Addition and Subtraction of Fractions

Grade 6 · Mathematics

Semester 2 | Period 5 | Week 25

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Subject: Mathematics

Semester: 2

Period: 5

Week: 25

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 25
Lesson Duration: 45 minutes
Week & Period: Week 25, Period 5
Topic: Addition and Subtraction of Fractions
Sub-topic: Proper, Improper, and Mixed Fractions

Learning Objectives
By the end of the lesson, students should be able to:
Define proper, improper, and mixed fractions
Add and subtract fractions with like and unlike denominators
Add and subtract fractions from whole numbers
Solve real-life word problems on addition and subtraction of fractions

Previous Knowledge
Students already know simple operations with whole numbers and basic concept of fractions as part of a whole.

Instructional Materials
Mathematics textbook for Grade 6

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher revises the concept of fractions by asking learners to identify fractions in real life (e.g., half a cake, quarter of a paper). Learners fold papers to show 1/2, 1/3, and 1/4.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definition of Fractions

A fraction is a number that represents a part of a whole. It is written in the form a/b, where:

  • a (numerator) → shows the number of parts taken.
  • b (denominator) → shows the total number of equal parts the whole is divided into.

Types of fractions:

  1. Proper fraction – Numerator is smaller than denominator.
    Example: 3/4, 7/9, 2/5.
    Each is less than 1.
  2. Improper fraction – Numerator is greater than or equal to denominator.
    Example: 9/5, 10/10, 15/8

Each is greater than or equal to 1.

  1. Mixed fraction (or mixed number) – Contains a whole number and a fraction.
    Example: 2 1/3, 4 2/5.

Conversion tip:

  • Mixed → Improper: Multiply the denominator by the whole number, add the numerator, keep denominator.
    Example: 2 1/3=(2×3+1)3=7/3

Addition of Fractions with Like Denominators

Rule: Add the numerators, keep the denominator the same.

Examples:

  1. 3/8+2/8=5/8
  2. 5/12+4/12=9/12=3/4 (simplify).

Addition of Fractions with Unlike Denominators

Rule: Find the Least Common Denominator (LCD/LCM of denominators), convert, then add.

Examples:

  1. 2/3+1/4
    LCM(3,4) = 12 → 8/12+3/12=11/12
  2. 5/6+3/8
    LCM(6,8) = 24 → 20/24+9/24=29/24= 1 5/24.
  3. 7/10+11/15
    LCM(10,15) = 30 → 21/30+22/30=43/30=1 13/30.

 

Subtraction of Fractions

Rule: Same as addition — denominators must be the same.

Examples:

  1. 7/10–3/5
    Convert → 7/10–6/10=1/10
  2. 9/12–2/12=7/12
  3. 3/4–2/9
    LCM(4,9) = 36 → 27/36–8/36=19/36

 

Adding and Subtracting Fractions from Whole Numbers

Convert the whole number to a fraction with the same denominator.

Examples:

  1. 5– 2/3
    Convert: 5=15/3.
    15/3–2/3=13/3=4 1/3.
  2. 3+7/8
    Convert: 3=24/8.
    24/8+7/8=31/8= 3 7/8.
  3. 6–5/4
    Convert: 6=24/4.
    24/4–5/4=19/4=4 3/4.

Word Problem Examples

  1. If a boy ate 3/8 of a cake in the morning and 1/8 in the evening, how much cake did he eat altogether?
    Solution: 3/8+1/8=4/8=1/2.
  2. A farmer used 5/6 of his land for rice and 1/12 for cassava. What fraction of the land did he use altogether?
    Solution: LCM(6,12) = 12 → 10/12+1/12=11/12
  3. A girl had 4 whole oranges. She gave her brother 5/6 of an orange. How many oranges does she have left?
    Solution: 4–5/6=24/6–5/6=19/6=3 1/6.

Learners’ Activities (Expanded)

  • Learners fold papers to create fraction strips for visualizing denominators.
  • In groups, learners solve at least 5 problems each on addition and subtraction (like and unlike denominators).
  • Learners explain their steps aloud to peers.
  • Learners apply fractions to real-life items (e.g., sharing pencils, slicing bread, dividing money).

 

Assessment Checks (Oral & Written)

  1. Solve: 3/5+2/7.
  2. Solve: 2–3/4.
  3. Add: 4/9+5/6.
  4. Subtract: 7/8–3/16.
  5. Word problem: A student reads 2/3 of a book on Monday and 1/6 on Tuesday. What fraction of the book has she read?

Notes (Expanded & Detailed)

  • Fractions represent parts of a whole.
  • To add or subtract fractions, the denominators must be the same.
  • For unlike denominators, use the LCM method.
  • Mixed numbers can be changed to improper fractions to make calculation easier.
  • Always simplify answers to the lowest terms.
  • Fractions are practical in daily life: sharing food, measuring ingredients, dividing money, and calculating time.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reviews types of fractions and methods of addition and subtraction. Learners summarize steps in their own words.

Evaluation Method (Expanded):
Exit slip/quiz: Solve 4/9 + 5/18 and 7/8 – 3/16. Teacher will collect slips and provide oral feedback.

Assignment (Expanded):
Solve: 1 1/2 + 3/4, 2 2/3 – 5/6, 3 + 7/9.

Follow-up Activity:
Practice with fraction strips at home, showing parents their working steps.

Differentiation / Inclusive Strategies
Group weaker learners with stronger ones for peer teaching. Use visual aids like paper folding for learners struggling with abstract concepts.

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