63/36 in simplest form
Understand the Problem
The question is asking to simplify the fraction 63/36 to its lowest terms. To solve this, we will find the greatest common divisor (GCD) of the numerator and denominator and divide both by that number.
Answer
The simplified fraction is \( \frac{7}{4} \).
Answer for screen readers
The simplified fraction is ( \frac{7}{4} ).
Steps to Solve
- Find the GCD of 63 and 36
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numbers 63 and 36.
The factors of 63 are 1, 3, 7, 9, 21, and 63.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The greatest factor common to both lists is 9.
Thus, $GCD(63, 36) = 9$.
- Divide the numerator and denominator by the GCD
Now that we know the GCD is 9, we divide both the numerator (63) and the denominator (36) by 9.
So we calculate:
$$ \frac{63 \div 9}{36 \div 9} = \frac{7}{4} $$
- Final Result
The simplified fraction of $\frac{63}{36}$ is:
$$ \frac{7}{4} $$
The simplified fraction is ( \frac{7}{4} ).
More Information
When simplifying fractions, finding the GCD is essential. Simplifying helps in expressing numbers in more manageable forms and can be useful in various mathematical applications, such as solving equations or using ratios.
Tips
- A common mistake is forgetting to find the GCD correctly. Always list out the factors or use the Euclidean algorithm to ensure you have the correct GCD.
- Another error is dividing incorrectly. Make sure to perform each division step carefully.
