Fraction subtraction involves finding the difference between two or more fractions. The process varies slightly depending on whether the fractions have the same denominator (common denominator) or different denominators. Here's a breakdown of how to perform fraction subtraction:
Subtracting Fractions with Common Denominators
When fractions share the same denominator, the subtraction process is straightforward.
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Keep the Denominator: Retain the common denominator.
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Subtract the Numerators: Subtract the numerators of the fractions.
For example, according to the reference material:
- 2/5 - 1/5 = (2-1)/5 = 1/5
Example Table
| Fraction 1 | Fraction 2 | Subtraction | Result |
|---|---|---|---|
| 3/7 | 1/7 | 3/7 - 1/7 | 2/7 |
| 5/8 | 2/8 | 5/8 - 2/8 | 3/8 |
Subtracting Fractions with Different Denominators
When subtracting fractions with different denominators, a key first step is to find a common denominator.
- Find the Least Common Denominator (LCD):
- Identify the denominators of the fractions.
- Find the least common multiple (LCM) of these denominators. This LCM will be the LCD.
- Convert to Equivalent Fractions:
- For each fraction, determine what number the original denominator should be multiplied by to equal the LCD.
- Multiply both the numerator and the denominator by this number, thus producing an equivalent fraction with the LCD.
- Subtract Numerators: Once the denominators are the same, proceed with subtracting the numerators.
- Simplify: If possible, simplify the resulting fraction to its simplest form.
Example
Subtract 1/3 from 1/2
- Find the LCD:
- The denominators are 3 and 2.
- The LCM of 3 and 2 is 6, so LCD = 6.
- Convert to Equivalent Fractions:
- For 1/2: 2 x 3 = 6, so multiply numerator and denominator by 3: (1 x 3)/(2 x 3) = 3/6
- For 1/3: 3 x 2 = 6, so multiply numerator and denominator by 2: (1 x 2)/(3 x 2) = 2/6
- Subtract Numerators:
- 3/6 - 2/6 = (3-2)/6 = 1/6
Practical Insights
- Simplification: Always reduce the resulting fraction to its lowest terms. For example, 4/8 can be simplified to 1/2.
- Visual Aids: Consider using visual aids, like fraction bars, to help understand the process, especially when learning about finding common denominators.
- Practice: Consistent practice is crucial for mastering fraction subtraction.
