Model Subtractions of Fractions

Key Concepts

• Subtract fractions using fraction strips
• Subtract fractions using numberline
• Subtract fractions directly.

Introduction: 

We know that fractions are referred to as part of a whole. We can easily add two like fractions like the way we add whole numbers. 

We learned to add like fractions using fraction strips, using number lines and direct addition. 

When we added two like fractions directly, the steps we followed are 

1. Add the numerators  

2. Write the denominator once  

For example, 

3/5+1/5= 3+1/5= 4/5

Subtraction of fractions is also the same as the addition of fractions. 

The different ways of subtracting like fractions are 

1. Using fraction strips  

2. Using number lines  

3. Subtracting directly 

While subtracting directly, we will be subtracting the numerators rather than adding them up 

Let us learn to subtract fractions in different methods. 

Using fraction strips: 

Using fraction strips, we can represent a fraction with several unit fractions  

For example 

and so on …… 

In the same way, we can model a subtraction equation with several unit fractions and then we can take an amount away to find the difference. 

Let us look at the example 

Fractions that have like denominators are the fractions with common denominators. That means their denominators are the same. 

7/8−2/8

To subtract like fractions using fraction strips, we first look at the common denominator and divide a whole into that many unit fractions. 

Hence, while finding the difference using fraction strips, we remove the number ofshaded parts we were subtracting and count how many are left. 

7/8−2/8= 5/8

Example 1: 

Mr. Walter uses 4/5

of a color sheet for making greeting cards. How much of the color sheet is left? 

Solution: 

It is given that 4/5 of a color sheet is used to make greeting cards. 

Here, the denominator says in how many parts the color sheet is divided and the numerator says how many parts are used.  

If we represent one color sheet with  

It has been divided into 5 equal parts. 

Out of these 5 equal parts, 4 parts are used  

Now from the above fraction strip, we can say that one part out of 5 parts is left with him. 

5/5−4/5= 1/5

Example 2:  

A flower garden is divided into eighths. If  2/8 of the garden is used to grow yellow roses. What fraction is left to grow other flowers? 

Solution: 

It is given that a garden is divided into eighths. 

That means if represented by the garden It is divided into eighths 

Out of these 8 parts, 2/8  of the garden is used to grow yellow roses 

That is 

The fraction of the garden left for other flowers is 

⸫ 8/8− 2/8= 6/8

Using number line 

What is a number line? 

A number line is a straight, horizontal line with numbers placed at even increments along the length. 

How to represent a fraction on a number line? 

      To represent fractions on a number line, follow these steps: 

• Split up the number line between 0 and 1 into the number of parts shown by the denominator. Make sure each of the parts is the same size. 
• Starting at 0, count forward the number of parts shown by the numerator. 

• Mark your point on the number line. 

So, using number lines, we can add or subtract fractions. Let us use the number line, for example, 2 above. 

Example: A flower garden is divided into eighths. If  [2/8] of the garden is used to grow yellow roses. What fraction is left to grow other flowers? 

Let us draw a number line divided into eighths. 

8/8= 1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8

Now since 2/8 of the garden is used to grow yellow roses, let us separate 2/8 from 8/8

8/8= 1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8

1/8+1/8=2/8

      We are left with 1/8+1/8+1/8+1/8+1/8+1/8= 6/8

      That is   8/8−2/8= 6/8

      That is     

8/8−2/8 = 6/8

Example 2:  

Find 5/7−2/7

Solution: 

First draw a number line and plot 5/7

Now, let us look at the subtrahend 2/7, the part that has to be taken away from 5/7.

2/7 means, 2 out of 7 parts, we can count backwards or jump backwards from the minuend 5/7. 

So, subtracting 2/7 from 5/7  means we jump backwards 2 steps. 

⸫ 5/7−2/7=3/7

Example 2: 

Find  7/9− 3/9

Solution: 

Draw a number line and plot 7/9

Since we need to subtract 3/9, jump 3 steps backwards from 7/9

⸫7/9 − 3/9= 4/9

Subtracting directly 

To SUBTRACT fractions with like or the same denominator, just subtract the numerators, then copy the common denominator. Always reduce your final answer to its lowest term. 

For example, 

Find 10/27−4/27

Solution: 

The two fractions have the same denominators, which means we can subtract them easily. 

So, subtract the numerators, then write the denominator once. 

That is

10−4/27= 6/27

The answer can still be further simplified using a common divisor of 3. 

6/27÷3/3= 29

Example 2: 

Rick shared his bag of grapes with friends. He gave 2/10  of the bag to Melisa and 4/10 of the bag to Ryan. What fraction of the bag of grapes does Rick have left? 

Solution: 

Given that Rick has a bag of grapes and he shared with his friends 

Let us divide the bag into 10 parts.  

Fraction of bag of grapes Rick gave to Melisa = 2/10

Fraction of bag of grapes Rick gave to Ryan = 4/10

Total fraction of bag of grapes given to his friends = 2/10+4/10=2+4/10=6/10

The fraction of bag of grapes left with Rick = 10/10−6/10= 4/10

The answer can still be further simplified using a common divisor 2  

4/10÷2/2=2/5

⸫ The fraction of bag of grapes left with Rick = 2/5

 Concept Map:

Exercise:

1. Indicate hops on each number line and complete the subtraction sentences.

             12/13-8/13 = ___________

• Captain has  of the pizza and he eats  of it. What fraction is left with him?
• Patrick grated 2/3 of a block of cheese to make macaroni. What fraction of the block is left?
• Jennifer wants to layer her dollhouse pillows in blue and green fabrics. She uses 1/9 of a yard of blue fabric and 4/9 of a yard of green fabric. How many more yards of green fabric does Jennifer use than blue fabric?
• It snowed 65/7 inches in Raleigh on Christmas Eve. The town recorded 33/7 inches of snow on New Year’s Day. How much more snow was registered on Christmas Eve than on New Year’s Day?
• Arthur has of a 7/8 pound of crushed nuts. If of a 3/8 pound of nuts is used to garnish a few crumble pies, what fraction of the nuts are left?
• Daisy had 9/10 of jar of candies. She shared some of them with her friends, and now she is 3/10 left with of the jar. What fraction of the candies was shared with her friends?
• A farmer had 5/4 crates of red and white onions. If 1/4 of a crate contained red onions, what fraction of crate contained white onions?
• If of a 4/5 canwas filled with pinapples and Ryan 2/5 ate of the can, what fraction of the canned pinapples remained?

 What have we learned:

• Subtraction of like fractions using fraction strips
• Subtraction of fractios using numberline
• Subtractig fractions directly