To find the lowest form of a fraction, follow these detailed steps:
Step 1: Understand the Fraction
- A fraction consists of a numerator (top number) and a denominator (bottom number).
- For example, in the fraction 8/12, 8 is the numerator, and 12 is the denominator.
Step 2: Find the Greatest Common Divisor (GCD)
- The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
- You can find the GCD using methods such as listing the factors, using the Euclidean algorithm, or prime factorization.
Step 3: Divide Both Numerator and Denominator by the GCD
- Once you have the GCD, divide both the numerator and the denominator by this number.
- Continuing with our example, if the GCD of 8 and 12 is 4, then:
- 8 ÷ 4 = 2
- 12 ÷ 4 = 3
- Therefore, 8/12 simplifies to 2/3.
Step 4: Verify the Simplified Fraction
- Ensure that the new fraction cannot be simplified further.
- Check if the numerator and denominator share any common factors other than 1.
Step 5: Conclusion
- The resulting fraction (2/3 in our example) is in its lowest form.
- Whenever you simplify a fraction, always express it in the simplest terms for clarity in communication.
By following these steps, you can efficiently reduce any fraction to its lowest form.