To subtract fraction sums, you first need to find the sums and then perform the subtraction, ensuring you have a common denominator before subtracting the numerators.
Here's a breakdown of the process:
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Simplify any fraction sums individually: Before you can subtract, you might have expressions like
(1/2 + 1/4) - (1/3 + 1/6). In this case, simplify the expressions in parentheses first. -
Find a Common Denominator: If the fractions you're subtracting don't have the same denominator, find the least common multiple (LCM) of the denominators. This will be your common denominator.
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Convert Fractions to Equivalent Fractions: Convert each fraction to an equivalent fraction with the common denominator. To do this, multiply the numerator and denominator of each fraction by the same number, which will result in the common denominator.
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Subtract the Numerators: Once all fractions have the same denominator, subtract the numerators of the fractions. The denominator remains the same.
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Simplify the Result: After subtracting, simplify the resulting fraction, if possible. This means reducing the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common factor (GCF).
Example:
Let's subtract the sum 1/2 + 1/4 from the sum 2/3 + 1/6.
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Simplify sums individually:
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1/2 + 1/4- Find the common denominator (4):
1/2 = 2/4 - Add:
2/4 + 1/4 = 3/4
- Find the common denominator (4):
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2/3 + 1/6- Find the common denominator (6):
2/3 = 4/6 - Add:
4/6 + 1/6 = 5/6
- Find the common denominator (6):
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Now we have:
5/6 - 3/4 -
Find a Common Denominator: The LCM of 6 and 4 is 12.
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Convert Fractions:
5/6 = (5 * 2) / (6 * 2) = 10/123/4 = (3 * 3) / (4 * 3) = 9/12
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Subtract:
10/12 - 9/12 = 1/12
Therefore, (2/3 + 1/6) - (1/2 + 1/4) = 1/12
In Summary: When subtracting fraction sums, simplify each sum first, then find a common denominator, convert the fractions, subtract the numerators, and simplify the final fraction.
