Reduce the fraction 36/48 to its lowest terms.
A. 3/4
B. 112/48
C. 6/8
D. 11/4
The Correct Answer and Explanation is :
Correct Answer: A. ( \frac{3}{4} )
To reduce the fraction ( \frac{36}{48} ) to its lowest terms, we need to find the greatest common divisor (GCD) of the numerator (36) and the denominator (48). The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: Find the GCD of 36 and 48.
We can find the GCD using the prime factorization method:
- Prime factorization of 36:
- 36 = ( 2^2 \times 3^2 )
- Prime factorization of 48:
- 48 = ( 2^4 \times 3^1 )
Step 2: Identify the common factors.
The common prime factors of 36 and 48 are:
- For ( 2 ): The smallest power is ( 2^2 ).
- For ( 3 ): The smallest power is ( 3^1 ).
Thus, the GCD is:
[
GCD = 2^2 \times 3^1 = 4 \times 3 = 12
]
Step 3: Divide both the numerator and denominator by the GCD.
Now we divide both the numerator and denominator of ( \frac{36}{48} ) by their GCD (12):
[
\frac{36 \div 12}{48 \div 12} = \frac{3}{4}
]
Conclusion:
The fraction ( \frac{36}{48} ) reduces to ( \frac{3}{4} ), which is its lowest terms.
Correct Answer: A. ( \frac{3}{4} )
This process illustrates the importance of understanding prime factorization and the concept of the GCD in simplifying fractions. Reducing fractions not only makes them easier to work with but also helps in making calculations clearer and more concise. When working with fractions in mathematical problems, always look to reduce them to their simplest form for better accuracy and understanding.