29
Opposite numbers. The absolute value (modulus)
Textbook, pp. 132–137
GoalKnow opposite numbers and the absolute value (modulus) of a number; compute it.
New words
opposite numbers · qarama-qarshi sonlarabsolute value (modulus) · modulorigin · koordinata boshidistance · masofa
Explanation
Two numbers that are the same distance from the origin but on opposite sides are opposite numbers: a and −a. For example 7 and −7. The opposite of 0 is 0, and −(−a) = a. The absolute value (modulus) of a number is the distance from its point to the origin. It is written |a|: |−5| = 5, |5| = 5, |0| = 0. A modulus is never negative. Opposite numbers have equal moduli: |a| = |−a|.
Worked examples
The opposite of −7 is 7, of 12 is −12. |−3| + |5| = 3 + 5 = 8.
The numbers with modulus 6 are 6 and −6, since both are 6 units from 0.
Class activity
“Mirror”: on the floor number line, 0 acts as a mirror. The teacher says a number and a pupil stands on its mirror image, the opposite number. Then the two pupils count their distance from 0 (the modulus).
Practice
1
Write the opposite of −7.
7
2
Find |−12|.
12
3
Compute |−3| + |5|.
8
4
Why can a modulus never be negative?
The modulus is a distance, and a distance is zero or positive.