, 4, 6, 12$.
For $16$, its factors are $1, 2, 4, 8, 16$.
The largest common factor is $4$.
- Divide both numbers by the GCF
Now divide both parts of the ratio by the GCF.
$$ \text{For } 12:16, \frac{12}{4} : \frac{16}{4} $$
This results in:
$$ 3:4 $$
- Write the simplified ratio
The final simplified ratio from the original ratio is $3:4$.
The simplified ratio is $3:4$.
More Information
Simplifying ratios makes proportions easier to understand and can help in various real-world applications, such as cooking, mixing solutions, or comparing quantities.
Tips
- Not finding the correct GCF: Make sure to list all factors correctly.
- Forgetting to divide both terms by the GCF, which leads to incorrect simplification.
