# Meaning Of Fractions Types of Fractions And Mixed Numbers Mathematics JSS 1 First Term Lesson Notes Week 4

**Subject**: Mathematics

**Class**: JSS 1

**Term**: First Term

**Week**: 4

**Age**: 12 years

**Topic**: Fractions

**Sub-topic**: Common Fractions, Types of Fractions, Simple Conversion

**Duration**: 40 minutes

**Behavioural Objectives**:

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

- Identify and describe common fractions.
- Distinguish between proper, improper, and mixed fractions.
- Convert between improper fractions and mixed fractions.

**Keywords**: Fraction, Numerator, Denominator, Proper Fraction, Improper Fraction, Mixed Number

**Set Induction**:

Start with a real-life example. Show a pizza cut into equal parts. Ask pupils, “If we have 4 slices out of 8, what fraction of the pizza is that?”

**Entry Behaviour**:

Pupils should already know how to count numbers and understand the concept of a whole.

**Learning Resources and Materials**:

- Visual aids (slices of pizza, shapes cut into parts)
- Fraction charts
- Drawing board
- Fraction strips

**Building Background / Connection to Prior Knowledge**:

Review the concept of whole numbers and division to link with fractions.

**Embedded Core Skills**:

- Critical thinking
- Problem-solving
- Basic arithmetic

**Learning Materials**:

- Essential Mathematics for JSS1 by AJS Oluwasanmipg
- New General Mathematics for JSS1 by M.F. Macrae et al

**Instructional Materials**:

- Visual aids (shapes, drawings)
- Fraction strips

**Content**:

**Definition**:

A fraction is a number that represents a part of a whole. It is written as one number (numerator) divided by another (denominator). For example, 1/2 means 1 part out of 2 equal parts.**Common Fractions**:**Proper Fractions**: Numerator is less than the denominator. Example: 3/4, 2/5.**Improper Fractions**: Numerator is greater than or equal to the denominator. Example: 5/4, 7/3.**Mixed Numbers**: Consists of a whole number and a fraction. Example: 1 1/2, 2 3/4.

**Simple Conversion**:**Improper to Mixed Fractions**: Divide the numerator by the denominator. Example: 7/4 = 1 3/4.**Mixed to Improper Fractions**: Multiply the whole number by the denominator and add the numerator. Example: 2 1/3 = (2 x 3) + 1 / 3 = 7/3.

#### Topic: Fractions

**A: Common Fractions**

**Meaning of Fractions**:- A fraction shows a part of a whole.
- It is written as one number divided by another.
- Example: 3/4 means 3 parts out of 4.

**General Form of a Fraction**:- Written as
`a/b`

, where:`a`

is the numerator (the top number).`b`

is the denominator (the bottom number).

- Written as
**Types of Fractions**:**i. Common (Vulgar) Fractions**:- Written as one number over another.
**Examples**:- 9/11
- 3/8

**ii. Decimal Fractions**:- Written with a decimal point.
- Example: 0.75 is a decimal fraction.

**B: Types of Fractions (Common)**

**Proper Fractions**:- Numerator is less than the denominator.
**Examples**:- 4/7
- 3/5

**Improper Fractions**:- Numerator is greater than or equal to the denominator.
**Examples**:- 11/5
- 4/3

**Mixed Numbers**:- Contains a whole number and a fraction.
**Examples**:- 1 1/2 (1 whole and 1/2)
- 2 3/4 (2 whole and 3/4)

### Conversion Examples

**1. Converting Improper Fractions to Mixed Numbers**:

**Method**: Divide the numerator by the denominator. The quotient is the whole number, and the remainder is the numerator of the fractional part.**Example 1**: 4/3- 4 divided by 3 is 1 with a remainder of 1.
- Mixed Number: 1 1/3

**Example 2**: 57/10- 57 divided by 10 is 5 with a remainder of 7.
- Mixed Number: 5 7/10

**Example 3**: 93/20- 93 divided by 20 is 4 with a remainder of 13.
- Mixed Number: 4 13/20

**Example 4**: 113/3- 113 divided by 3 is 37 with a remainder of 2.
- Mixed Number: 37 2/3

**2. Converting Mixed Numbers to Improper Fractions**:

**Method**: Multiply the whole number by the denominator and add the numerator. This result is the numerator of the improper fraction.**Example 1**: 5 1/2- 5 times 2 plus 1 is 11.
- Improper Fraction: 11/2

**Example 2**: 3 2/5- 3 times 5 plus 2 is 17.
- Improper Fraction: 17/5

**Example 3**: 7 1/8- 7 times 8 plus 1 is 57.
- Improper Fraction: 57/8

**Example 4**: 10 1/3- 10 times 3 plus 1 is 31.
- Improper Fraction: 31/3

### Evaluation

**Examples of Fractions**:- List five examples each of proper fractions, improper fractions, and mixed numbers.

**Fractions from Figures**:- Using provided shapes, identify and write the fraction, stating whether it is proper, improper, or mixed.

### Reading Assignment

*Essential Mathematics for JSS1*by AJS Oluwasanmipg, pages 35-36.*New General Mathematics for JSS1*by M.F. Macrae et al., pages 29-30.

### Weekend Assignment

**Identify Proper Fractions**:- Which of the following is not a proper fraction?
- (a) 1/4
- (b) 3/4
- (c) 3/2
- (d) 5/8

- Which of the following is not a proper fraction?
**Convert to Improper Fraction**:- Express 3 1/7 as an improper fraction.
- (a) 22/7
- (b) 23/7
- (c) 7/22
- (d) 22/7

- Express 3 1/7 as an improper fraction.
**Shaded Fraction**:- What fraction of the figure shown is shaded?
- (a) 2/11
- (b) 3/9
- (c) 8/3
- (d) 4/11

- What fraction of the figure shown is shaded?
**Convert to Mixed Fraction**:- Express 99/5 as a mixed fraction.
- (a) 19 4/5
- (b) 18 4/5
- (c) 19 5/4
- (d) 18 5/4

- Express 99/5 as a mixed fraction.
**Figure Descriptions**:- The figures above can best be described as:
- (a) 2 1/2 – mixed number
- (b) 2 3/4 – proper fraction
- (c) 2 3/4 – improper fraction
- (d) 2 3/4 – decimal

- The figures above can best be described as:

### Theory

**Distinguish Fractions**:- Describe the types of fractions and provide two examples for each.

**Conversion**:- Convert 103/5 to a mixed fraction.
- Convert 11 2/5 to an improper fraction.

**Evaluation** (Fill-in-the-Blank Questions):

- The top number in a fraction is called the _____ (a) numerator, (b) denominator, (c) fraction, (d) divisor.
- The bottom number in a fraction is called the _____ (a) numerator, (b) denominator, (c) fraction, (d) divisor.
- A fraction where the numerator is less than the denominator is called a _____ fraction. (a) proper, (b) improper, (c) mixed, (d) decimal.
- The fraction 7/4 is an example of an _____ fraction. (a) proper, (b) improper, (c) mixed, (d) decimal.
- The fraction 3 1/2 is a _____ number. (a) proper, (b) improper, (c) mixed, (d) decimal.
- Convert 9/4 to a mixed number. It is _____ (a) 2 1/4, (b) 2 3/4, (c) 1 2/4, (d) 2 2/4.
- Convert 4 2/5 to an improper fraction. It is _____ (a) 22/5, (b) 20/5, (c) 18/5, (d) 25/5.
- Which of the following is not a proper fraction? (a) 2/3, (b) 5/6, (c) 7/4, (d) 3/8.
- The fraction 1 1/3 can be written as _____ in improper fraction form. (a) 4/3, (b) 5/3, (c) 3/1, (d) 7/3.
- The mixed number 2 1/2 is equivalent to the improper fraction _____ (a) 5/2, (b) 4/2, (c) 7/2, (d) 6/2.
- Convert the improper fraction 8/3 to a mixed number. It is _____ (a) 2 2/3, (b) 3 1/3, (c) 2 1/3, (d) 1 2/3.
- The fraction 5/8 is a _____ fraction. (a) proper, (b) improper, (c) mixed, (d) decimal.
- The improper fraction 13/4 is a _____ number. (a) proper, (b) mixed, (c) decimal, (d) improper.
- To convert 5 3/4 to an improper fraction, you get _____ (a) 23/4, (b) 22/4, (c) 25/4, (d) 24/4.
- Which is an example of a proper fraction? (a) 4/3, (b) 2/4, (c) 5/5, (d) 7/6.

**Class Activity Discussion (FAQs)**:

- What is a fraction?

A fraction shows parts of a whole. It is written as one number over another. - What is the numerator in a fraction?

The numerator is the top number in a fraction. - What is the denominator in a fraction?

The denominator is the bottom number in a fraction. - What is a proper fraction?

A proper fraction has a numerator less than its denominator. - What is an improper fraction?

An improper fraction has a numerator greater than or equal to its denominator. - How do you convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The whole number is the quotient, and the remainder becomes the numerator of the fraction part. - How do you convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator of the fraction part. - What is a mixed number?

A mixed number consists of a whole number and a fraction. - Can you give an example of a mixed number?

An example is 2 1/2. - How can you simplify a fraction?

Divide the numerator and denominator by their greatest common factor. - What is the fraction 5/4 as a mixed number?

It is 1 1/4. - How do you know if a fraction is proper or improper?

If the numerator is less than the denominator, it’s proper; if greater, it’s improper. - What is the simplest form of the fraction 8/12?

It is 2/3. - How do you compare two fractions?

Find a common denominator or convert them to decimal form. - Why do we need to learn about fractions?

Fractions help us understand and work with parts of a whole in various real-life situations.

**Presentation**:

**Step 1**: Review the previous topic of basic division and parts of a whole.**Step 2**: Introduce fractions by explaining numerators and denominators with visual aids.**Step 3**: Allow pupils to provide examples and correct them as needed.

**Teacher’s Activities**:

- Use visual aids to explain fractions.
- Demonstrate converting improper fractions to mixed numbers and vice versa.
- Provide examples and practice problems.

**Learners’ Activities**:

- Participate in discussions.
- Solve given examples and practice problems.
- Work in pairs to convert fractions.

**Assessment**:

Observe pupils’ understanding through their responses to evaluation questions and class activities.

**Evaluation Questions**:

- What is a fraction?
- How do you write a fraction?
- What is the difference between proper and improper fractions?
- Convert 7/3 to a mixed number.
- Convert 2 2/5 to an improper fraction.
- Identify the numerator in 3/7.
- Identify the denominator in 5/6.
- What is a mixed number?
- How do you simplify 12/16?
- Convert 8 3/4 to an improper fraction.

**Conclusion**:

Review the main points of the lesson and correct any misunderstandings. Mark pupils’ work and provide feedback on their performance..