Dividing Mixed Numbers and Whole Numbers
Overview
- The lecture covers how to divide mixed numbers and whole numbers.
- Two examples:
- Mixed number divided by a whole number.
- Whole number divided by a mixed number.
Key Steps for Division
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Convert Mixed Numbers and Whole Numbers to Improper Fractions
- For mixed numbers: Multiply the whole number by the denominator and add the numerator. Keep the denominator the same.
- For whole numbers: Place the number over 1.
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Use the KSF Method (Keep, Switch, Flip)
- Keep the first fraction.
- Switch division to multiplication.
- Flip the second fraction (reciprocal).
-
Simplification through Cancellation (if possible)
- Look for common factors between numerators and denominators.
- Simplify fractions before multiplying.
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Multiply Straight Across
- Multiply numerators with numerators, denominators with denominators.
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Convert Improper Fractions to Mixed Numbers
- Divide the numerator by the denominator.
- Remainder becomes the new numerator, denominator stays the same.
Example 1: Mixed Number Divided by Whole Number
- Problem: 8 2/3 divided by 2
- Convert to improper fractions: 26/3 and 2/1
- Apply KSF: 26/3 x 1/2
- Simplify using cancellation: Common factor is 2
- Multiply: 13 x 1 = 13, 3 x 1 = 3
- Convert to mixed number: 13/3 = 4 1/3
Example 2: Whole Number Divided by Mixed Number
- Problem: 7 divided by 3 3/5
- Convert to improper fractions: 7/1 and 18/5
- Apply KSF: 7/1 x 5/18
- No cancellation possible
- Multiply: 7 x 5 = 35, 1 x 18 = 18
- Convert to mixed number: 35/18 = 1 17/18
Final Notes
- Both methods (using or not using cancellation) result in the same answer.
- Simplification can occur before or after multiplication.
- Simplified results are necessary for final answers.
- Always check the fractional part for further simplification.
These steps ensure correct division of mixed numbers and whole numbers. Practice with different examples to become proficient.
Thanks for watching and learning! Peace.