Solving fraction operations involves a few key steps to ensure you're adding, subtracting, multiplying, or dividing correctly. This guide focuses on addition and subtraction, incorporating the provided reference.
Adding and Subtracting Fractions
The primary challenge when adding or subtracting fractions is ensuring they have a common denominator. Here's how to do it:
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Find the Least Common Denominator (LCD): The LCD is the smallest multiple that the denominators of both fractions share. This is a crucial first step.
- Example: For 1/4 and 1/6, the LCD is 12.
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Write Equivalent Fractions: Convert each original fraction into an equivalent fraction using the LCD as the new denominator. To do this, determine what number you need to multiply the original denominator by to get the LCD, and then multiply both the numerator and denominator by that number.
- Example:
- 1/4 = (1 x 3) / (4 x 3) = 3/12
- 1/6 = (1 x 2) / (6 x 2) = 2/12
- Example:
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Add or Subtract Numerators: Once the fractions have the same denominator, you can add or subtract the numerators. The denominator remains the same.
- Example: 3/12 + 2/12 = (3 + 2) / 12 = 5/12
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Write the Result: The result is the new fraction with the combined numerator over the common denominator.
- Example: The final answer to 1/4 + 1/6 is 5/12.
Example Problem
Let's add 2/5 and 1/3 together:
- Find the LCD: The LCD of 5 and 3 is 15.
- Write Equivalent Fractions:
- 2/5 = (2 x 3) / (5 x 3) = 6/15
- 1/3 = (1 x 5) / (3 x 5) = 5/15
- Add Numerators: 6/15 + 5/15 = (6 + 5) / 15 = 11/15
- Write the Result: The final answer is 11/15.
Key Takeaways
- Always find the least common denominator first.
- Ensure you multiply both the numerator and denominator when creating equivalent fractions.
- Only add or subtract the numerators; the denominator stays the same.
