9/36 in simplest form
Understand the Problem
The question is asking how to simplify the fraction 9/36 to its lowest terms.
Answer
The simplified form of \( \frac{9}{36} \) is \( \frac{1}{4} \).
Answer for screen readers
The simplified form of the fraction ( \frac{9}{36} ) is ( \frac{1}{4} ).
Steps to Solve
- Identify the Greatest Common Divisor (GCD)
To simplify the fraction, we need to find the greatest common divisor of the numerator (9) and the denominator (36). The GCD is the largest number that divides both 9 and 36.
- Calculate the GCD
We can list the factors of both numbers:
- Factors of 9: 1, 3, 9
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The largest common factor is 9, so $GCD(9, 36) = 9$.
- Divide both the numerator and denominator by the GCD
We divide both the numerator and the denominator of the fraction $ \frac{9}{36} $ by 9:
$$ \frac{9 \div 9}{36 \div 9} = \frac{1}{4} $$
- Final Check of the Fraction
After simplifying, check if the fraction $ \frac{1}{4} $ is in its lowest terms. Since 1 is the only factor of 1, and its only divisor is itself, this fraction is already in its lowest terms.
The simplified form of the fraction ( \frac{9}{36} ) is ( \frac{1}{4} ).
More Information
When simplifying fractions, finding the GCD is a fundamental step. It ensures that you divide by the largest number possible, resulting in the simplest form of the fraction. In this case, we learned that ( \frac{9}{36} = \frac{1}{4} ), meaning that 9 is one-fourth of 36.
Tips
- Not finding the GCD: Some may attempt to simplify directly without calculating the GCD, leading to incorrect simplifications.
- Dividing incorrectly: Ensure that you divide both the numerator and denominator by the same number to maintain equality.