Class Notes: Converting Improper Fractions to Mixed Numbers Using Long Division

Objective

Learn how to convert an improper fraction to a mixed number using long division.

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Steps to Convert an Improper Fraction to a Mixed Number

1. Divide the numerator by the denominator using long division.
2. Write the quotient as the whole number part of the mixed number.
3. The denominator remains the same as the original fraction.
4. The remainder becomes the numerator of the fractional part.

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Example 1: 7/2

• Divide 7 by 2:
  • 2 goes into 7 3 times (2 × 3 = 6)
  • Remainder: 7 - 6 = 1
• Mixed number: 3 1/2

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Example 2: 14/3

• Divide 14 by 3:
  • 3 goes into 14 4 times (3 × 4 = 12)
  • Remainder: 14 - 12 = 2
• Mixed number: 4 2/3

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Example 3: 33/5

• Divide 33 by 5:
  • 5 goes into 33 6 times (5 × 6 = 30)
  • Remainder: 33 - 30 = 3
• Mixed number: 6 3/5
• To check: (6 × 5) + 3 = 33

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Example 4: 35/8

• Divide 35 by 8:
  • 8 goes into 35 4 times (8 × 4 = 32)
  • Remainder: 35 - 32 = 3
• Mixed number: 4 3/8
• To check: (4 × 8) + 3 = 35

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Key Points

• Quotient = whole number part
• Remainder = numerator of the fraction
• Denominator stays the same

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Practice: Try converting the following improper fractions:

• 33/5
• 35/8

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Note

A separate video explains how to convert improper fractions to mixed numbers without using long division.