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Workbook

ABSOLUTE VALUE

The absolute value of a number a, denoted by a , is the distance between the origin and the point on
the number line with coordinate a. The point with coordinate -3 is three units from the origin, so we
write 3 3  and say that the absolute value of -3 is 3.

Definition: For any real number a, the absolute value of a, denoted by a , is defined by

 a,if a 0
a  
  a,if a 0

Remark: For any non-zero real number a , the number a is always positive.

 a R, a 0and a   a 

Example 1: Find the value of each of the following.

a) 4 = b) 4 = c) 0 = d) 2 3 = e) 3 2 =

f)  4 = g) 4.6 = h)   2 = I)   5 =
3

Example 2: Calculate the following.

a) | -8 | + | 2 | - | -2 |= b) 3 5 8 4     3 2 =

1 1
3

c)     5 2 =
3 2 4 4 3

d) 1 3 7   = e) 3  6 1 8    2 

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