Simple Equations Involving Fractions

Grade 9 · Mathematics

Semester 1 | Period 2 | Week 11

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Subject: Mathematics

Semester: 1

Period: 2

Week: 11

WEEK 11

Class: Grade 9
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Simple Equations Involving Fractions
Focus: Solving Equations Involving Fractions & Word Problems

SPECIFIC OBJECTIVES:

By the end of the lesson, pupils should be able to:

  1. Define simple equations involving fractions.
  2. Solve simple equations involving one variable in fractions.
  3. Apply cross-multiplication and LCM in solving fractional equations.
  4. Translate real-life word problems into fractional equations.
  5. Solve word problems involving fractions in daily life.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Group work and drills
  • Real-life application

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and marker
  • Flashcards with sample equations
  • Worksheets for exercises
  • Chart showing steps for solving fractional equations

 

PERIOD 1 & 2: Solving Simple Equations Involving Fractions

PRESENTATION

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Introduces equations involving fractions, e.g., x/2+3=5

Pupils listen and ask questions.

Step 2 – Explanation

Demonstrates solving by eliminating denominators using LCM or cross-multiplication.

Pupils observe and take notes.

Step 3 – Demonstration

Solves worked examples step by step.

Pupils practice with guidance.

Step 4 – Note Taking

Writes examples on the board.

Pupils copy notes.

 

NOTE ON BOARD:

  • To solve equations involving fractions:
  1. Eliminate the denominator by multiplying through by the LCM.
  2. Simplify the equation.
  3. Solve for the unknown.
  • Example: x/3 + 2=5  ⇒  x+6=15  ⇒  x=9

 

EVALUATION (5 exercises):

  1. Solve: x/2=6.
  2. Solve: y/3+4=10.
  3. Solve: p/5−2=3.
  4. Solve: a/4+7=12.
  5. Solve: m/6−3=5.

 

CLASSWORK (5 questions):

  1. Solve: x/7+2=5.
  2. Solve: y/8−1=3.
  3. Solve: a/9+4=10.
  4. Solve: m/2−5=1.
  5. Solve: p/3+6=12.

 

ASSIGNMENT (5 tasks):

  1. Solve: x/4+3=7.
  2. Solve: y/5−2=6.
  3. Solve: a/10+5=9.
  4. Solve: p/6−4=2.
  5. Solve: m/12+7=15.

PERIOD 3 & 4: Solving More Complex Equations Involving Fractions

PRESENTATION

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Introduces equations with fractions on both sides, e.g., x/2+1=5/3.

Pupils listen.

Step 2 – Explanation

Explains using LCM of denominators to eliminate fractions.

Pupils observe and participate.

Step 3 – Demonstration

Works out examples step by step.

Pupils solve similar problems with guidance.

Step 4 – Note Taking

Writes solved examples on the board.

Pupils copy notes.

 

NOTE ON BOARD:

  • To solve equations with fractions on both sides:
    • Multiply through by the LCM of denominators.
    • Rearrange and simplify.
  • Example: x/2+1=5/3.
    LCM = 6 → 3x+6=10.
      x=4/3.

 

EVALUATION (5 exercises):

  1. Solve: x2/+3=7/2.
  2. Solve: y/3−2=1/6.
  3. Solve: a/4+5=7/2.
  4. Solve: m/5−1=2/5.
  5. Solve: p/6+2=5/3.

 

CLASSWORK (5 questions):

  1. Solve: x/8+3=11/4.
  2. Solve: y/10−1=1/5.
  3. Solve: a/12+4=7/3.
  4. Solve: m/9−2=1/3.
  5. Solve: p/15+5=11/3.

 

ASSIGNMENT (5 tasks):

  1. Solve: x/20+2=3/4.
  2. Solve: y/7−4=2/7.
  3. Solve: a/14+1=5/7.
  4. Solve: m/16−3=5/8.
  5. Solve: p/18+2=10/9.

 

PERIOD 5: Word Problems Leading to Simple Equations Involving Fractions

PRESENTATION

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains how real-life problems can be expressed as fractional equations.

Pupils listen.

Step 2 – Explanation

Gives example: “A number divided by 3 plus 5 equals 9. Find the number.” → x/3+5=9.

Pupils observe.

Step 3 – Demonstration

Solves more word problems involving fractions step by step.

Pupils solve with guidance.

Step 4 – Note Taking

Writes worked examples on the board.

Pupils copy notes.

 

NOTE ON BOARD:

  • Translate word problems into equations.
  • Solve step by step.
  • Example: “A number divided by 4 plus 2 is 6. Find the number.”
    → x/4+2=6.
    → Multiply both sides by 4 → x+8=24.
    → x=16.

 

EVALUATION (5 exercises):

  1. A number divided by 5 plus 3 equals 8. Find the number.
  2. A number divided by 6 minus 2 equals 4. Find the number.
  3. A number divided by 7 plus 4 equals 9. Find the number.
  4. A number divided by 8 minus 5 equals 7. Find the number.
  5. A number divided by 9 plus 6 equals 12. Find the number.

 

CLASSWORK (5 questions):

  1. A number divided by 10 plus 2 equals 7. Find the number.
  2. A number divided by 12 minus 3 equals 5. Find the number.
  3. A number divided by 15 plus 4 equals 9. Find the number.
  4. A number divided by 20 minus 6 equals 8. Find the number.
  5. A number divided by 25 plus 7 equals 12. Find the number.

ASSIGNMENT (5 tasks):

  1. A father’s age divided by 3 plus 10 equals 30. Find the father’s age.
  2. A farmer sold chickens such that the number divided by 4 plus 6 equals 20. Find the number of chickens.
  3. A number divided by 5 minus 3 equals 9. Find the number.
  4. The sum of a number divided by 2 and 7 equals 15. Find the number.
  5. Create one word problem that can be solved using equations involving fractions.