Multiply Mixed Fractions

Key Concepts:

• Multiply unit fractions
• Multiply fractions
• Multiply mixed fractions

Introduction: 

What is a fraction? 

A fraction is the part of a whole. It can be written as the combination of the numerator and the denominator. 

Types of fractions: 

Fractions are divided into 4 types: 

• Unit fraction 
• Proper fraction 
• Improper fraction 
• Mixed fraction 

Unit fraction: 

A fraction with 1 as its numerator and positive integer as its denominator is called an unit fraction. 

Proper fraction: 

If the numerator is less than its denominator, then the fraction is called a proper fraction. 

Improper fraction: 

If the numerator is greater than its denominator, then the fraction is called an improper fraction. 

Mixed fraction: 

A mixed fraction is defined as the combination of a whole number and a fraction. 

Fractions on a number line: 

Fractions on a number line are represented as shown. 

Real life examples: 

The real-life examples of fractions include parts of a pizza, cake, etc., 

Multiplication of fractions: 

The product of a fraction with another fraction is known as multiplication of fractions. Fraction multiplication can be done as per the following steps: 

Step 1: Multiply both the numerators. 

Step 2: Multiply both the denominators. 

Step 3: Reduce the fraction product obtained to lowest terms. 

Fraction multiplication can be represented using the following formula: 

ab×cd=acbd 𝐚𝐛×𝐜𝐝=𝐚𝐜𝐛𝐝

Example: Multiply

23×1223×12

Solution: 

Multiplication of the given fractions is explained using the following square diagram model. 

From the above figure, given fractions are represented with two square models. The first fraction

2323

is represented with blue, second fraction

1212 with pink and the product fraction

1313 with green colour. Upon multiplying the fractions

23×1223×12, we get the product

2626. 

1.3.1 Multiply unit fractions 

How can you multiply unit fractions? 

The below example shows how to multiply unit fractions with the area models. 

Example 1: Multiply

13×14𝟏𝟑×𝟏𝟒

Example 2:  Multiply

14×15𝟏𝟒×𝟏𝟓

using an area model. 

Solution:  

The below area model shows the visual representation of unit fractions

1414

and

1515. 

14×15=1×14×5=12014×15=1×14×5=120

1.3.2 Multiply fractions 

Represent fractions on a number line: 

Fraction is a part of the whole. Fractions can be represented on the number line by dividing them into an equal number of parts of a whole. 

Let us consider the fraction

1616

to represent on the number line. 

Divide the given fraction into 6 equal parts to represent on the number line as shown. 

Plot fractions on a number line: 

The following steps explain how to plot fractions on a number line. 

Step 1: Draw the number line from 0 to 1. 

Step 2: Check whether the given fraction is proper or improper fraction. If it is improper, then convert it into mixed fraction and represent it on the number line. 

Step 3: Draw equal number of parts on the number line 

Step 4: Starting from the initial point on the left, count forward to the number of parts of the numerator. 

Step 5: Mark the point on the number line. 

Example 1: Represent the fraction

37

on the number line. 

Solution:  

Plotting the given fraction

3737

on the number line using the following visual representation. 

Example 2: Multiply

23×34

using a number line. 

Solution: 

Here from the given fractions, 

13

= 1 out of 3 equal parts, So

13 of

3434 is

1414

2323

= 2 out of 3 equal parts, So

23 of

3434 is 2 times

1414

23×34=2×33×4=612

, reducing the product to its simplest form we get

12

1.3.3. Multiply mixed fractions 

How to convert mixed fraction to improper fraction? 

Conversion of mixed fractions can be explained with the following steps: 

Step 1: Multiply the denominator by a whole number. 

Step 2: Add the numerator of the fraction. 

Step 3: The result obtained is the improper fraction. 

Example 1: Convert the mixed fraction 3

12

into an improper fraction. 

Solution: 

Mixed fraction conversion can be explained using below visual representation. 

From the above figure, if we divide the whole into 2 equal parts, then the denominator of the fraction is 2. 

Here the fraction is portioned into 7 parts as shown in the above image with green color shaded regions. So, the improper fraction is:  

How to multiply mixed numbers? 

Let us consider the following example. 

Exercise:

1. Multiply 2/5 x 1/12
   
   
2. Use the model to find the product of 5/6 x 1/2
   
   
3. Use the number line to find the product of 3/4 x 2/9
   
   
4. Multiply 3×1/5 x 2/3
   
   
5. Use an area model to find the product of 1 x1/8 x 3×1/3
   
   
6. Use an equation to find the product of 4×1/8 x 5×1/2
   
   
7. Multiply 1/4 x 7/8
   
   
8. Multiply 5/7 x 7/9
   
   
9. Use the area model to find the product of 2/3×1/12
   
   
10. Multiply 5/9 x 1/9

What have we learned:

• Understand fraction and its types.
• Multiply fractions with area models.
• Multiply unit fractions.
• Multiply fractions with equations.
• Multiply mixed fraction.
• Multiply fractions on a number line.

Concept Map: