Addition of Mixed Fractions

Key Concepts

• Definition of mixed fractions
• Addition of mixed fractions using fraction strips
• Addition of mixed fractions using number line

Introduction: 

Until now, we learned to add or subtract fractions with the same denominators using fractions strips, on number line and also directly. 

Now let us learn about how to add mixed fractions using fraction strips or on number lines. 

To do that, we should know what mixed fractions are. 

Mixed fractions:  

All those fractions consisting of a whole number and proper fraction are called mixed fractions. 

For example, 

3*1/5, 1*1/3, 2*3/4 etc., 

It is easy to add fractions that have the same kind of parts. 

For example,  

To add 1/4 and 2/4, we will think of chocolate divided into four equal parts. One-fourth means one piece out of four, and two-fourths means two pieces out of four. In total, we have three pieces out of four. 

So, the answer is 3/4. 

Let us consider another example: 

If Rodrigo has one dollar and one quarter and Flynn has 2 dollars and two quarters. If they both put their money together, how much money do they have together? 

Solution: 

If Rodrigo has one dollar and one quarter. That means he has 1*1/4 dollars. 

If Flynn has 2 dollars and two quarters. That is Flynn has 2*2/4 dollars. 

If they both put their money together, they would have 3 dollars and 3 quarters.  

Here, they have added their dollars and the quarters. This makes 3*3/4 dollars. 

1*1/4 + 2*2/4 = (1+2) + (1/4+2/4)  = 3*3/4 dollars 

When you added the dollars and then added the quarters, you added the whole and the fractions. 

We can also use fraction strips or number lines to model this addition. 

For example 

Let us use fraction strips to add the above fractions. 

1*1/4 Dollars can be represented as 

2*2/4 Dollars can be represented as  

On adding  

⸫ 1*1/4 + 2*2/4  = 3*3/4

Explanation: 

1. Addition of Mixed fraction using Fraction Strips: 

Let us learn to add mixed fractions using fraction strips. Here, for better understanding, we will use rectangular fraction strips. 

Example 1:  

Model 2*1/3+1*2/3 and give the sum 

Solution:  

Let us represent 2*1/3 in the following way 

Representing 1*2/3 using fraction strips, we get 

To add these two mixed fractions, we need to first add the whole number part and the fractional part. 

⸫2*1/3+1*2/3=4

Example 2:  

Shade parts and write the addition sentence with the answer. 

1. Shade 6/5 and 1/5 in the given figure and add 

Solution:  

Shade 6/5 in yellow and 6/5 in blue 

Now total parts shared are 7/5 From the above shaded pictures, we can see that we have shaded one whole and 2 parts in another whole. 

That is  6/5+1/5= 7/5, which can be converted into a mixed fraction as 1*2/5

2. Add 2*1/2+1*2/2  by shading the parts 

Solution:  

Let us shade 2*1/2 using green color and 1/2 using yellow.  

It can be seen that all three wholes are shaded. 

Therefore, 2*1/2+1/2 = 3 

2. Adding mixed fraction on the Number line 

We can also add mixed fractions on the number line. 

To add mixed fractions on the number line, we must know how to represent a mixed fraction on the number line. 

For example, let us represent 1*2/5  on the number line. 

We follow the below steps 

• Draw the number line. 
• Since the denominator of the proper fraction is 5, divide the space between each number on the number line into five equal parts.  
• Then mark numbers and then add the given mixed fraction. 

To add mixed fractions on the number line, we have to move towards the right side of the number line. 

Let us check these examples 

Example 1 

Add 1*1/4+1*2/4 on the number line 

Solution: 

Step 1: Draw the number line. Since the denominator is 4, divide the space between any two numbers into four parts. 

Step 2: Mark 1*1/4  on the number line  

Step 3: From 1*1/4 move 1*2/4 to the right side and mark the point where it lands 

Step 4:  Therefore,

1*1/4 + 1*2/4 = 2*3/4

This way mixed fractions can be added using fraction strips or on the number line. 

Exercise:

• Add 1*3/5 + 2*2/5 using fraction strips.
• Add 1*3/8+1*6/8  using fraction strips.
• Add. Shade parts with different colors. Give your answer as a mixed number. 3/5+4/5

• Add 1*3/8+7/8 using fraction strips.
• Add 1*3/5+2/5 using number line.
• Sam bought 2*1/2  kg of sugar from one shop and 6*1/2  kg of sugar from the other shop. How much sugar did he buy in all?
• Ron walked 3*2/5   km on Monday, 4*1/5   km on Tuesday and 2*1/5   km on Wednesday. What distance did he walk in all?
• A recipe calls for 2*2/5  cups of walnuts and 3*1/5  cups of pecans. How many cups of nuts are needed in all for the recipe?

Concept Map:

What have we learned:

•   Addition of mixed fractions using fraction strips
• Addition of mixed fractions on the number line