ADD AND SUBTRACT INTEGERS USING COUNTERS

We can use the following colored counters to model the sum of integers with different signs. 

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 : 

Evaluate :

(-4) + (+3) 

Solution : 

Start with four negative counters to represent -4 and three positive counters to represent +3. 

Mark the zero pairs. 

In the above figure, if you remove the three zero pairs, the result will be one negative counter. 

So, the answer is -1. 

Therefore,

(-4) + (+3)  =  -1

Example 2 : 

Evaluate :

(+5) - (+2) 

Solution :

Write the given subtraction as addition. 

(+5) - (+ 2)  =  (+ 5) + (-2)

Start with five positive counters to represent +5 and two negative counters to represent -2. 

Mark zero pairs. 

In the above figure, if you remove two zero pairs, the result will be three positive counters. 

So, the answer is +3. 

Therefore,

(+5) - (+2)  =  +3

Example 3 : 

Find the sum of +4 and -7. 

Solution : 

Start with four positive counters to represent +4 and seven negative counters to represent -7. 

Mark zero pairs.

In the above figure, if you remove four zero pairs, the result will be three negative counters. 

So, the answer is -3. 

Therefore,

(+4) + (-7)  =  -3

Example 4 : 

Evaluate :

(+4) + (+3) 

Solution : 

Start with four positive counters to represent +4 and three positive counters to represent +3. 

In the above figure, there are seven positive counters.

So, the answer is 7. 

Therefore,

(+4) + (+3)  =  +7 

Example 5 : 

Evaluate :

(-5) + (-2) 

Solution : 

Start with five negative counters to represent -5 and two negative counters to represent -2. 

In the above figure, there are seven negative counters. 

So, the answer is -7. 

Therefore,

(-5) + (-2)  =  -7

Example 6 : 

Find the sum of +2 and -3. 

Solution : 

Start with two positive counters to represent +2 and three negative counters to represent -3. 

Mark zero pairs.

In the above figure, if you remove two zero pairs, the result will be one negative counter. 

So, the answer is -1. 

Therefore,

(+2) + (-3)  =  -1

Example 7 : 

Find the sum of -5 and +2. 

Solution : 

Start with five negative counters to represent -5 and two positive counters to represent +2. 

Mark zero pairs.

In the above figure, if you remove two zero pairs, the result will be three negative counters. 

So, the answer is -3. 

Therefore,

(-5) + (+2)  =  -3.

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