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Model Additions of Fractions with Examples

Key Concepts

  • Addition of fractions using an area model concept
  • Addition of fractions using  fraction strips
  • Addition of fractions using number line.

Addition of fractions: 

Addition of fractions can be modelled in three ways: 

  1. Using an area model concept 
  1. Using fraction strips  
  1. Using number line 

Let us learn one by one 

  1. Using an area model concept 
    An area model is a great visual tool because it can be used to make sense of virtually any fraction problem. 
    An area model represents a fraction as a rectangle, divided into equal parts. 
    For example, 
    To represent  3 / 5 , we divide a rectangle into 5 equal parts and shade 3 parts. 

Using an area model is also helpful in adding and subtracting fractions with like and unlike denominators. 

To add we will follow the following steps: 

  • Set up area models for each fraction. 
  • Then over lay the models to add them in case of like fractions.  

Example 1:  

Add   5 / 6+ 3 / 6

Solution:  

First divide a rectangle into 6 equal pieces. That means each individual piece is  1 / 6 of the whole. 

If 5 pieces are shaded, they represent the fraction 5 / 6. 

Similarly, divide a rectangle into 6 equal pieces and shade 3 pieces. They represent the fraction 3 / 6

Now, To add  5 / 6 and 3 / 6, we need to shade 8 parts out of 6 parts,  

When one over laid on the other, there are 8 shaded parts.  

We know that if we shaded 6 parts out of 6 parts it gives us a whole. 

To shade the rest of two parts, we need to consider one more rectangle divide it into 6 equal parts and shade 2 parts.  

Example 2: 

Mary and John are working on a sports banner. They painted 5 / 8 of the banner blue and 2 / 8 of the banner yellow.  How much of the banner have they painted? 

Solution:  

Here, let us consider the banner I rectangular form and divide into 8 equal parts. 

Out of these 8 parts, 5 parts are coloured in blue. 

And two parts are coloured in yellow. 

Totally there are 7 parts painted in blue and yellow colors. 

  1. Using Fraction strips 
    Fraction strips are rectangular pieces (electronic or copied on paper strips) to represent different parts of the same whole. They can be cut apart and manipulated to see how various parts can be added together to make the whole or compare different fractional amounts for equivalency 
  • They can be of various colours and sizes 
  • Fraction strips help us to visualize and explore fraction relationships 

Example 1:

Add   1 / 2+ 1 / 4

Example 2 :

Find 5 / 10+ 2 / 10

Solution: 

Divide one whole into 10 equal parts 

Use five 1 / 10 strips to show 5 / 10, colour them in blue 

Use two 1 / 10 strips to show 2 / 10 and colour them in yellow     

Hence five 1 / 10 strips joined with two 1 / 10  strips, we will get seven 1 / 10 strips 

  1. Using Number line: 
    To add fractions using number line, we need to know how to represent a fraction on the number line 
    For example, to show 3/4 on number line 
    First, draw a number line that goes from 0 to 1 

Then, divide the number line into equal parts. The denominator tells us the total number of parts the number line to be divided into Since the denominator is 4, we will divide the number line into 4 equal parts  

Then, label the fractions 

The numerator tells us the number of parts we are talking about. We always start with ‘0’ 

0 means 0/4 and 1 means 4/4

We can show 3/4 in the following way 

Now to add fractions on the number line, we need draw the number line as per the given fractions 

Firstly, look at the first fraction we are adding and plot it on the number line 

Remember, we can add only like fractions using Number line 

HOW TO ADD FRACTIONS ON THE NUMBER LINE? 

Next, look at the second fraction we are adding, then count forward or jump forward that many steps from the first fraction 

Example 1: 

Add 4/6+1/6 Using number line 

Solution: 

Step1: Look at the first fraction and plot it on the number line 

Here the first fraction is 4/6

Step 2:  

Look at the second fraction to be added, move forward that many steps from  4/6

Since the second fraction is  1/6, move one step forward 

We can simply add the numerators and write the denominator once. 

Example 2:    

Add 3/8+3/8 using number line 

Solution: 

Step 1: Draw number line and label 3/8

Step 2: Look at the fraction to be added and move forward that many steps 

Since the fraction to be added is

3838

   move three steps forward 

Remember: 

To add fractions on a number line 

  • The fractions must have the same denominator 
  • Use one number line only to add fractions 
  • Jump forward from the first fraction. The numerator of the fraction we are adding will tell us the number of steps to be taken.

Exercise:

  • There are two windows in Patrick’s kitchen. The larger window is 13/20 meters long. The smaller window is 5/20 meter long. What is the total length of both the windows? Use any method to get the total length
  • Violet swam 5/6 miles on Monday and  4/6 miles on Tuesday. How far violet did swam in all? Use fraction strips to find the total.
  • Find the sum of 4/6+1/6 using number line
  • Leona mailed two envelops. One weighed 3/10 pounds and the other weighed 6/10 pounds. How much did envelop weighed together? Use fraction strips to find the total weight.
  • Debbie spent 3/4 of an hour cleaning her room and  1/4 of an hour cleaning her bathroom. How many hours did Debbie spent cleaning? Use Number line to find the total time
  • Add 3/12+6/12 using fraction strips
  • Larry read 1/6 of the book on Monday and another 4/6 of the book on Tuesday. What fraction of his book has Larry read in all?

Concept Map:

What have we learned:

  • We learned to add fractions using an area model concept
  • We learned to add fractions using fraction strips
  • We learned to add fractions using Number line.

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