Class Notes: Dividing a Whole Number by a Fraction

Objective

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

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Key Steps

1. Rewrite the Whole Number as a Fraction

   • Example: 4 becomes 4/1; 8 becomes 8/1.

2. Use the "Keep, Change, Flip" Method

   • Keep the first fraction the same.
   • Change division to multiplication.
   • Flip (find the reciprocal of) the second fraction.

3. Multiply Across

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

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Example Problems & Solutions

1. ( 4 \div \frac{1}{3} )

• Write as fractions: ( \frac{4}{1} \div \frac{1}{3} )
• Apply "keep, change, flip":
  • ( \frac{4}{1} \times \frac{3}{1} )
• Multiply across:
  • Numerator: ( 4 \times 3 = 12 )
  • Denominator: ( 1 \times 1 = 1 )
• Result: ( \frac{12}{1} = 12 )

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2. ( 8 \div \frac{3}{4} )

• Write as fractions: ( \frac{8}{1} \div \frac{3}{4} )

• Apply "keep, change, flip":

  • ( \frac{8}{1} \times \frac{4}{3} )

• Multiply across:

  • Numerator: ( 8 \times 4 = 32 )
  • Denominator: ( 1 \times 3 = 3 )

• Result as improper fraction: ( \frac{32}{3} )

• To convert to a mixed number:

  • ( 3 ) goes into ( 32 ) ten times ((3 \times 10 = 30)), remainder (2).
  • So, ( \frac{32}{3} = 10 \frac{2}{3} )

• Alternate breakdown:

  • ( 32 = 30 + 2 )
  • ( \frac{30}{3} = 10 ), so ( 10 + \frac{2}{3} = 10 \frac{2}{3} )

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Summary

• Dividing a whole number by a fraction uses three steps: "keep, change, flip."
• Change the whole number to a fraction, flip the second fraction, multiply across, and convert the answer to a mixed number if necessary.