What is the simplest form of 4/6 in fractions
The Correct Answer and Explanation is :
The simplest form of the fraction ( \frac{4}{6} ) is ( \frac{2}{3} ).
Explanation
To simplify a fraction, we need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can evenly divide both the numerator and the denominator.
- Identifying the GCD:
- For the fraction ( \frac{4}{6} ), we first find the GCD of 4 and 6.
- The factors of 4 are: 1, 2, 4.
- The factors of 6 are: 1, 2, 3, 6.
- The common factors of 4 and 6 are: 1, 2.
- The greatest of these common factors is 2. Therefore, the GCD of 4 and 6 is 2.
- Dividing by the GCD:
- Next, we divide both the numerator and the denominator of ( \frac{4}{6} ) by the GCD:
- For the numerator: ( 4 \div 2 = 2 )
- For the denominator: ( 6 \div 2 = 3 )
- This gives us the simplified fraction ( \frac{2}{3} ).
- Verification:
- To verify that ( \frac{2}{3} ) is in its simplest form, we can check if there are any common factors between 2 and 3.
- The factors of 2 are: 1, 2.
- The factors of 3 are: 1, 3.
- The only common factor is 1, indicating that ( \frac{2}{3} ) cannot be simplified further.
- Conclusion:
- Thus, ( \frac{4}{6} ) simplifies to ( \frac{2}{3} ).
- Simplifying fractions is essential in mathematics to express numbers in their most basic form, making them easier to understand and work with.
In summary, the simplest form of ( \frac{4}{6} ) is ( \frac{2}{3} ), which results from dividing both numbers by their greatest common divisor, 2.