simplify 48/63
Understand the Problem
The question is asking to simplify the fraction 48/63 to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator.
Answer
The simplified fraction is $\frac{16}{21}$.
Answer for screen readers
The simplified fraction is $\frac{16}{21}$.
Steps to Solve
- Identify the GCD of the numerator and denominator
To simplify the fraction $\frac{48}{63}$, we need to find the GCD of 48 and 63.
- Find the prime factors of each number
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The prime factorization of 48 is:
- $48 = 2^4 \times 3^1$
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The prime factorization of 63 is:
- $63 = 3^2 \times 7^1$
- Determine the common factors
The common prime factor between 48 and 63 is 3. The smallest power of 3 that appears in both factorizations is $3^1$.
- Calculate the GCD
The GCD of 48 and 63 is: $$ GCD = 3^1 = 3 $$
- Divide the numerator and denominator by the GCD
Now, divide both the numerator and the denominator of the fraction by the GCD: $$ \frac{48 \div 3}{63 \div 3} = \frac{16}{21} $$
The simplified fraction is $\frac{16}{21}$.
More Information
The process of simplifying fractions helps in making calculations easier and more straightforward. The greatest common divisor effectively reduces the fraction to its simplest form, helping to recognize the relationship between the numbers.
Tips
One common mistake is to forget to check for the GCD thoroughly or to incorrectly calculate the GCD. It's also easy to overlook dividing both the numerator and the denominator by the GCD. Always double-check the calculations for accurate simplification.
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