P6 Mathematics - Term II

Topic 5: Fractions

Lesson 1: Multiplication and Division of Fractions

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

• Multiply fractions by fractions correctly
• Divide fractions using the correct method
• Solve simple word problems involving multiplication and division of fractions
• Apply fraction operations to real-life situations

Quick Review: Multiplication Tables

Let's warm up our brains!

Answer quickly:

• 3 × 4 = ?
• 5 × 6 = ?
• 4 × 8 = ?
• 7 × 3 = ?

Review: What is a Fraction?

A fraction represents a part of a whole.

Examples:

• 1/2 means one out of two equal parts
• 3/4 means three out of four equal parts
• 2/5 means two out of five equal parts

Remember:

• Top number = numerator
• Bottom number = denominator

Can We Multiply Fractions?

Think about this:

• What is half of one-third?
• Or in fraction notation: 1/2 × 1/3 = ?

Today you'll learn how to find the answer!

Rule for Multiplying Fractions

To multiply fractions:

Multiply the numerators together

Multiply the denominators together

Formula: a/b × c/d = (a × c)/(b × d)

Example 1: Multiplying Fractions

Problem: 1/2 × 1/3 = ?

Step 1: Multiply numerators: 1 × 1 = 1

Step 2: Multiply denominators: 2 × 3 = 6

Answer: 1/2 × 1/3 = 1/6

One-half of one-third equals one-sixth!

Example 2: With Simplification

Problem: 2/3 × 3/4 = ?

Step 1: Multiply numerators: 2 × 3 = 6

Step 2: Multiply denominators: 3 × 4 = 12

Step 3: Simplify: 6/12 = 1/2

Final Answer: 1/2

Example 3: Practice Together

Problem: 3/5 × 2/7 = ?

Work it out:

• Numerators: 3 × 2 = ?
• Denominators: 5 × 7 = ?
• Answer: ?

Think, then we'll solve together!

Your Turn: Practice

Work these problems in your exercise book:

a) 1/4 × 2/5
b) 3/7 × 1/2
c) 2/3 × 3/5
d) 5/6 × 2/3

Show all your working steps!

Dividing Fractions: The Magic Trick

To divide by a fraction:

Keep the first fraction

Flip the second fraction (reciprocal)

Multiply them together

Remember: Keep - Flip - Multiply (KFM)

What is a Reciprocal?

Reciprocal: Flip the fraction upside down

Examples:

• Reciprocal of 1/4 is 4/1
• Reciprocal of 2/3 is 3/2
• Reciprocal of 3/5 is 5/3

Key idea: Top becomes bottom, bottom becomes top

Example 1: Dividing Fractions

Problem: 1/2 ÷ 1/4 = ?

Step 1: Keep first fraction: 1/2

Step 2: Flip second fraction: 1/4 becomes 4/1

Step 3: Multiply: 1/2 × 4/1 = 4/2 = 2

Answer: 2

Example 2: With Explanation

Problem: 3/4 ÷ 2/3 = ?

Keep: 3/4
Flip: 2/3 becomes 3/2
Multiply: 3/4 × 3/2 = 9/8 = 1 1/8

Important: Remember to convert improper fractions to mixed numbers!

Example 3: Step by Step

Problem: 2/3 ÷ 4/9 = ?

Step 1: Keep: 2/3
Step 2: Flip: 4/9 becomes 9/4
Step 3: Multiply: 2/3 × 9/4 = 18/12
Step 4: Simplify: 18/12 = 3/2 = 1 1/2

Your Turn: Division Practice

Solve in your exercise book:

a) 1/2 ÷ 1/3
b) 3/5 ÷ 2/3
c) 4/7 ÷ 2/5

Remember: Keep - Flip - Multiply

Real-Life Application 1

Akello's Cake:

Akello has 1/2 of a cake. She gives 1/3 of what she has to her brother.

Question: What fraction of the whole cake did she give away?

Solution: 1/2 × 1/3 = 1/6

She gave away 1/6 of the whole cake.

Real-Life Application 2

Farmer's Beans:

A farmer has 3/4 of a sack of beans. He wants to divide it into portions of 1/8 sack each.

Question: How many portions will he get?

Solution: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6

He will get 6 portions.

Summary: Key Points

Multiplying Fractions:

• Multiply numerators together
• Multiply denominators together
• Simplify the answer

Dividing Fractions:

• Keep the first fraction
• Flip the second fraction
• Multiply them together

Why Are These Skills Important?

Fractions are used in:

• Cooking and recipes (measuring ingredients)
• Sharing food fairly
• Construction and measurements
• Dividing land or resources
• Business and money calculations

Understanding fractions helps you in everyday life!

Quick Assessment

Answer these in your exercise book:

1. 2/5 × 3/4 = ?
2. 1/3 × 2/7 = ?
3. 3/4 ÷ 1/2 = ?
4. 2/3 ÷ 3/5 = ?

Word Problem Challenge

Problem:

A recipe needs 1/2 kg of sugar. Okello wants to make 1/4 of the recipe. How much sugar does he need?

Think: Are we multiplying or dividing?
Solution: 1/2 × 1/4 = 1/8 kg

Okello needs 1/8 kg of sugar.

Homework

Complete these problems in your exercise book:

Part A: Multiplication (6 problems)

1. 1/3 × 2/5 2. 3/8 × 4/9 3. 2/7 × 3/4
2. 5/6 × 3/10 5. 4/5 × 5/8 6. 7/9 × 3/7

Part B: Division (4 problems)
7. 1/2 ÷ 1/4 8. 2/3 ÷ 1/6
9. 3/5 ÷ 2/3 10. 5/8 ÷ 3/4

Homework: Word Problems

Problem 11:
Akello walked 3/4 of the distance to school. Her friend Sarah walked 2/3 of what Akello walked. What fraction of the total distance did Sarah walk?

Problem 12:
A piece of cloth is 5/6 meters long. It is cut into pieces, each 1/12 meter long. How many pieces are there?

Looking Ahead

Next Lesson:
We will learn about BODMAS with fractions and operations on decimals.

Why it matters:
You'll use today's multiplication and division skills to solve more complex problems!

Keep practicing - you're doing great!

Remember

Multiplication: Multiply straight across, then simplify

Division: Keep - Flip - Multiply

Always: Show your working steps and simplify your answers

Practice makes perfect!