Fractions: Improper Fractions and Mixed Numbers

Introduction

• Improper Fraction: The numerator is greater than the denominator (e.g., ( \frac{8}{5} )).
• Mixed Number: A way to express improper fractions by stating the number of whole parts and the fractional part left over (e.g., ( 1 \frac{3}{5} )).
• Conversions between improper fractions and mixed numbers are often required in exams.

Understanding Improper Fractions

• Example: ( \frac{8}{5} ) means you have eight-fifths of a shape.
  • Divide a shape into 5 equal parts (fifths) and take 8 of those parts.
  • Similar process for ( \frac{7}{3} ), divide into thirds and take 7 parts.

Converting Improper Fractions to Mixed Numbers

• Process: Divide the numerator by the denominator.

  Example 1:

  • ( \frac{9}{4} ):
    • Divide 9 by 4 = 2 remainder 1.
    • Mixed number = 2 wholes and ( \frac{1}{4} ).

  Example 2:

  • ( \frac{23}{6} ):
    • Divide 23 by 6 = 3 remainder 5.
    • Mixed number = 3 and ( \frac{5}{6} ).

Converting Mixed Numbers to Improper Fractions

• Process:

  1. Multiply the whole number by the denominator.
  2. Add the product to the numerator of the fractional part.

  Example 1:

  • Mixed number ( 2 \frac{4}{7} ):
    • Multiply 2 by 7 = 14.
    • Add 14 to 4, giving ( \frac{18}{7} ).

  Example 2:

  • Mixed number ( 3 \frac{3}{5} ):
    • Multiply 3 by 5 = 15.
    • Add 15 to 3, giving ( \frac{18}{5} ).

Conclusion

• Understanding and converting between improper fractions and mixed numbers is essential for exams.
• Practice these conversions to become proficient.

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