Subtracting mixed numbers with unlike denominators involves several steps, focusing on finding a common denominator before performing the subtraction.
Here’s how to subtract mixed numbers with unlike denominators, broken down into simple steps:
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Find a Common Denominator:
- Identify the denominators of the fractional parts of the mixed numbers.
- Determine the least common multiple (LCM) of these denominators. This LCM will be your common denominator.
- Convert each fraction to an equivalent fraction with the common denominator. To do this, multiply both the numerator and denominator of each fraction by the factor that makes the original denominator equal to the common denominator.
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Subtract the Fractions:
- Once the fractions have the same denominator, subtract the numerators. Keep the common denominator the same.
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Subtract the Whole Numbers:
- Subtract the whole numbers of the mixed numbers.
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Combine the Results:
- Combine the result from subtracting the fractions and the result from subtracting the whole numbers to form the final mixed number.
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Simplify (if necessary):
- If the fractional part of the mixed number is an improper fraction (numerator is greater than or equal to the denominator), convert it to a mixed number and add the whole number part to the whole number part of your answer.
- Simplify the fraction if possible by dividing both the numerator and the denominator by their greatest common factor (GCF).
Example:
Let's say we want to subtract ( 2\frac{1}{5} ) from ( 6\frac{3}{10} ).
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Find a Common Denominator:
- The denominators are 5 and 10.
- The least common multiple (LCM) of 5 and 10 is 10.
- Convert ( \frac{1}{5} ) to an equivalent fraction with a denominator of 10: ( \frac{1}{5} \times \frac{2}{2} = \frac{2}{10} )
- So, ( 2\frac{1}{5} ) becomes ( 2\frac{2}{10} ).
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Subtract the Fractions:
- Subtract ( \frac{2}{10} ) from ( \frac{3}{10} ): ( \frac{3}{10} - \frac{2}{10} = \frac{1}{10} )
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Subtract the Whole Numbers:
- Subtract 2 from 6: ( 6 - 2 = 4 )
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Combine the Results:
- Combine the results to get the final mixed number: ( 4\frac{1}{10} )
According to the provided reference, after finding the common denominator and performing the subtraction, you subtract the fractions to get ( \frac{1}{10} ). Then, subtract the whole numbers, ( 6 - 2 = 4 ). The final answer is ( 4\frac{1}{10} ).
