12/32 in simplest form
Understand the Problem
The question is asking for the simplest form of the fraction 12/32. To solve this, we will need to find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by that number.
Answer
The simplest form of the fraction \( \frac{12}{32} \) is \( \frac{3}{8} \).
Answer for screen readers
The simplest form of the fraction ( \frac{12}{32} ) is ( \frac{3}{8} ).
Steps to Solve
- Find the GCD of 12 and 32
To simplify the fraction, we first need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (32). The GCD is the largest number that divides both numbers without leaving a remainder.
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 32 are: 1, 2, 4, 8, 16, 32
The common factors are 1, 2, and 4. The greatest common factor is 4.
- Divide both the numerator and denominator by the GCD
Now that we've found the GCD, we can simplify the fraction by dividing both the numerator and the denominator by 4.
$$ \frac{12 \div 4}{32 \div 4} $$
This simplifies to:
$$ \frac{3}{8} $$
- Final result
The simplest form of the fraction is:
$$ \frac{3}{8} $$
The simplest form of the fraction ( \frac{12}{32} ) is ( \frac{3}{8} ).
More Information
When converting fractions to their simplest form, finding the GCD is a crucial step. This ensures that the fraction is expressed with the smallest possible numerator and denominator, making it easier to work with and interpret.
Tips
- A common mistake is to forget to find the GCD and simply divide by small numbers, which may not simplify the fraction correctly.
- Another mistake is not checking their factors carefully, which can lead to inaccuracies in identifying the GCD.