To pre-simplify a fraction, you find the greatest common factor (GCF) of the numerator and denominator and then divide both by that GCF. This process results in an equivalent fraction in its simplest form.
Here's a step-by-step guide on how to pre-simplify fractions, based on the provided reference:
- Identify all the factors of the numerator: List all the numbers that divide evenly into the numerator.
- Identify all the factors of the denominator: List all the numbers that divide evenly into the denominator.
- Find the greatest common factor (GCF): Determine the largest number that is a factor of both the numerator and the denominator.
- Divide both numerator and denominator by the GCF: Divide both the top and bottom of the fraction by the GCF. This reduces the fraction to its simplest form.
- Convert to a mixed number (if applicable): If the simplified fraction is improper (numerator is greater than or equal to the denominator), convert it to a mixed number.
Example:
Let's simplify the fraction 12/18.
- Factors of the numerator (12): 1, 2, 3, 4, 6, 12
- Factors of the denominator (18): 1, 2, 3, 6, 9, 18
- Greatest Common Factor (GCF): The greatest common factor of 12 and 18 is 6.
- Divide by the GCF: Divide both the numerator and denominator by 6:
- 12 ÷ 6 = 2
- 18 ÷ 6 = 3
Therefore, the simplified fraction is 2/3.
Another Example (including improper fractions):
Simplify 20/8:
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 8: 1, 2, 4, 8
- GCF: 4
- Divide by GCF:
- 20 / 4 = 5
- 8 / 4 = 2
This gives you 5/2. Since this is an improper fraction:
- Convert to a mixed number: 5/2 = 2 1/2
