Page 91 - Maths Class 06

The absolute value (magnitude) of an integer is the distance between 0 and the integer +3 and -3 have
the same magnitude.

–3 –2 –1 0 1 2 3

EXAMPLE 1. Write the opposites of the following:
(a) Increase in weight (b) 50 km west (c) 305 AD
(d) Profit of ` 300 (e) 120 m above sea level
SOLUTION : (a) Decrease in weight (b) 50 km east (c) 305 BC
(d) Loss of ` 300 (e) 120 m below sea level

EX AM PLE 2. Represent the fol low ing num bers as in te gers with ap pro pri ate signs:
(a) An aeroplane is flying at a height of three thousand metres above the ground.
(b) A submarine is moving at a depth of eight hundred metres below the sea level.
(c) A deposit of two thousand rupees.
(d) A withdrawal of two hundred rupees.
SO LU TION : (a) + 3,000 (b) -800 (c) + 2,000 (d) -200

Comparison of Integers

Let us once again observe the number line given below:

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

You will observe that numbers increase as we move right and decrease as we move to the left.
For example, 7 > 4 and 7 lies to the right of the number 4.
Consider, the two numbers 3 and 8, obviously 3 8< and 3 lies to the left of number 8.

The inferences that can be drawn from the number line of integers are as follows:
1. An integer to the left is always smaller than the integer to the right.
2. All positive integers are smaller than zero.

3. Every negative integers are smaller than zero.
4. Every positive integer is greater than every negative integer.

5. The number farther from 0 on the right is greater e.g. 9 is farther than 4 from 0 on the right, so
( ) ( )9 > 4 .
6. The number farther from 0 on the left is smaller, e.g. -9 is farther than -4 from 0 on the left, so
- < -9 4.

NOTE

While comparing negative numbers the number with smaller value is greater. e.g. (–12) < –8.

EX AM PLE 3. Write five neg a tive in te gers:
(a) greater than –15 (b) less than –20

SO LU TION : (a) Five neg a tive in te gers greater than –15 are –14, –13, –12, –11, –10.
(b) Five negative integers less than –20 are –21, –22, –23, –24, –25.
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