Class Notes: Multiplying Mixed Numbers

Objective

Learn the steps to multiply two mixed numbers.

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Steps to Multiply Mixed Numbers

1. Convert Mixed Numbers to Improper Fractions

   • Keep the denominator the same.
   • New numerator = (whole number × denominator) + numerator.

2. Multiply the Improper Fractions

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

3. Convert the Result Back to a Mixed Number

   • Divide numerator by denominator to get the whole number part.
   • The remainder becomes the numerator of the fractional part.

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Example 1: Multiply 2 1/3 and 4 2/5

Step 1: Convert to Improper Fractions

• 2 1/3 = (2 × 3) + 1 = 7/3
• 4 2/5 = (4 × 5) + 2 = 22/5

Step 2: Multiply Across

• Numerators: 7 × 22 = 154
• Denominators: 3 × 5 = 15
• Product: 154/15

Step 3: Convert 154/15 to a Mixed Number

• Largest multiple of 15 less than 154 is 150.
• 150 ÷ 15 = 10, remainder 4.
• Mixed Number: 10 4/15

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Example 2: Multiply 3 1/4 and 2 5/6

Step 1: Convert to Improper Fractions

• 3 1/4 = (3 × 4) + 1 = 13/4
• 2 5/6 = (2 × 6) + 5 = 17/6

Step 2: Multiply Across

• Numerators: 13 × 17 = 221
• Denominators: 4 × 6 = 24
• Product: 221/24

Step 3: Convert 221/24 to a Mixed Number

• Largest multiple of 24 less than 221 is 216 (24 × 9).
• 221 - 216 = 5.
• Mixed Number: 9 5/24

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Summary

• Step 1: Convert mixed numbers to improper fractions.
• Step 2: Multiply numerators and denominators.
• Step 3: Convert the improper fraction result to a mixed number.

This method works for any pair of mixed numbers you want to multiply.