Addition and Subtraction of Fractions Mathematics JSS 1 First Term Lesson Notes Week 8

Subject: Mathematics
Class: JSS 1
Term: First Term
Week: 8
Age: 12 years
Topic: Addition and Subtraction of Fractions
Duration: 40 minutes

Behavioural Objectives

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

1. Add fractions with the same and different denominators.
2. Subtract fractions with the same and different denominators.

Keywords

Addition, Subtraction, Fractions, Common Denominator, Simplification

Set Induction

Start with a discussion on combining parts of a whole, like adding pieces of a pizza or subtracting portions from a set, to introduce the concepts of fraction addition and subtraction.

Entry Behaviour

Students should understand basic fraction concepts and how to find a common denominator.

Learning Resources and Materials

1. Fraction strips or visual aids
2. Whiteboard and markers
3. Worksheets with fraction problems
4. Calculators

Building Background/Connection to Prior Knowledge

Students should recall previous work on fraction equivalence and common denominators.

Embedded Core Skills

1. Numerical operations
2. Problem-solving
3. Critical thinking

Content

1. Addition of Fractions with the Same Denominator:
   • Add the numerators and keep the denominator the same.
   • Example: 2/7 + 3/7 = 5/7.
2. Addition of Fractions with Different Denominators:
   • Find a common denominator.
   • Convert fractions to equivalent fractions with the common denominator.
   • Add the numerators and keep the common denominator.
   • Example: 1/4 + 2/5.
     • Common denominator is 20: 1/4 = 5/20, 2/5 = 8/20.
     • So, 5/20 + 8/20 = 13/20.
3. Subtraction of Fractions with the Same Denominator:
   • Subtract the numerators and keep the denominator the same.
   • Example: 5/8 – 3/8 = 2/8 = 1/4 (simplified).
4. Subtraction of Fractions with Different Denominators:
   • Find a common denominator.
   • Convert fractions to equivalent fractions with the common denominator.
   • Subtract the numerators and keep the common denominator.
   • Example: 3/4 – 1/6.
     • Common denominator is 12: 3/4 = 9/12, 1/6 = 2/12.
     • So, 9/12 – 2/12 = 7/12.

Evaluation

1. Add: 3/5 + 1/10.
2. Subtract: 7/8 – 1/4.
3. Find the sum of 2/3 and 5/6.
4. Find the difference between 4/7 and 2/5.
5. Add: 1/2 + 3/8.

Class Activity Discussion

1. How do you add fractions with the same denominator?
   • Add the numerators and keep the same denominator.
2. What is the process for adding fractions with different denominators?
   • Find a common denominator, convert, and then add.
3. How do you subtract fractions with the same denominator?
   • Subtract the numerators and keep the same denominator.
4. What is the method for subtracting fractions with different denominators?
   • Find a common denominator, convert, and then subtract.
5. Why is it important to simplify fractions after adding or subtracting?
   • To make the fractions easier to understand and work with.
6. How can you find a common denominator quickly?
   • List multiples of each denominator and find the least common multiple.
7. What are some real-life examples of fraction addition and subtraction?
   • Sharing pizza, measuring ingredients, etc.
8. What should you do if you get an improper fraction when adding or subtracting?
   • Convert it to a mixed number if necessary.
9. How do you check your work when adding or subtracting fractions?
   • Review steps, check calculations, and simplify if possible.
10. Can you always use the same common denominator for all fraction problems?
    • No, use the least common multiple for efficiency.
11. What is the simplest way to find the sum of 1/3 and 1/6?
    • Find the common denominator (6), convert fractions, then add.
12. How do you convert an improper fraction to a mixed number?
    • Divide the numerator by the denominator and express as a whole number and a fraction.
13. How do you handle fractions with unlike denominators in word problems?
    • Identify the least common denominator and convert fractions before solving.
14. What is an example of a fraction addition problem in a recipe?
    • Combining 1/4 cup and 2/3 cup of an ingredient.
15. How do you simplify the result of 9/15 after subtraction?
    • Divide both numerator and denominator by their greatest common divisor, 3, to get 3/5.

Subtraction of Fractions

Example 1: Simplify the Following

a. 2/3 – 1/4
Solution:

1. Find a common denominator. The least common multiple of 3 and 4 is 12.
2. Convert the fractions:
   2/3 = 8/12
   1/4 = 3/12
3. Subtract the numerators:
   8/12 – 3/12 = 5/12

b. 3/4 – 5/8
Solution:

1. Find a common denominator. The least common multiple of 4 and 8 is 8.
2. Convert the fractions:
   3/4 = 6/8
   5/8 = 5/8
3. Subtract the numerators:
   6/8 – 5/8 = 1/8

c. 5 3/4 – 2 4/5
Solution:

1. Convert mixed fractions to improper fractions:
   5 3/4 = 23/4
   2 4/5 = 14/5
2. Find a common denominator. The least common multiple of 4 and 5 is 20.
3. Convert the fractions:
   23/4 = 115/20
   14/5 = 56/20
4. Subtract the numerators:
   115/20 – 56/20 = 59/20 = 2 19/20

Example 2: Simplify the Following

a. 5 1/6 – 3 2/3 + 6 7/12
Solution:

1. Convert mixed fractions to improper fractions:
   5 1/6 = 31/6
   3 2/3 = 11/3
   6 7/12 = 79/12
2. Find a common denominator. The least common multiple of 6, 3, and 12 is 12.
3. Convert the fractions:
   31/6 = 62/12
   11/3 = 44/12
   79/12 = 79/12
4. Perform the operations:
   62/12 – 44/12 + 79/12 = 97/12 = 8 1/12

b. 2 1/2 + 3 + 7/10 – 2/5 – 2
Solution:

1. Convert mixed fractions to improper fractions:
   2 1/2 = 5/2
   3 = 3/1
   7/10 = 7/10
   2/5 = 2/5
   2 = 2/1
2. Find a common denominator. The least common multiple of 2, 1, 10, and 5 is 10.
3. Convert the fractions:
   5/2 = 25/10
   3/1 = 30/10
   7/10 = 7/10
   2/5 = 4/10
   2/1 = 20/10
4. Perform the operations:
   25/10 + 30/10 + 7/10 – 4/10 – 20/10 = 38/10 = 3 4/10 = 3 2/5

c. 2 1/2 + 3/4 – 11/6 + 4 – 1 2/3
Solution:

1. Convert mixed fractions to improper fractions:
   2 1/2 = 5/2
   3/4 = 3/4
   11/6 = 11/6
   4 = 4/1
   1 2/3 = 5/3
2. Find a common denominator. The least common multiple of 2, 4, 6, and 3 is 12.
3. Convert the fractions:
   5/2 = 30/12
   3/4 = 9/12
   11/6 = 22/12
   4/1 = 48/12
   5/3 = 20/12
4. Perform the operations:
   30/12 + 9/12 – 22/12 + 48/12 – 20/12 = 45/12 = 3 9/12 = 3 3/4

Evaluation

1. Simplify the following:
   1. 2 1/2 – 1 4/5 + 2 3/2 – 1
   2. 7 1/2 + 3 1/6 – 3 1/4
   3. 4 5/6 – 2 2/3 + 7/12
2. Convert the following mixed numbers and perform the operations:
   1. 3 1/2 – 2 3/4 + 1 2/5
   2. 5 1/3 + 4 2/5 – 6 1/6
3. Simplify:
   1. 7/8 – 2/3 + 5/6
   2. 9/10 – 3/5 + 1/2
4. Solve the following word problems:
   1. Maria has 4 1/4 kg of flour. She uses 2 2/5 kg for a recipe. How much flour does she have left?
   2. John drank 3 3/8 liters of juice from a bottle that originally contained 5 2/3 liters. How much juice is left in the bottle?

Presentation

1. Step 1: Review addition and subtraction of fractions with like denominators.
2. Step 2: Introduce addition and subtraction of fractions with unlike denominators.
3. Step 3: Practice problems with the class, guiding them through each step.

Teacher’s Activities

1. Explain the steps for adding and subtracting fractions.
2. Provide examples and practice exercises.
3. Assist students with problem-solving and simplification.

Learners’ Activities

1. Solve addition and subtraction problems on their own and in groups.
2. Discuss their solutions and methods with the class.
3. Practice simplifying fractions.

Assessment

1. Review students’ solutions for accuracy.
2. Provide feedback on problem-solving techniques and simplification.
3. What is 1/4 + 2/4?
   a) 1/2
   b) 3/4
   c) 1/4
   d) 2/4
4. What is 3/5 – 1/5?
   a) 2/5
   b) 4/5
   c) 3/5
   d) 1/5
5. Simplify 2/3 + 1/6.
   a) 1/2
   b) 5/6
   c) 4/6
   d) 3/6
6. Subtract 3/8 from 5/8.
   a) 2/8
   b) 3/8
   c) 1/4
   d) 1/8
7. What is 4/7 + 2/7?
   a) 6/7
   b) 4/14
   c) 5/7
   d) 2/7
8. Simplify 5/12 – 1/4.
   a) 1/3
   b) 7/12
   c) 2/12
   d) 3/12
9. What is 7/10 + 2/10?
   a) 9/10
   b) 1/10
   c) 7/20
   d) 8/10
10. Subtract 2/5 from 3/5.
    a) 1/5
    b) 2/5
    c) 3/10
    d) 4/5
11. What is 1/2 + 1/3?
    a) 5/6
    b) 1/6
    c) 2/5
    d) 2/3
12. Simplify 7/9 – 2/9.
    a) 5/9
    b) 4/9
    c) 1/3
    d) 6/9
13. What is 3/4 + 1/8?
    a) 7/8
    b) 5/8
    c) 1/2
    d) 1
14. Subtract 1/6 from 5/6.
    a) 1/3
    b) 4/6
    c) 2/6
    d) 1/2
15. What is 2/5 + 3/10?
    a) 7/10
    b) 1/2
    c) 3/5
    d) 5/10
16. Simplify 4/5 – 1/10.
    a) 7/10
    b) 3/5
    c) 8/10
    d) 1/2
17. What is 3/8 + 1/4?
    a) 5/8
    b) 4/8
    c) 7/8
    d) 1/2

Evaluation Questions

1. What is the first step in adding fractions with different denominators?
2. How do you convert fractions to have a common denominator?
3. What is the result of 3/7 + 2/7?
4. How do you subtract 5/6 from 7/8?
5. Simplify the fraction 8/12 after subtraction.
6. What is the least common multiple of 4 and 5?
7. Convert 14/9 to a mixed number.
8. How do you handle improper fractions in subtraction problems?
9. Find the common denominator for 1/4 and 2/3.
10. What is 3/5 – 1/10?

Conclusion

The teacher will check students’ answers, ensure understanding of the addition and subtraction of fractions, and provide further practice as needed.