27:6 simplified
Understand the Problem
The question is asking to simplify the fraction 27:6 to its simplest form. This can be done by finding the greatest common divisor (GCD) of 27 and 6 and dividing both numbers by the GCD.
Answer
The simplest form of the fraction 27:6 is $9:2$.
Answer for screen readers
The simplest form of the fraction 27:6 is $9:2$.
Steps to Solve
- Find the Greatest Common Divisor (GCD)
To simplify the fraction, we first need to find the GCD of the numbers 27 and 6. The factors of 27 are 1, 3, 9, and 27. The factors of 6 are 1, 2, 3, and 6.
The GCD is the largest number that appears in both lists of factors, which is 3.
- Divide Both Numbers by the GCD
Next, we divide both numbers in the fraction by the GCD:
- Divide 27 by 3:
$$ \frac{27}{3} = 9 $$ - Divide 6 by 3:
$$ \frac{6}{3} = 2 $$
- Write the Simplified Fraction
Now we can write the simplified fraction: $$ \frac{27}{6} = \frac{9}{2} $$
The simplest form of the ratio 27:6 is 9:2.
The simplest form of the fraction 27:6 is $9:2$.
More Information
When simplifying ratios or fractions, finding the GCD is essential. Did you know that simplifying fractions helps in finding easier and more manageable numbers for calculations in real-life applications?
Tips
- A common mistake is forgetting to divide both numbers by the GCD, which results in an incorrect ratio.
- Another mistake is miscalculating the GCD itself. Always double-check the factors of both numbers.
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