A good way to add or subtract integers is to understand the concept of absolute value. Knowing this idea, you can add and subtract integers easily.
 
 
Absolute Value
 
Absolute value of an integer is its distance from zero. Opposite numbers have the same absolute value. For example, the absolute values of –3 and 3 or –5 and 5 are the same (Figure 2.7).

Figure 2.7

The absolute value of any number is a whole number. Absolute value of a number usually shown by placing the number between segments | |. These are some samples of showing absolute values of numbers.

1. |–12| = 12
    
2. |+39| = 39
    
3. |20| = 20
    
4. |–31| = 31
    
5. |0| = 0

Practice 4. Which number is at the furthest point from zero on a number line?
–2, 23, –34, 8, 29, 32, –22
 
Answer
 
 
How to Add and Subtract Integers?
 
In adding and subtracting integers, we always deal with two cases.
 

1. All the integers are of like signs. Examples below are of this case.
    
   1. + 32 + 121 + 45 + 10 + 38
       
   2.  –21 – 45 – 67 – 76 – 101 – 3
       

   In all such cases, add the absolute values of the numbers. Then choose the sign of the numbers as the sign of the result.
   For example, in (a) the sign of the result is +. In (b), the sign of the result is –.
    

2. Two integers are of unlike signs. (–12 + 45) or (43 – 121) are samples of such case. To find the result, subtract the smaller absolute value from the larger one. Determine the sign of the number with larger absolute value. Use this sign as the sign of the result.
   For example, in (–12 + 45) or (43 – 121), we find the results as below.
   
       –12 + 45 = +33
       43 – 121 = –78.

Practice 5. Calculate.

(a) 32 + 121 + 22 + 56 + 11
 
(b) –11 – 32 – 43 – 11 – 54
 
(c) 21 + 11 – 5 + 23 – 7 – 23

 
Answer
 
Practice 6. Place the sum of each row in the right column. Then add up the numbers in this column. This should be zero.

Table 2.8
 

Answer

 
Real Life Application 3. In Table 2.10, the operations of a company are shown during five days. Using integers, find the final profit of the company.

Table 2.10

Answer

 
General Rules for Combing Integers

If a and b are integers, then

a + (–b) = a – b
a – (+b) = a – b
a – (–b) = a + b
a + (+b) = a + b

Practice 7. Compute

(a) 32 – (+45)
 
(b) –49 + (–23)
 
(c) 31 + (+28)
 
(d) –46 – (–26)

Answer
 
 
Practice 8. Calculate

(a) 12 + (–32) – 25
 
(b) –21 – (+43) + 19
 
(c) 15 – (–32) + 17
 
Answer
 
 
Real Life Application 4. The altitudes of Valley A and Mountain B are
–84 ft and 63 ft. What is the difference between these altitudes?

Answer


Practical Exercise 1 Compute
 
(a) –11 + 23 – (+31) – (–87)
 
(b) 34 – 43 – (–11) + (–34)
 
(c) –24 – (–11) – (–29)
 

Answer
 

Now let's do Practice Exercise 2-2 (top).