Mathematics 6 Term 1 Week 8: Division of Fractions

Main Ideas / Lessons Conveyed

• Division of fractions answers “how many groups of the divisor fit into the dividend.”
• Dividing by a fraction makes the result larger because dividing by a quantity smaller than 1 is the same as multiplying by its reciprocal (which is greater than 1).
• A key prerequisite skill is multiplying fractions, including its relationship to division of fractions.
• The core method for dividing fractions is Keep, Change, Flip:
  • Keep the first number (dividend)
  • Change ÷ into multiplication (×)
  • Flip the second number (divisor) using its reciprocal
  • Multiply and simplify
• Mixed numbers require an extra step: convert them to improper fractions first.
• Answers must be simplified and written in simplest form.
• Real-life connections include:
  • fair sharing
  • measuring/packing
  • cutting/partitioning materials

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Methodology: Keep, Change, Flip

A) Dividing (general case): fraction(s) and/or whole numbers

Use when you have (fraction or whole number) ÷ (fraction or whole number).

• Keep the dividend (the first number).
• Change “÷” into multiplication (so division becomes ×).
• Flip the divisor by finding its reciprocal:
  • Reciprocal of ( \frac{a}{b} ) is ( \frac{b}{a} )
  • A whole number ( n ) can be written as ( \frac{n}{1} ), so its reciprocal is ( \frac{1}{n} )
• Multiply the fractions (or whole-number-as-fractions).
• Simplify the result if possible (cancel common factors, reduce fractions).

B) Reciprocals (what “flip” means)

• Swap numerator and denominator:
  • ( \frac{1}{2} \rightarrow \frac{2}{1} )
  • ( \frac{3}{4} \rightarrow \frac{4}{3} )
• Examples:
  • reciprocal of ( \frac{2}{5} ) is ( \frac{5}{2} )
  • reciprocal of ( \frac{7}{3} ) is ( \frac{3}{7} )

C) Mixed numbers (extra step)

Before applying Keep-Change-Flip:

1. Convert each mixed number to an improper fraction:
   • ( a\ \frac{b}{c} = \frac{ac+b}{c} )
2. Then proceed with:
   • Keep (dividend)
   • Change ÷ to ×
   • Flip divisor (reciprocal)
   • Multiply
   • Simplify

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Examples Used to Illustrate the Method

• Chocolate bars problem

  • ( 4 \div \frac{1}{2} )
  • Becomes ( 4 \times \frac{2}{1} = 8 )
  • Meaning: 8 half-sized pieces from 4 whole bars

• Packing prawns

  • ( 3 \div \frac{3}{4} )
  • Flip by multiplying: ( 3 \times \frac{4}{3} = 4 )
  • Meaning: 4 bags of ( \frac{3}{4} ) kg from 3 kg

• Whole number divided by a fraction

  • ( 56 \div 5 ) (taught as whole number written with denominator 1)
  • ( 56 \div \frac{5}{1} = 56 \times \frac{1}{5} = 16 )

• Fraction divided by a fraction

  • ( \frac{4}{5} \div \frac{1}{10} )
  • ( \frac{4}{5} \times \frac{10}{1} ), simplify to get 8

• Another fraction divided by a whole number/fraction

  • ( \frac{1}{3} \div 16 )
  • Worked as flipping 16 effectively to ( \frac{1}{16} ), giving 2

• Mixed numbers

  • Example: ( 18 \div (1\ \frac{1}{2}) )
    • Convert: ( 1\ \frac{1}{2} = \frac{3}{2} )
    • ( 18 \times \frac{2}{3} = 12 )
  • Example: ( (2\ \frac{1}{2}) \div (1\ \frac{1}{2}) )
    • Convert to improper fractions:
      • ( 2\ \frac{1}{2} = \frac{5}{2} ), ( 1\ \frac{1}{2} = \frac{3}{2} )
    • Compute, then convert the result back to a mixed number (as needed)

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Common Mistakes to Avoid

1. Flipping the wrong number
   • Only the divisor (the second number) gets flipped.
2. Forgetting to change ÷ to ×
   • If you flip the divisor (reciprocal), you must also change division to multiplication.
3. Forgetting to convert mixed numbers
   • Mixed numbers must be converted to improper fractions before Keep-Change-Flip.
4. Forgetting to simplify
   • Reduce the final answer to simplest form.

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Real-Life / Fairness Applications Emphasized

• Fair sharing: dividing cake/resources equally so each person receives the same portion
• Measuring/packing: determining how many packets/bags can be made from given amounts
• Cutting materials: finding how many equal fractional pieces can be produced

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Speaker(s) / Sources Featured

• Mrs. Reyes (chocolate bars example)
• Mrs. Wong (packing prawns example)
• Aling Leoni (potato packets example)
• Jeremy (sugar bags example)
• Ailing Leoni / Aling Leone (same name appears with slight subtitle variation; used in mixed number examples)
• Janette (fairness/sharing example)