Simplifying fractions in pre-algebra involves finding common factors in the numerator and the denominator and then removing them. Here’s how to do it step-by-step:
Understanding Fraction Simplification
Simplifying a fraction means reducing it to its simplest form. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. According to our references, the process involves three main steps:
Steps to Simplify Fractions
- Identify Common Factors:
- Begin by looking for factors that are shared by both the numerator (the top number) and the denominator (the bottom number) of the fraction.
- If it is not immediately obvious, rewrite the numerator and denominator, either by showing common factors or by factoring them into prime numbers.
- Example: For the fraction 12/18, we can write 12 as 2 x 6 and 18 as 3 x 6. The common factor is 6.
- Example (Prime Factorization): For the fraction 15/25, we can write 15 as 3 x 5 and 25 as 5 x 5. The common factor is 5.
- Remove Common Factors:
- Use the equivalent fractions property to divide both the numerator and the denominator by their common factor. This is like "canceling out" the common factor.
- Example: Using the previous example, 12/18 becomes (2 x 6) / (3 x 6). Canceling the 6 gives us 2/3. For 15/25, it becomes (3 x 5) / (5 x 5), canceling the 5 gives us 3/5.
- Multiply Remaining Factors:
- Once all common factors have been removed, multiply any remaining factors in the numerator and denominator.
- Example: The simplified fractions 2/3 and 3/5 are already in their simplest forms, and there's nothing more to multiply.
Examples
Here are some additional examples to illustrate the process:
| Original Fraction | Rewrite With Common Factors | Simplify (Remove Common Factors) | Simplified Fraction |
|---|---|---|---|
| 8/12 | (2 x 4) / (3 x 4) | 2/3 | 2/3 |
| 20/30 | (2 x 10) / (3 x 10) | 2/3 | 2/3 |
| 21/49 | (3 x 7) / (7 x 7) | 3/7 | 3/7 |
| 24/36 | (2 x 2 x 2 x 3) / (2 x 2 x 3 x 3) | 2/3 | 2/3 |
Tips for Simplification
- Always try to find the greatest common factor (GCF) for the quickest simplification, though using any common factor will work over multiple steps.
- If you can’t find a common factor right away, try dividing both numbers by small prime numbers (2, 3, 5, 7, and so on).
- A fraction is completely simplified when the numerator and denominator no longer share any common factors other than 1.
By following these steps, you can simplify fractions effectively in pre-algebra.
