Page 120 - Start Up Mathematics_6

Example 8: (a) Write the next four negative integers greater than –7.

(b) Write the next four negative integers less than –20.
Solution: (a) –6, –5, –4 and –3 (b) –21, –22, –23 and –24
Example 9: Write True or False for the following statements. Write the false statement correctly.

(a) –12 is to the right of –11 on a number line.
(b) +50 is to the right of –50 on a number line.
(c) The smallest positive integer is +1.

(d) There is no integer between –1 and 1.
(e) There is no greatest or smallest integer.
Solution: (a) False; Correct Statement: –12 is to the left of –11 on a number line.

(b) True
(c) True
(d) False; Correct Statement: 0 is an integer and it lies between –1 and 1.

(e) True
Example 10: Draw a number line and answer the following:
(a) Which number is reached if we move 5 numbers to the right of –3?
(b) Which number is reached if we move 6 numbers to the left of +3?

(c) In which direction should we move to reach –8 from –2?
Solution: (a)
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
We will reach 2.

(b)
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
We will reach –3.

(c) –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

We should move towards left to reach –8 from –2.

Absolute Value of an Integer
The numerical value of an integer regardless of its sign (positive or negative) is called the absolute
value of an integer. Absolute value of an integer a is denoted by a. It is either positive or zero.
For example, the absolute value of –7 is equal to 7. Symbolically, we write –7 = 7.

The absolute value of 3 is equal to 3. Symbolically, we write 3 = 3.
The absolute value of 0 is 0 itself and is written as 0 = 0.

Absolute value of an integer is also known as its modulus.

Example 11: What is the absolute value of (x + 3), if x is less than –3?
Solution: Since, x < –3, therefore x + 3 < 0.
Hence x + 3 = –(x + 3)

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