Class 5 - Multiplication of Fractions: Easy Methods and Solved Examples

Multiplication of fractions is an essential math skill that helps us solve real world problems. Unlike addition or subtraction of fractions, multiplying fractions is often simpler because you do not need to find a common denominator to multiply fractions.

 When we multiply fractions, we are finding a part of a part.

For example, if you eat 1/2 of a pizza, and then eat 1/2 of that you half, you have eaten 1/4 of the whole pizza. 

• Multiplication of fractions means finding a fraction of another fraction

• The process is straightforward compared to addition

• Simplification can happen before or after multiplication

• Results are often smaller than the original fractions

Table of Contents

• Basic Multiplication of Fractions
• Multiplying Fractions with Whole Numbers
• Multiplying Mixed Fractions
• Multiplication of Fractions with Variables
• Solved Examples on Multiplication of Fractions
• Practice Questions on Multiplication of Fractions

Basic Multiplication of Fractions

When we multiply two fractions, we multiply the numerators together and the denominators together. This is the fundamental rule of fraction multiplication.

The rule is simple and easy to remember:

• Multiply the numerators together

• Multiply the denominators together

• Simplify the result if possible

Formula: (a/b) × (c/d) = (a × c)/(b × d)

Example 1: Simple Fraction Multiplication

Problem: 2/3 × 1/4 = ?

Solution:

Step 1: Multiply numerators

• 2 × 1 = 2

Step 2: Multiply denominators

• 3 × 4 = 12

Step 3: Write the result

• 2/12

Step 4: Simplify

• 2/12 = 1/6 (divide both by 2)

Answer: 1/6

Example 2: Multiplying Three Fractions

Problem: 1/2 × 2/3 × 3/4 = ?

Solution:

Step 1: Multiply all numerators

• 1 × 2 × 3 = 6

Step 2: Multiply all denominators

• 2 × 3 × 4 = 24

Step 3: Write the result

• 6/24

Step 4: Simplify

• 6/24 = 1/4 (divide both by 6)

Answer: 1/4

Cancellation Method (Cross Cancellation)

Before multiplying, we can simplify by canceling common factors. This makes calculations easier.

How to Use Cancellation:

1. Look at numerators and denominators

2. Find common factors

3. Cancel (divide) them out

4. Multiply what remains

Example 1: Multiplication with Cancellation

Problem: 3/4 × 2/9 = ?

Solution Using Cancellation:

Step 1: Look for common factors

• Numerators: 3, 2

• Denominators: 4, 9

• 3 and 9 share a common factor of 3

Step 2: Cancel the common factor

• 3/4 × 2/9 = 3/4 × 2/9

• = 1/4 × 2/3

Step 3: Multiply what remains

• (1 × 2)/(4 × 3) = 2/12

Step 4: Simplify

• 2/12 = 1/6

Answer: 1/6

Example 2: Multiplying Proper and Improper Fractions

Problem: 5/8 × 3/2 = ?

Solution:

Step 1: Check for cancellation

• 2 and 8 share a common factor of 2

Step 2: Cancel

• 5/8 × 3/2 = 5/4 × 3/1

Step 3: Multiply

• (5 × 3)/(4 × 1) = 15/4

Step 4: Convert to mixed number (if needed)

• 15/4 = 3 3/4

Answer: 15/4 or 3 3/4

Multiplying Fractions with Whole Numbers

Any whole number can be written as a fraction by placing it over 1. This allows us to use the same multiplication rules.

Examples of Converting Whole Numbers:

• 3 = 3/1

• 7 = 7/1

• 10 = 10/1

• 1 = 1/1

To multiply a fraction by a whole number:

1. Write the whole number as a fraction (over 1)

2. Multiply the numerators

3. Multiply the denominators

4. Simplify the answer

Formula: (a/b) × c = (a/b) × (c/1) = (a × c)/b

Example 1: Fraction Times Whole Number

Problem: 2/5 × 3 = ?

Solution:

Step 1: Write whole number as fraction

• 3 = 3/1

Step 2: Multiply

• (2/5) × (3/1) = (2 × 3)/(5 × 1) = 6/5

Step 3: Simplify or convert

• 6/5 = 1 1/5 (mixed number)

Answer: 6/5 or 1 1/5

Example 2: Whole Number Times Fraction

Problem: 4 × 3/8 = ?

Solution:

Step 1: Convert whole number

• 4 = 4/1

Step 2: Multiply

• (4/1) × (3/8) = (4 × 3)/(1 × 8) = 12/8

Step 3: Simplify

• 12/8 = 3/2 = 1 1/2

Answer: 3/2 or 1 1/2

Example 3: Multiple Fractions and Whole Numbers

Problem: 2 × 1/3 × 3 = ?

Solution:

Step 1: Convert whole numbers

• 2/1 × 1/3 × 3/1

Step 2: Multiply all numerators

• 2 × 1 × 3 = 6

Step 3: Multiply all denominators

• 1 × 3 × 1 = 3

Step 4: Write result

• 6/3

Step 5: Simplify

• 6/3 = 2

Answer: 2

Example 4: Whole Number and Fraction with Cancellation

Problem: 5 × 2/10 = ?

Solution:

Step 1: Convert and look for common factors

• 5/1 × 2/10

• 5 and 10 share a factor of 5

Step 2: Cancel

• 5/1 × 2/10 = 1/1 × 2/2 = 1/1 × 1/1

Step 3: Multiply

• 1 × 1 = 1

Answer: 1

Multiplying Mixed Fractions

A mixed fraction (or mixed number) has a whole number part and a fraction part. Examples include 2 1/3, 4 3/4, and 1 5/8. To multiply mixed fractions, we first convert them to improper fractions, then multiply using the regular process.

Formula: Whole × Denominator + Numerator = New Numerator

Keep the same denominator.

Examples:

• 2 1/3 = (2 × 3 + 1)/3 = 7/3

• 4 3/4 = (4 × 4 + 3)/4 = 19/4

• 1 5/8 = (1 × 8 + 5)/8 = 13/8

To multiply mixed fractions:

1. Convert each mixed fraction to an improper fraction

2. Multiply the numerators

3. Multiply the denominators

4. Simplify and convert back to mixed number if needed

Example 1: Basic Mixed Fraction Multiplication

Problem: 1 1/2 × 2 1/4 = ?

Solution:

Step 1: Convert to improper fractions

• 1 1/2 = (1 × 2 + 1)/2 = 3/2

• 2 1/4 = (2 × 4 + 1)/4 = 9/4

Step 2: Multiply

• (3/2) × (9/4) = (3 × 9)/(2 × 4) = 27/8

Step 3: Convert back to mixed number

• 27/8 = 3 3/8

Answer: 3 3/8

Example 2: Three Mixed Fractions

Problem: 1 1/2 × 1 1/3 × 2 = ?

Solution:

Step 1: Convert all to improper fractions

• 1 1/2 = 3/2

• 1 1/3 = 4/3

• 2 = 2/1

Step 2: Multiply numerators

• 3 × 4 × 2 = 24

Step 3: Multiply denominators

• 2 × 3 × 1 = 6

Step 4: Write result

• 24/6

Step 5: Simplify

• 24/6 = 4

Answer: 4

Multiplication of Fractions with Variables

Variables represent unknown numbers. When multiplying fractions with variables, we follow the same rules as with regular numbers.

Rule for Multiplying Fractions with Variables

1. For like expressions: apply the same multiplication rule

2. Multiply numerators together (including variables)

3. Multiply denominators together

4. Simplify by canceling common factors

Example 1: Simple Variable Fraction Multiplication

Problem: x/3 × 2/5 = ?

Solution:

Step 1: Multiply numerators

• x × 2 = 2x

Step 2: Multiply denominators

• 3 × 5 = 15

Step 3: Write answer

• 2x/15

Answer: 2x/15

Example 2: Variables in Multiple Fractions

Problem: a/4 × b/3 = ?

Solution:

Step 1: Multiply numerators

• a × b = ab

Step 2: Multiply denominators

• 4 × 3 = 12

Step 3: Write answer

• ab/12

Answer: ab/12

Solved Examples on Multiplication of Fractions

Example 1: Complex Fraction Multiplication

Problem: 5/6 × 8/15 × 3/4 = ?

Solution:

Method 1 (Direct Multiplication):

Step 1: Multiply numerators

• 5 × 8 × 3 = 120

Step 2: Multiply denominators

• 6 × 15 × 4 = 360

Step 3: Write result

• 120/360

Step 4: Simplify by finding GCD

• GCD(120, 360) = 120

• 120/360 = 1/3

Answer: 1/3

Method 2 (Using Cancellation):

Step 1: Look for cancellations

• 5/6 × 8/15 × 3/4

• 5 and 15 have factor 5: 5/6 × 8/15 × 3/4 = 1/6 × 8/3 × 3/4

• 3 and 3 cancel: 1/6 × 8/3 × 3/4 = 1/6 × 8/4

• 8 and 4 have factor 4: 1/6 × 8/4 = 1/6 × 2 = 2/6 = 1/3

Answer: 1/3

Example 2: Mixed Number Word Problem

Problem: A rectangular garden has length 3 1/2 meters and width 2 1/4 meters. What is its area?

Solution:

Step 1: Identify what we need

• Area = length × width

• Length = 3 1/2 m

• Width = 2 1/4 m

Step 2: Convert to improper fractions

• 3 1/2 = 7/2

• 2 1/4 = 9/4

Step 3: Multiply

• (7/2) × (9/4) = (7 × 9)/(2 × 4) = 63/8

Step 4: Convert to mixed number

• 63/8 = 7 7/8 square meters

Answer: The area is 7 7/8 square meters.

Example 3: Recipe Adjustment Problem

Problem: A cookie recipe calls for 2 3/4 cups of flour. If you want to make 1/2 of the recipe, how much flour do you need?

Solution:

Step 1: Identify the operation

• We need to find 1/2 of 2 3/4 cups

• This means: 1/2 × 2 3/4

Step 2: Convert mixed number

• 2 3/4 = 11/4

Step 3: Multiply

• (1/2) × (11/4) = 11/8

Step 4: Convert to mixed number

• 11/8 = 1 3/8 cups

Answer: You need 1 3/8 cups of flour.

Example 4: Calculating Discounts

Problem: A shirt originally costs 80 dollars. It is on sale for 3/4 of the original price. How much does the shirt cost after discount?

Solution:

Step 1: Identify what we need

• Sale price = 3/4 × original price

• 3/4 × 80

Step 2: Convert 80 to fraction

• 80 = 80/1

Step 3: Multiply

• (3/4) × (80/1) = (3 × 80)/(4 × 1) = 240/4

Step 4: Simplify

• 240/4 = 60

Answer: The shirt costs 60 dollars after the discount.

Example 5: Finding a Fraction of an Amount

Problem: There are 120 students in a school. 2/3 of them are interested in sports. How many students are interested in sports?

Solution:

Step 1: Find 2/3 of 120

• (2/3) × 120

Step 2: Convert 120 to fraction

• (2/3) × (120/1)

Step 3: Multiply

• (2 × 120)/(3 × 1) = 240/3

Step 4: Simplify

• 240/3 = 80

Answer: 80 students are interested in sports.

Practice Questions on Multiplication of Fractions

1: Simple Fraction Multiplication

Multiply the following fractions:

1. 1/2 × 1/3 = ?

2. 2/5 × 1/4 = ?

3. 3/4 × 2/3 = ?

4. 1/6 × 3/4 = ?

5. 2/3 × 3/5 = ?

2: Fraction Multiplication with Cancellation

Multiply using cancellation method:

1. 3/4 × 2/9 = ?

2. 4/5 × 5/8 = ?

3. 6/7 × 7/12 = ?

4. 5/6 × 9/10 = ?

5. 8/9 × 3/4 = ?

3: Fractions Multiplied by Whole Numbers

Multiply fractions and whole numbers:

1. 3 × 1/5 = ?

2. 1/4 × 8 = ?

3. 2/3 × 6 = ?

4. 5 × 2/5 = ?

5. 3/8 × 4 = ?

4: Mixed Fraction Multiplication

Multiply mixed fractions:

1. 1 1/2 × 1/3 = ?

2. 2 1/4 × 2 = ?

3. 1 1/2 × 2 1/3 = ?

4. 3 1/2 × 2/7 = ?

5. 2 2/3 × 1 1/2 = ?