Page 39 - Mathematics

Absolute value of a real number

The absolute value of a real number x, denoted by x is the non-negative value of

x regardless of its sign. For example 2 = and 2−= 2.Consider the following
2
number line.

2 units 2 units Tanzania Institute of Education

The distance from 0 to −2 and that from 0 to 2 is the same, that is 2 units. Thus,

2 is an absolute value of both 2 and −2. The absolute value of a number is the
magnitude of that number regardless of its sign.

x
The absolute value of a number x is written as x such that x = if x ≥ and
0
x
x = − if x < 0,and its distance is represented on a number line from 0. This
distance is always positive or zero.
1 1
For example; 0.75 = 0.75, − 0.143 = 0.143, − = , 0 = 0, and 2−= 2.
2 2
,
In general, for any two positive and negative numbers x and x− their absolute
values are equal, that is, x = − . x

Example 2.19

Evaluate each of the following:
(a) 2− (c) 0 (e) 36− × (g) 52+

(b) 10 (d) 82− (f) 26−

Solution

2
2
(a) −= (d) 82− = 6 = 6 (g) 52+ = 7 = 7

(b) 10 = 10 (e) 3 6− × = − 18 = 18
4
0
(c) 0 = (f) 26− = −= 4

Example 2.20 Mathematics Form One

13 4
Find the absolute value of − +
10 5

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Mathematics form 1.indd 33 25/10/2024 09:51:10
Mathematics form 1.indd 33