Class Notes: Dividing Fractions by Whole Numbers

Objective

Learn how to divide a fraction by a whole number using the "keep, change, flip" method, and how to simplify answers.

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Step-by-Step Process

1. Convert the Whole Number to a Fraction

   • Example: 5 → 5/1

2. Apply "Keep, Change, Flip"

   • Keep: Keep the first fraction as is.
   • Change: Change the division symbol to multiplication.
   • Flip: Flip the second fraction (find the reciprocal).

3. Multiply the Fractions

   • Multiply the numerators together.
   • Multiply the denominators together.

4. Simplify, if possible

   • Reduce the resulting fraction to its lowest terms.

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Example Problems

Example 1

Problem:
(\frac{2}{3} \div 5)

• Convert 5 to a fraction: (5 = \frac{5}{1})
• Apply "keep, change, flip":
  • Keep: (\frac{2}{3})
  • Change: (\div \to \times)
  • Flip: (\frac{5}{1} \to \frac{1}{5})
• Multiply:
  [ \frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15} ]
• Answer: (\frac{2}{15})

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Example 2

Problem:
(\frac{4}{5} \div 3)

• Convert 3 to a fraction: (3 = \frac{3}{1})
• Apply "keep, change, flip"
• Multiply: [ \frac{4}{5} \times \frac{1}{3} = \frac{4 \times 1}{5 \times 3} = \frac{4}{15} ]
• Answer: (\frac{4}{15})

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Practice Problems with Simplifying

1. (\frac{8}{9} \div 4)

• Convert 4 to a fraction: (4 = \frac{4}{1})
• Keep: (\frac{8}{9})
• Change: (\div \to \times)
• Flip: (\frac{4}{1} \to \frac{1}{4})
• Multiply: [ \frac{8}{9} \times \frac{1}{4} = \frac{8 \times 1}{9 \times 4} = \frac{8}{36} ]
• Simplify: (8/36 = 2/9) (divide top and bottom by 4)
• Answer: (\frac{2}{9})

2. (\frac{12}{7} \div 3)

• Convert 3 to a fraction: (3 = \frac{3}{1})
• Keep: (\frac{12}{7})
• Change: (\div \to \times)
• Flip: (\frac{3}{1} \to \frac{1}{3})
• Multiply: [ \frac{12}{7} \times \frac{1}{3} = \frac{12 \times 1}{7 \times 3} = \frac{12}{21} ]
• Simplify: (12/21 = 4/7) (divide top and bottom by 3)
• Answer: (\frac{4}{7})

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Additional Tips

• If you notice common factors between numerators and denominators, you can cancel them before multiplying.
• Both multiplying across then simplifying, or cancelling first, yield the same answer.

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Summary

• Always convert the whole number to a fraction.
• Use "keep, change, flip" for division of fractions.
• Multiply across, then simplify your answer.
• Cancelling common factors early can make calculations easier.