63/72 simplified
Understand the Problem
The question is asking to simplify the fraction 63/72 to its lowest terms, which involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number.
Answer
The simplified fraction of $\frac{63}{72}$ is $\frac{7}{8}$.
Answer for screen readers
The simplified fraction of $\frac{63}{72}$ is $\frac{7}{8}$.
Steps to Solve
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Find the greatest common divisor (GCD) To simplify the fraction, we first need to find the GCD of the numerator (63) and the denominator (72). We can do this by listing the factors or using the Euclidean algorithm.
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List the factors For 63, the factors are: 1, 3, 7, 9, 21, 63.
For 72, the factors are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
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Identify the GCD The common factors of 63 and 72 are 1, 3, and 9. The greatest of these is 9, so the GCD is 9.
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Divide the numerator and the denominator by the GCD Now we will divide both the numerator and the denominator by the GCD (9):
$$ \frac{63}{72} = \frac{63 \div 9}{72 \div 9} = \frac{7}{8} $$
- Write the simplified fraction Thus, the fraction 63/72 simplified to its lowest terms is $\frac{7}{8}$.
The simplified fraction of $\frac{63}{72}$ is $\frac{7}{8}$.
More Information
The process of simplification helps to express fractions in their simplest form, making them easier to work with. The GCD can also be found using prime factorization or the Euclidean algorithm, which is an efficient method for finding the GCD of two numbers.
Tips
- Forgetting to find the GCD correctly can lead to incorrect simplification.
- Dividing only one part of the fraction instead of both the numerator and denominator.
