simplify 26:39
Understand the Problem
The question is asking us to simplify the ratio 26:39. This involves finding the greatest common divisor of the two numbers and dividing both by that number to reduce the ratio to its simplest form.
Answer
The simplified ratio is $2:3$.
Answer for screen readers
The simplified ratio of 26:39 is $2:3$.
Steps to Solve
- Identify the two numbers in the ratio
The given ratio is 26:39, where 26 is the first number (A) and 39 is the second number (B).
- Find the greatest common divisor (GCD)
To simplify the ratio, we first need to find the GCD of 26 and 39.
The GCD can be found by listing the factors of both numbers or using the Euclidean algorithm.
For 26, the factors are: 1, 2, 13, 26
For 39, the factors are: 1, 3, 13, 39
The greatest common factor is 13.
- Divide both numbers by the GCD
Now that we have the GCD, we divide both numbers in the ratio by 13:
$$ \frac{26}{13} : \frac{39}{13} $$
This gives us:
$$ 2 : 3 $$
- State the simplified ratio
The simplified ratio of 26:39 is 2:3.
The simplified ratio of 26:39 is $2:3$.
More Information
When simplifying ratios, finding the GCD helps reduce the numbers to their simplest form, making comparisons easier. Ratio simplification is frequently used in problems involving proportions in mathematics, cooking, and many real-life applications.
Tips
- A common mistake is to only divide one number by the GCD and leave the other unchanged. Always remember to divide both numbers by the GCD to maintain the correctness of the ratio.
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