24/9 in simplest form
Understand the Problem
The question is asking to simplify the fraction 24/9 to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by that number.
Answer
The simplified form of the fraction is $\frac{8}{3}$.
Answer for screen readers
The simplified form of the fraction $\frac{24}{9}$ is $\frac{8}{3}$.
Steps to Solve
- Find the GCD of 24 and 9
To simplify the fraction $\frac{24}{9}$, we first need to determine the greatest common divisor (GCD) of 24 and 9. The GCD is the largest number that can divide both 24 and 9 without leaving a remainder.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 9 are: 1, 3, 9
The common factors of 24 and 9 are: 1, 3.
Thus, the GCD is 3.
- Divide both numerator and denominator by the GCD
Now we will divide both the numerator (24) and the denominator (9) by the GCD, which is 3.
Calculating the new numerator:
$$ \frac{24}{3} = 8 $$
Calculating the new denominator:
$$ \frac{9}{3} = 3 $$
- Write the simplified fraction
Now that we have both the simplified numerator and denominator, we can write the simplified fraction:
$$ \frac{24}{9} = \frac{8}{3} $$
The simplified form of the fraction $\frac{24}{9}$ is $\frac{8}{3}$.
More Information
The fraction $\frac{8}{3}$ cannot be reduced further, as the numerator and denominator do not have common factors other than 1. This simple form represents an improper fraction, which is perfectly valid and might also be expressed as a mixed number: $2\frac{2}{3}$.
Tips
- Forgetting to find the GCD correctly; double-check the factors.
- Dividing only one part of the fraction; ensure both numerator and denominator are divided by the GCD.
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