Class Notes: Multiplying Fractions and Whole Numbers

Objective

Learn how to multiply fractions by whole numbers and convert improper fractions to mixed numbers.

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Steps to Multiply Fractions by Whole Numbers

1. Rewrite the whole number as a fraction (put it over 1).
2. Multiply numerators together.
3. Multiply denominators together.
4. Simplify the resulting fraction if needed.
5. Convert the improper fraction to a mixed number (optional).

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Example Problems

Example 1

• Problem: ( \frac{2}{3} \times 9 )
• Solution:
  • Rewrite 9 as ( \frac{9}{1} )
  • Multiply across: ( 2 \times 9 = 18 ), ( 3 \times 1 = 3 )
  • ( \frac{18}{3} = 6 )

Example 2

• Problem: ( 15 \times \frac{4}{5} )
• Solution:
  • Rewrite 15 as ( \frac{15}{1} )
  • Multiply across: ( 15 \times 4 = 60 ), ( 1 \times 5 = 5 )
  • ( \frac{60}{5} = 12 )

Example 3

• Problem: ( 7 \times \frac{2}{3} )
• Solution:
  • Rewrite 7 as ( \frac{7}{1} )
  • Multiply across: ( 7 \times 2 = 14 ), ( 1 \times 3 = 3 )
  • ( \frac{14}{3} ) (improper fraction)
  • To convert to mixed number:
    • ( \frac{14}{3} = \frac{12}{3} + \frac{2}{3} = 4 + \frac{2}{3} = 4 \frac{2}{3} )

Example 4

• Problem: ( 8 \times \frac{4}{5} )
• Solution:
  • Rewrite 8 as ( \frac{8}{1} )
  • Multiply across: ( 8 \times 4 = 32 ), ( 1 \times 5 = 5 )
  • ( \frac{32}{5} ) (improper fraction)
  • To convert to mixed number:
    • 5 goes into 32 six times (( 5 \times 6 = 30 )), remainder 2
    • ( \frac{32}{5} = 6 \frac{2}{5} )
    • Alternate method: ( \frac{30}{5} + \frac{2}{5} = 6 + \frac{2}{5} = 6 \frac{2}{5} )

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Additional Tip

• For more examples on converting improper fractions to mixed numbers, search "improper fraction to mixed number organic chemistry tutor" on YouTube.

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Summary

• Always write whole numbers as fractions before multiplying by another fraction.
• Multiply numerators and denominators directly.
• Simplify where possible.
• To convert an improper fraction to a mixed number, see how many times the denominator fits into the numerator, write the result as the whole number, and express the remainder as a fraction.