Canceling fractions, also known as simplifying fractions, involves reducing a fraction to its simplest form by dividing both the numerator (top number) and the denominator (bottom number) by their common factors. Here's a breakdown of the process:
Steps to Cancel Fractions
The general steps, based on the provided reference, are as follows:
- Factorize the Numerator: Break down the numerator into its prime factors or simpler factors.
- Factorize the Denominator: Break down the denominator into its prime factors or simpler factors.
- Order the Factors (Optional): While not strictly necessary, ordering the factors can help visually identify common factors more easily.
- Cancel Common Factors: Identify factors that appear in both the numerator and the denominator. Cancel one common factor at a time until there are no more common factors. This is essentially dividing both the numerator and the denominator by the same number.
- Multiply Remaining Factors: Multiply the remaining factors in the numerator to get the simplified numerator. Multiply the remaining factors in the denominator to get the simplified denominator.
Example
Let's simplify the fraction 12/18.
| Step | Action | Result |
|---|---|---|
| 1. Factorize Numerator | Find the factors of 12. | 12 = 2 x 2 x 3 |
| 2. Factorize Denominator | Find the factors of 18. | 18 = 2 x 3 x 3 |
| 3. Optional Step | Order the factors (already ordered). | N/A |
| 4. Cancel Common Factors | Divide both by common factors. | 12/18 = (2 x 2 x 3) / (2 x 3 x 3) = ( |
| 5. Multiply Remaining Factors | Multiply the remaining numbers | The simplified numerator is 2. The simplified denominator is 3. |
Therefore, 12/18 simplified is 2/3.
Important Considerations
- You can only cancel factors, not terms that are added or subtracted. For instance, you cannot cancel in (2 + 4) / 4. You must simplify the numerator first: (2+4)/4 = 6/4 = 3/2.
- If everything in the numerator or denominator cancels out, the remaining value is 1, not 0. For example, 3/3 = 1/1 = 1.
By following these steps, you can effectively cancel and simplify fractions to their simplest form.
