Multiplication and Division of Fractions

Grade 6 · Mathematics

Semester 2 | Period 5 | Week 26

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Subject: Mathematics

Semester: 2

Period: 5

Week: 26

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 26
Lesson Duration: 45 minutes
Week & Period: Week 26, Period 5
Topic: Multiplication and Division of Fractions
Sub-topic: Proper, Improper, and Mixed Fractions

Learning Objectives
By the end of the lesson, students should be able to:
Multiply fractions correctly
Divide fractions using reciprocal rule
Simplify answers to lowest terms
Apply multiplication and division of fractions to real-life problems

Previous Knowledge
Students already know how to add and subtract fractions and can simplify fractions.

Instructional Materials
Mathematics textbook for Grade 6

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: What is 1/2 of 10? Learners respond: 5. Teacher introduces multiplication of fractions.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definitions and Rules

  1. Multiplication of Fractions
  • To multiply fractions:
    Multiply the numerators together and multiply the denominators together.
    Result is simplified if possible.

Formula:

a/b×c/d=(a×c)/(b×d)

Example:

2/3×3/4=6/12=1/2

  1. Multiplication of a Whole Number by a Fraction
  • Write the whole number as a fraction over 1.

3×2/5=3/1×2/5=6/5=1 1/5

  1. Division of Fractions
  • To divide fractions:
    Change division to multiplication and take the reciprocal (invert numerator and denominator) of the divisor.

Formula:

a/b÷c/d=a/b×d/c

Example:

3/4÷2/5=3/4×5/2=15/8=1 7/8

  1. Reciprocal
  • The reciprocal of a fraction is obtained by swapping numerator and denominator.
    Example: Reciprocal of 3/5 is 5/3.
  • Every number multiplied by its reciprocal equals 1.
  1. Simplification
  • Always express fractions in their lowest terms (divide numerator and denominator by their Greatest Common Factor).
    Example: 12/20=3/5.

Worked Examples

Multiplication of Fractions

  1. 5/6×2/9=10/54=5/27
  2. 7/8×4/21=28/168=1/6
  3. 9/10×15/18=135/180=3/4

Multiplication with Whole Numbers

  1. 6×5/12=30/12=5/2=2 1/2
  2. 9×3/7=27/7=3 6/7

Division of Fractions

  1. 5/6÷2/3=5/6×3/2=15/12=5/4=1 1/4
  2. 7/9÷14/27=7/9×27/14=189/126=3/2
  3. 4÷2/3=4/1×3/2=12/2=6

 

Word Problem Examples

  1. A recipe needs 2/3 of a cup of sugar. If 4 such recipes are made, how much sugar is needed?

4×2/3=8/3=2 2/3 cups

  1. A farmer has 3/4 hectare of land. He divides it equally among 3 sons. How much does each get?

3/4÷3=3/4×1/3=3/12=1/4

  1. A water tank is 5/6 full. If half of the water is used, what fraction of the tank is still full?

5/6×1/2=5/12

  1. A bag of flour weighing 7/8 kg is shared equally among 4 people. How much does each person get?

7/8÷4=7/8×1/4=7/32 kg

Learners’ Activities (Expanded)

  • Learners practice multiplying and dividing fractions in pairs on the chalkboard.
  • Learners demonstrate the reciprocal rule by flipping cards with numerator and denominator.
  • Learners solve at least 5 word problems in groups (teacher provides different contexts: food sharing, land division, money, cooking).
  • Learners use real-life objects (like oranges, paper strips, or water in bottles) to model multiplication and division of fractions.

 

Assessment Checks

  1. Solve: 2/7×3/5.
  2. Solve: 4÷2/3.
  3. Solve: 3/8÷1/4.
  4. Simplify: 6/10×15/18.
  5. Word Problem: A student drinks 3/5 litre of juice each day. How much will she drink in 7 days?

 

Notes (Expanded & Detailed)

  • Multiplication of fractions is simple: numerator × numerator, denominator × denominator.
  • Division of fractions uses reciprocals: invert the second fraction and multiply.
  • Whole numbers can be written as fractions over 1 for easy calculation.
  • Always simplify answers and convert improper fractions to mixed numbers where necessary.
  • Applications in daily life: cooking, sharing food, dividing land, construction, and finance.
  • Understanding fractions helps in higher mathematics, especially ratios, percentages, algebra, and probability.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Multiplication and division of fractions involve simple rules. Reciprocals are important in division.

Evaluation Method (Expanded):
Exit slip/quiz: Solve 5/6 × 3/4 and 2/5 ÷ 7/10. Teacher will collect slips and provide oral feedback.

Assignment (Expanded):
Multiply: 3/4 × 5/6, 2 × 7/8. Divide: 4/9 ÷ 2/3, 7/10 ÷ 1/5.

Follow-up Activity:
Learners try scaling up or down recipes at home using fractional quantities.

Differentiation / Inclusive Strategies
Practical, real-life examples for learners who struggle with abstract fractions. Peer explanations encouraged.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low