24/32 simplified
Understand the Problem
The question is asking for the simplification of the fraction 24/32. To solve this, we will find the greatest common divisor (GCD) of 24 and 32 and divide both the numerator and denominator by that number.
Answer
The simplified form of the fraction is \( \frac{3}{4} \).
Answer for screen readers
The simplified form of the fraction ( \frac{24}{32} ) is ( \frac{3}{4} ).
Steps to Solve
- Find the GCD of 24 and 32
To simplify the fraction, we first need to determine the greatest common divisor (GCD) of 24 and 32. The GCD is the largest number that divides both numbers evenly.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 32 are: 1, 2, 4, 8, 16, 32
The common factors are: 1, 2, 4, 8
Thus, the GCD is 8.
- Divide both the numerator and denominator by the GCD
Now we divide both the numerator and denominator of the fraction by the GCD:
$$ \frac{24 \div 8}{32 \div 8} $$
Calculating this gives:
$$ \frac{3}{4} $$
- Final simplified fraction
The final simplified fraction is:
$$ \frac{3}{4} $$
The simplified form of the fraction ( \frac{24}{32} ) is ( \frac{3}{4} ).
More Information
This result shows that both 24 and 32 share common factors, with 8 being the greatest. Dividing by the GCD streamlines the fraction to its simplest form, highlighting efficient properties in fractions.
Tips
- A common mistake is not finding the correct GCD, which can lead to incorrect simplifications. Always list the factors systematically to ensure accuracy.
- Another mistake is forgetting to divide both the numerator and denominator by the GCD, resulting in an incomplete simplification.
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