Subtracting fractions involves a few key steps to ensure you're working with compatible numbers. Here's how you do it, based on the reference provided:
To subtract fractions, you need to follow these three crucial steps:
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Ensure the Denominators are the Same: The denominators (the bottom numbers of the fractions) must be identical. This is crucial because you can only directly subtract fractions that represent parts of the same whole.
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Find a Common Denominator (if necessary): If the denominators are different, you need to find a common denominator. This is a number that both denominators can divide into evenly. To do this, you must multiply the numerator and denominator of the fractions by the same number, to arrive at the common denominator.
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Subtract the Numerators: Once the denominators are the same, subtract the numerators (the top numbers of the fractions). The result becomes the new numerator, while the denominator stays the same.
Let's illustrate with an example:
Example:
Subtract 1/3 from 1/2.
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Step 1: The denominators are different (3 and 2).
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Step 2: Find a common denominator. The least common multiple of 2 and 3 is 6. Convert both fractions:
- 1/2 = (1 3) / (2 3) = 3/6
- 1/3 = (1 2) / (3 2) = 2/6
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Step 3: Subtract the numerators: 3/6 - 2/6 = (3 - 2) / 6 = 1/6
Therefore, 1/2 - 1/3 = 1/6
Here's a summary in a table:
| Step | Description | Example (Subtract 1/3 from 1/2) |
|---|---|---|
| 1. Check Denominators | Are the denominators the same? | No, they are 2 and 3. |
| 2. Find Common Denominator | Find a common multiple of the denominators and convert the fractions. | Common denominator: 6. 1/2 becomes 3/6. 1/3 becomes 2/6. |
| 3. Subtract Numerators | Subtract the numerators, keeping the common denominator. | (3 - 2) / 6 = 1/6 |
By following these steps, you can confidently subtract fractions!
