Simplifying fractions involves reducing them to their simplest form. This means expressing the fraction using the smallest possible whole numbers while maintaining the same value. Here's how to do it:
Steps to Simplify Fractions
The core process involves finding the Greatest Common Factor (GCF), also known as the Highest Common Factor (HCF), and then dividing.
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Find the Highest Common Factor (HCF): Determine the largest number that divides evenly into both the numerator (top number) and the denominator (bottom number) of the fraction. This is the HCF.
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Divide: Divide both the numerator and the denominator by the HCF. This process reduces the fraction to its simplest form.
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Write the Simplified Fraction: The resulting fraction after the division is the simplified version. If you started with a mixed number (a whole number and a fraction), keep the whole number and write the simplified fraction next to it.
Example
Let's simplify the fraction 12/18.
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Step 1: Find the HCF. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The highest common factor of 12 and 18 is 6.
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Step 2: Divide. Divide both the numerator and the denominator by 6:
- 12 ÷ 6 = 2
- 18 ÷ 6 = 3
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Step 3: Write the Simplified Fraction. Therefore, 12/18 simplified is 2/3.
Table Summarizing the Process
| Step | Description | Example (for 12/18) |
|---|---|---|
| Find the HCF | Determine the highest common factor of the numerator and denominator. | HCF of 12 and 18 is 6 |
| Divide | Divide both the numerator and denominator by the HCF. | 12 ÷ 6 = 2, 18 ÷ 6 = 3 |
| Write Simplified Form | Express the fraction using the results of the division. | 2/3 |
