What is 36:39 in simplest form?
Understand the Problem
The question is asking to simplify the ratio of 36 to 39. To solve this, we need to find the greatest common divisor (GCD) of the two numbers and divide both by this number.
Answer
The simplified ratio is $12:13$.
Answer for screen readers
The simplified ratio of 36 to 39 is $12:13$.
Steps to Solve
- Find the GCD of 36 and 39
To simplify the ratio, we must first find the greatest common divisor (GCD) of 36 and 39. We can do this by listing the factors of both numbers.
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 39: 1, 3, 13, 39
The largest common factor is 3, so the GCD(36, 39) = 3.
- Divide both numbers by the GCD
Now, we divide both parts of the ratio by the GCD to simplify the ratio.
The new ratio will be:
$$ \frac{36}{3} : \frac{39}{3} = 12 : 13 $$
- State the simplified ratio
After performing the division, we conclude that the simplified ratio of 36 to 39 is 12:13.
The simplified ratio of 36 to 39 is $12:13$.
More Information
Simplifying ratios is a useful skill in various mathematical contexts, such as proportions in recipes or comparing quantities in real life. The ratio 12:13 conveys that for every 12 parts of one quantity, there are 13 parts of another.
Tips
A common mistake is to incorrectly identify the GCD, leading to incorrect simplification. To avoid this, ensure you check all factors systematically.
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