MODELING INTEGER SUBTRACTION

We can use the following colored counters to model the subtraction of integers.

When you add a positive integer (yellow counter) and a negative integer (red counter), the result is 0.

1 + (-1)  =  0

One red and one yellow counter form a zero pair. 

Example 1 : 

Subtract -3 from -4. 

Solution : 

We have to find the result of

-4 - (-3)

Start with 4 negative counters to represent -4.

Take away 3 negative counters to represent subtracting -3.

Then, we have 

In the above figure, we have left with one negative counter.

So, the result is -1. 

Therefore,

-4 - (-3)  =  -1

Example 2 : 

Subtract -3 from 6. 

Solution : 

We have to find the result of

6 - (-3)

Start with 6 positive counters counters to represent 6.

Because we subtract -3, we have to take away three negative counters. 

But, we don't find negative counters in the above figure. 

In order to have negative counters, let us add three zero pairs. 

Now, take away 3 negative counters to represent subtracting -3.

Then, we have

In the above figure, we have left with 9 positive counters.

So, the result is 9. 

Therefore, 

6 - (-3)  =  9

Example 3 : 

Subtract 4 from -6. 

Solution : 

We have to find the result of

-6 - (4)

Start with 6 negative counters counters to represent -6.

Because we subtract 4, we have to take away four positive counters. 

But, we don't find positive counters in the above figure. 

In order to have positive counters, let us add four zero pairs. 

Now, take away 4 positive counters to represent subtracting  4.

Then, we have

In the above figure, we have left with 10 negative counters.

So, the result is -10. 

Therefore, 

-6 - (4)  =  -10

Example 4 : 

Subtract 4 from 6. 

Solution : 

We have to find the result of

6 - (4)

Start with 6 positive counters to represent 6.

Take away 4 positive counters to represent subtracting 4.

Then, we have 

In the above figure, we have left with 2 positive counters.

So, the result is 2. 

Therefore, 

6 - (4)  =  2

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