Solving operations with mixed numbers requires converting them to improper fractions first, then performing the operation, and finally simplifying the result. Here's a breakdown:
Step-by-Step Guide to Solving Operations with Mixed Numbers
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Convert Mixed Numbers to Improper Fractions: A mixed number has a whole number part and a fractional part (e.g., 2 1/2). To convert it to an improper fraction:
- Multiply the whole number by the denominator of the fraction.
- Add the numerator to the result.
- Keep the same denominator.
Example: Converting 2 1/2 to an improper fraction:
- 2 * 2 = 4
- 4 + 1 = 5
- Therefore, 2 1/2 = 5/2
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Perform the Operation: Once all mixed numbers are converted to improper fractions, perform the operation as usual:
- Addition and Subtraction: Find a common denominator and add or subtract the numerators.
- Multiplication: Multiply the numerators and multiply the denominators.
- Division: Multiply the first fraction by the reciprocal of the second fraction (flip the second fraction).
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Simplify the Result:
- Reduce the Fraction: Simplify the improper fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor (GCF).
- Convert back to a Mixed Number (if necessary): If the result is an improper fraction and you need a mixed number, divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.
Examples of Operations with Mixed Numbers
Addition:
1 1/4 + 2 1/2 = 5/4 + 5/2 = 5/4 + 10/4 = 15/4 = 3 3/4
Subtraction:
3 1/2 - 1 1/4 = 7/2 - 5/4 = 14/4 - 5/4 = 9/4 = 2 1/4
Multiplication:
2 1/2 1 1/5 = 5/2 6/5 = 30/10 = 3
Division:
3 1/2 ÷ 1 1/4 = 7/2 ÷ 5/4 = 7/2 * 4/5 = 28/10 = 14/5 = 2 4/5
Summary
Solving operations with mixed numbers involves converting them to improper fractions, performing the indicated operation (+, -, *, /), simplifying the result, and optionally converting back to a mixed number. Careful attention to detail is required for accurate calculations.
