8/12 – 4/8 reduced to the lowest terms
The Correct Answer and Explanation is :
To reduce the fraction ( \frac{8}{12} ) to its lowest terms, follow these steps:
Step 1: Find the greatest common divisor (GCD)
The first step in reducing a fraction is finding the greatest common divisor (GCD) of the numerator (8) and the denominator (12). The GCD is the largest number that can divide both 8 and 12 without leaving a remainder.
- Factors of 8: ( 1, 2, 4, 8 )
- Factors of 12: ( 1, 2, 3, 4, 6, 12 )
The common factors between 8 and 12 are 1, 2, and 4. The greatest common factor is 4.
Step 2: Divide both the numerator and denominator by the GCD
Now, divide both the numerator and the denominator by the GCD (4).
[
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
]
Thus, ( \frac{8}{12} ) reduced to its lowest terms is ( \frac{2}{3} ).
Step 3: Explanation
Reducing a fraction means simplifying it to its smallest equivalent form, where both the numerator and denominator have no common factors other than 1. In this case, both 8 and 12 were divisible by 4, allowing us to simplify the fraction to ( \frac{2}{3} ). The key is finding the greatest common divisor, which ensures that the fraction is reduced as much as possible.
Related Example: Reducing ( \frac{4}{8} )
To reduce ( \frac{4}{8} ), follow the same process:
- GCD of 4 and 8 is 4.
- Divide both by 4: ( \frac{4 \div 4}{8 \div 4} = \frac{1}{2} ).
So, ( \frac{4}{8} ) simplifies to ( \frac{1}{2} ).
Conclusion
The fraction ( \frac{8}{12} ) reduced to its lowest terms is ( \frac{2}{3} ), and ( \frac{4}{8} ) reduces to ( \frac{1}{2} ). Both processes involve finding the GCD and dividing the numerator and denominator by this value.