Adding and subtracting proper and improper fractions for Primary 4

Class: Primary Four
Term: First Term
Week: 8
Age: 9 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Basic Operations
Focal competence: Adding and subtracting proper, improper and mixed fractions
Key competencies/values: Communication; Critical Thinking and Problem Solving; ICT and Digital Competencies
Skills:

• Identifying fraction types
• Identifying common and uncommon denominators
• Finding the Lowest Common Multiple (LCM) of simple numbers
• Finding equivalent fractions
• Using fraction charts or counting blocks to add and subtract fractions
• Adding and subtracting fractions with common denominators
• Adding and subtracting fractions with uncommon denominators
• Simplifying fraction answers where necessary

Previous Lesson: Addition and subtraction of whole numbers
Topic: Addition And Subtraction Of Fractions
Subject Matter: Adding and subtracting proper and improper fractions with common and uncommon denominators

Specific Objectives

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

Cognitive Domain

• Identify proper and improper fractions.
• State the meaning of numerator and denominator.
• Differentiate between fractions with common denominators and fractions with uncommon denominators.
• Perform addition of proper and improper fractions with common denominators.
• Perform subtraction of proper and improper fractions with common denominators.
• Find the Lowest Common Multiple (LCM) of two simple denominators.
• Change fractions with uncommon denominators to equivalent fractions with a common denominator.
• Add proper and improper fractions with uncommon denominators.
• Subtract proper and improper fractions with uncommon denominators.
• Simplify fraction answers where necessary.
• Convert simple improper fraction answers to mixed numbers where necessary.

Affective Domain

• Show enthusiasm while solving fraction problems.
• Appreciate the importance of fractions in everyday life.
• Show patience and accuracy when solving fraction problems involving more than one step.

Psychomotor Domain

• Use fraction charts, strips or blocks to model fraction addition and subtraction.
• Use multiplication facts to find common multiples.
• Accurately write the steps involved in solving fraction problems.

Social Domain

• Collaborate with peers to solve guided fraction examples.
• Explain the steps used in solving a fraction problem to classmates.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• Primary 4 Mathematics Textbook
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Fraction charts
• Fraction strips
• Fraction blocks or counting blocks
• Flash cards showing different fractions
• Cardboard cut-outs representing fractions
• Number cards
• Multiplication chart
• LCM chart

Rationale for the Lesson

This lesson helps pupils build a strong understanding of fractions and prepares them for more advanced mathematical operations. Addition and subtraction of fractions are useful in everyday situations involving sharing, measuring, cooking, time and quantities. Pupils first build confidence with fractions that have the same denominator before learning how to work with fractions whose denominators are different. Learning to find a common denominator also strengthens pupils’ understanding of multiplication, multiples, equivalent fractions and numerical reasoning.

Prerequisite/Previous Knowledge

Pupils should have a basic understanding of fractions, be able to identify the numerator and denominator, distinguish between proper and improper fractions, perform simple addition and subtraction of whole numbers, and list simple multiples of numbers.

Lesson Content/Board Summary

Addition And Subtraction Of Fractions

Understanding Fractions: Numerator and Denominator

A fraction represents a part of a whole. It has two main parts:

1. Numerator: The top number in a fraction. It tells us how many parts are being considered.
2. Denominator: The bottom number in a fraction. It tells us the total number of equal parts into which the whole is divided.

For example, in the fraction \( \frac{2}{3} \):

• The numerator is 2.
• The denominator is 3.

Types of Fractions

1. Proper Fraction: A fraction whose numerator is smaller than its denominator.
   Examples: \( \frac{1}{2}, \frac{3}{4}, \frac{2}{7} \)
2. Improper Fraction: A fraction whose numerator is equal to or greater than its denominator.
   Examples: \( \frac{5}{3}, \frac{7}{4}, \frac{8}{8} \)

Fractions With Common Denominators

Fractions have a common denominator when their denominators are the same.

Examples:

• \( \frac{2}{7} \) and \( \frac{3}{7} \)
• \( \frac{5}{8} \) and \( \frac{1}{8} \)
• \( \frac{7}{10} \) and \( \frac{3}{10} \)

Adding Fractions with Common Denominators

To add fractions with the same denominator:

1. Add the numerators.
2. Keep the denominator the same.
3. Simplify the answer where necessary.

Example 1: Adding Proper Fractions

Question: Add \( \frac{2}{7} + \frac{3}{7} \)

Solution:

The denominators are already the same.

\[
\frac{2}{7}+\frac{3}{7}
=
\frac{2+3}{7}
=
\frac{5}{7}
\]

Answer: \( \frac{5}{7} \)

Example 2: Adding Improper Fractions

Question: Add \( \frac{5}{4}+\frac{2}{4} \)

Solution:

\[
\frac{5}{4}+\frac{2}{4}
=
\frac{5+2}{4}
=
\frac{7}{4}
\]

The improper fraction can also be written as:

\[
\frac{7}{4}=1\frac{3}{4}
\]

Answer: \( \frac{7}{4} \) or \( 1\frac{3}{4} \)

Subtracting Fractions with Common Denominators

To subtract fractions with the same denominator:

1. Subtract the numerators.
2. Keep the denominator the same.
3. Simplify the answer where necessary.

Example 1: Subtracting Proper Fractions

Question: Subtract \( \frac{3}{8} \) from \( \frac{7}{8} \).

Solution:

\[
\frac{7}{8}-\frac{3}{8}
=
\frac{7-3}{8}
=
\frac{4}{8}
\]

Simplify:

\[
\frac{4}{8}=\frac{1}{2}
\]

Answer: \( \frac{1}{2} \)

Example 2: Subtracting Improper Fractions

Question: Subtract \( \frac{3}{5} \) from \( \frac{9}{5} \).

Solution:

\[
\frac{9}{5}-\frac{3}{5}
=
\frac{9-3}{5}
=
\frac{6}{5}
\]

\[
\frac{6}{5}=1\frac{1}{5}
\]

Answer: \( \frac{6}{5} \) or \( 1\frac{1}{5} \)

Fractions With Uncommon Denominators

Fractions have uncommon or unlike denominators when their denominators are different.

Examples:

• \( \frac{1}{2} \) and \( \frac{1}{3} \)
• \( \frac{2}{3} \) and \( \frac{3}{4} \)
• \( \frac{5}{6} \) and \( \frac{1}{4} \)

Fractions with uncommon denominators cannot be added or subtracted directly. We first change them to equivalent fractions that have the same denominator.

Equivalent Fractions

Equivalent fractions are fractions that have the same value even though they are written with different numerators and denominators.

For example:

\[
\frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{4}{8}
\]

To form an equivalent fraction, multiply both the numerator and denominator by the same number.

For example:

\[
\frac{1}{3}\times\frac{2}{2}=\frac{2}{6}
\]

Therefore:

\[
\frac{1}{3}=\frac{2}{6}
\]

Finding the Lowest Common Multiple (LCM)

The Lowest Common Multiple is the smallest number that is a multiple of two or more given numbers.

We can use the LCM of two denominators as their common denominator.

Example: Find the LCM of 3 and 4

Multiples of 3 are:

3, 6, 9, 12, 15, 18, …

Multiples of 4 are:

4, 8, 12, 16, 20, …

The smallest number found in both lists is 12.

LCM of 3 and 4 = 12.

Adding Fractions With Uncommon Denominators

To add fractions with uncommon denominators:

1. Look at the denominators.
2. Find the LCM of the denominators.
3. Use the LCM as the common denominator.
4. Change each fraction to an equivalent fraction having the common denominator.
5. Add the numerators.
6. Keep the common denominator.
7. Simplify the answer where necessary.

Example 1: \( \frac{1}{2}+\frac{1}{3} \)

Question: Add \( \frac{1}{2}+\frac{1}{3} \).

Solution:

Step 1: The denominators are 2 and 3.

Step 2: Find their LCM.

Multiples of 2: 2, 4, 6, 8, …

Multiples of 3: 3, 6, 9, …

Therefore:

LCM of 2 and 3 = 6.

Step 3: Change both fractions to sixths.

For \( \frac{1}{2} \):

\[
\frac{1}{2}
=
\frac{1\times3}{2\times3}
=
\frac{3}{6}
\]

For \( \frac{1}{3} \):

\[
\frac{1}{3}
=
\frac{1\times2}{3\times2}
=
\frac{2}{6}
\]

Step 4: Add the equivalent fractions.

\[
\frac{3}{6}+\frac{2}{6}
=
\frac{5}{6}
\]

Answer: \( \frac{5}{6} \)

Example 2: \( \frac{2}{3}+\frac{3}{4} \)

Question: Add \( \frac{2}{3}+\frac{3}{4} \).

Solution:

The denominators are 3 and 4.

LCM of 3 and 4 = 12.

Change \( \frac{2}{3} \) to twelfths:

\[
\frac{2}{3}
=
\frac{2\times4}{3\times4}
=
\frac{8}{12}
\]

Change \( \frac{3}{4} \) to twelfths:

\[
\frac{3}{4}
=
\frac{3\times3}{4\times3}
=
\frac{9}{12}
\]

Now add:

\[
\frac{8}{12}+\frac{9}{12}
=
\frac{17}{12}
\]

Convert the improper fraction to a mixed number:

\[
\frac{17}{12}=1\frac{5}{12}
\]

Answer: \( \frac{17}{12} \) or \( 1\frac{5}{12} \)

Example 3: Adding Improper Fractions With Uncommon Denominators

Question: Add \( \frac{5}{3}+\frac{7}{6} \).

Solution:

The denominators are 3 and 6.

LCM of 3 and 6 = 6.

\[
\frac{5}{3}
=
\frac{5\times2}{3\times2}
=
\frac{10}{6}
\]

\( \frac{7}{6} \) already has denominator 6.

Therefore:

\[
\frac{10}{6}+\frac{7}{6}
=
\frac{17}{6}
\]

Convert to a mixed number:

\[
\frac{17}{6}=2\frac{5}{6}
\]

Answer: \( \frac{17}{6} \) or \( 2\frac{5}{6} \)

Subtracting Fractions With Uncommon Denominators

To subtract fractions with uncommon denominators:

1. Look at the denominators.
2. Find the LCM of the denominators.
3. Use the LCM as the common denominator.
4. Change each fraction to an equivalent fraction having the common denominator.
5. Subtract the numerators.
6. Keep the common denominator.
7. Simplify the answer where necessary.

Example 1: \( \frac{5}{6}-\frac{1}{4} \)

Question: Subtract \( \frac{1}{4} \) from \( \frac{5}{6} \).

Solution:

The denominators are 6 and 4.

Multiples of 6: 6, 12, 18, …

Multiples of 4: 4, 8, 12, 16, …

LCM of 6 and 4 = 12.

Change \( \frac{5}{6} \) to twelfths:

\[
\frac{5}{6}
=
\frac{5\times2}{6\times2}
=
\frac{10}{12}
\]

Change \( \frac{1}{4} \) to twelfths:

\[
\frac{1}{4}
=
\frac{1\times3}{4\times3}
=
\frac{3}{12}
\]

Now subtract:

\[
\frac{10}{12}-\frac{3}{12}
=
\frac{7}{12}
\]

Answer: \( \frac{7}{12} \)

Example 2: \( \frac{7}{8}-\frac{1}{3} \)

Question: Subtract \( \frac{1}{3} \) from \( \frac{7}{8} \).

Solution:

The denominators are 8 and 3.

LCM of 8 and 3 = 24.

\[
\frac{7}{8}
=
\frac{7\times3}{8\times3}
=
\frac{21}{24}
\]

\[
\frac{1}{3}
=
\frac{1\times8}{3\times8}
=
\frac{8}{24}
\]

Therefore:

\[
\frac{21}{24}-\frac{8}{24}
=
\frac{13}{24}
\]

Answer: \( \frac{13}{24} \)

Example 3: Subtracting Improper Fractions With Uncommon Denominators

Question: Subtract \( \frac{3}{4} \) from \( \frac{11}{6} \).

Solution:

The denominators are 6 and 4.

LCM of 6 and 4 = 12.

\[
\frac{11}{6}
=
\frac{11\times2}{6\times2}
=
\frac{22}{12}
\]

\[
\frac{3}{4}
=
\frac{3\times3}{4\times3}
=
\frac{9}{12}
\]

Subtract:

\[
\frac{22}{12}-\frac{9}{12}
=
\frac{13}{12}
\]

Convert to a mixed number:

\[
\frac{13}{12}=1\frac{1}{12}
\]

Answer: \( \frac{13}{12} \) or \( 1\frac{1}{12} \)

Simplifying Fraction Answers

A fraction should be simplified to its lowest terms where possible.

For example:

\[
\frac{2}{8}+\frac{4}{8}
=
\frac{6}{8}
\]

Both 6 and 8 can be divided by 2:

\[
\frac{6\div2}{8\div2}
=
\frac{3}{4}
\]

Answer: \( \frac{3}{4} \)

Important Rules

• If the denominators are the same, add or subtract the numerators and keep the denominator.
• Do not add or subtract the denominators.
• If the denominators are different, first find a common denominator.
• The LCM of the denominators can be used as the common denominator.
• When forming an equivalent fraction, whatever number multiplies the denominator must also multiply the numerator.
• After adding or subtracting, simplify the answer where possible.
• Convert an improper fraction to a mixed number where required.

Common Error to Avoid

It is wrong to add the numerator and denominator separately.

For example:

\[
\frac{1}{2}+\frac{1}{3}\neq\frac{2}{5}
\]

The correct method is:

\[
\frac{1}{2}+\frac{1}{3}
=
\frac{3}{6}+\frac{2}{6}
=
\frac{5}{6}
\]

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Cooperative Learning, Problem Solving, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 4 minutes

Teaching Skill: Recalling/Questioning

Teacher’s Activity: The teacher asks pupils to recall the meaning of a fraction and identify the numerator and denominator in fractions such as \( \frac{1}{2} \), \( \frac{3}{4} \) and \( \frac{5}{3} \). The teacher also asks pupils to distinguish between proper and improper fractions.

Pupils’ Activity: Pupils respond to the questions and identify the different parts and types of fractions.

Learning Point: Recall of fraction concepts

Step 2: Revision of Addition and Subtraction With Common Denominators

Time: 5 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher revises \( \frac{2}{7}+\frac{3}{7} \) and \( \frac{7}{8}-\frac{3}{8} \). The teacher reminds pupils that when the denominators are the same, only the numerators are added or subtracted.

Pupils’ Activity: Pupils solve the examples with the teacher and explain why the denominator remains unchanged.

Learning Point: Operations involving common denominators

Step 3: Introducing Uncommon Denominators

Time: 5 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher displays \( \frac{1}{2} \) and \( \frac{1}{3} \) using fraction strips or diagrams. The teacher shows that halves and thirds represent differently sized parts and therefore cannot be added directly. The teacher introduces the idea of changing the fractions to equivalent fractions with the same denominator.

Pupils’ Activity: Pupils observe the fraction strips and compare the sizes of halves and thirds.

Learning Point: Meaning of uncommon denominators

Step 4: Finding the LCM of Denominators

Time: 6 minutes

Teaching Skill: Explanation/Guided Discovery

Teacher’s Activity: The teacher demonstrates how to list multiples to find the LCM of simple pairs such as 2 and 3, 3 and 4, and 4 and 6. The teacher explains that the LCM can be used as the common denominator.

Pupils’ Activity: Pupils list multiples and identify the first common multiple.

Learning Point: Finding the Lowest Common Multiple

Step 5: Adding Fractions With Uncommon Denominators

Time: 7 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher demonstrates \( \frac{1}{2}+\frac{1}{3} \), guiding pupils to find the LCM, change the fractions to equivalent fractions and add. The teacher gives \( \frac{2}{3}+\frac{3}{4} \) as another guided example.

Pupils’ Activity: Pupils find the LCM, convert the fractions and add the numerators.

Learning Point: Adding fractions with uncommon denominators

Step 6: Subtracting Fractions With Uncommon Denominators

Time: 7 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher demonstrates \( \frac{5}{6}-\frac{1}{4} \). Pupils are guided to find the LCM of 6 and 4, convert both fractions to twelfths and then subtract.

Pupils’ Activity: Pupils follow the steps and solve another example such as \( \frac{7}{8}-\frac{1}{3} \).

Learning Point: Subtracting fractions with uncommon denominators

Step 7: Guided Practice

Time: 4 minutes

Teaching Skill: Problem Solving/Guided Practice

Teacher’s Activity: The teacher gives pupils the following examples:

1. \( \frac{2}{5}+\frac{1}{5} \)
2. \( \frac{1}{2}+\frac{1}{4} \)
3. \( \frac{5}{6}-\frac{1}{3} \)
4. \( \frac{3}{4}+\frac{2}{3} \)

Pupils’ Activity: Pupils solve the problems individually or in pairs and show their working.

Learning Point: Choosing the correct method according to the denominators

Step 8: Evaluation/Review

Time: 4 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates learning by asking the following questions:

1. What is a proper fraction?
2. What is meant by a common denominator?
3. What is meant by an uncommon denominator?
4. Add \( \frac{1}{5}+\frac{3}{5} \).
5. Subtract \( \frac{6}{9}-\frac{2}{9} \).
6. Find the LCM of 3 and 4.
7. Add \( \frac{1}{3}+\frac{1}{4} \).
8. Subtract \( \frac{5}{6}-\frac{1}{4} \).
9. Add \( \frac{5}{3}+\frac{1}{6} \).
10. Explain why \( \frac{1}{2}+\frac{1}{3} \) is not \( \frac{2}{5} \).

Pupils’ Activity: Pupils answer orally and in writing and show the necessary steps.

Learning Point: Assessment of fraction addition and subtraction

Step 9: Note-Taking

Time: 2 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils to copy the essential Board Summary, especially the rules for common and uncommon denominators.

Pupils’ Activity: Pupils copy the notes carefully into their notebooks.

Learning Point: Recording lesson notes

Step 10: Conclusion

Time: 1 minute

Teaching Skill: Reinforcement

Teacher’s Activity: The teacher reminds pupils that fractions with the same denominator can be added or subtracted directly, while fractions with different denominators must first be changed to equivalent fractions with a common denominator.

Pupils’ Activity: Pupils repeat the main rules.

Learning Point: Fraction operation summary

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following problems in your Mathematics notebook. Show your working clearly.

1. \( \frac{4}{10}+\frac{3}{10} \)
2. \( \frac{9}{12}-\frac{5}{12} \)
3. \( \frac{1}{2}+\frac{1}{4} \)
4. \( \frac{2}{3}+\frac{1}{6} \)
5. \( \frac{5}{6}-\frac{1}{3} \)
6. \( \frac{7}{8}-\frac{1}{4} \)
7. \( \frac{3}{5}+\frac{2}{3} \)
8. \( \frac{11}{6}-\frac{3}{4} \)
9. \( \frac{5}{4}+\frac{2}{3} \)
10. Draw a diagram to show why \( \frac{1}{2}+\frac{1}{4}=\frac{3}{4} \).

Lesson Keywords

• Fraction – A part of a whole.
• Numerator – The top number of a fraction, showing how many parts are taken.
• Denominator – The bottom number of a fraction, showing the total number of equal parts.
• Proper Fraction – A fraction whose numerator is smaller than its denominator.
• Improper Fraction – A fraction whose numerator is equal to or greater than its denominator.
• Common Denominator – When two or more fractions have the same denominator.
• Uncommon Denominators – Denominators that are different.
• Equivalent Fractions – Fractions that have the same value even though they have different numerators and denominators.
• Multiple – A number obtained by multiplying another number by a whole number.
• Lowest Common Multiple (LCM) – The smallest number that is a multiple of two or more given numbers.
• Simplify – To write a fraction in its lowest equivalent form.

Differentiation

Support for weaker learners: Begin with fractions that already have common denominators before moving to uncommon denominators. Use fraction strips, diagrams or physical fraction blocks. When introducing uncommon denominators, start with simple pairs where one denominator is a multiple of the other, such as \( \frac{1}{2}+\frac{1}{4} \) or \( \frac{1}{3}+\frac{1}{6} \). Allow pupils to use a multiplication chart when finding the LCM. Guide them through the sequence: check the denominators, find the LCM if necessary, change to equivalent fractions, add or subtract, then simplify.

Extension for faster learners: Challenge pupils with improper fractions, larger denominators, three fractions and answers requiring simplification or conversion to mixed numbers. Examples include \( \frac{2}{3}+\frac{5}{8} \), \( \frac{7}{4}-\frac{2}{3} \), and \( \frac{1}{2}+\frac{1}{3}+\frac{1}{6} \).

Suggested Lesson Videos

For further understanding, search on YouTube for: “Adding and subtracting fractions with unlike denominators for kids”, “LCM for adding fractions”, “Equivalent fractions for kids” or “Adding and subtracting fractions for Primary 4”.