Page 44 - ICSE Math 6

Example 6: In each of the following pairs, which integer is to the right of the other on the number
line?
(a) 2, 7 (b) –2, –9 (c) 0, –3 (d) –11, 100
Solution: (a) On the number line, 7 is to the right of 2.

(b) On the number line, –2 is to the right of –9.
(c) On the number line, 0 is to the right of –3.
(d) On the number line, 100 is to the right of –11.
Example 7: Write all the integers which lie between the given pairs of integers in increasing order.
(a) 0 and –5 (b) –3 and 3 (c) –101 and –97

Solution: (a) Integers between 0 and –5 in increasing order are –4, –3, –2 and –1.
(b) Integers between –3 and 3 in increasing order are –2, –1, 0, 1 and 2.
(c) Integers between –101 and –97 in increasing order are –100, –99 and –98.
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) The smallest positive integer is +1. (b) There is no integer between –1 and 1.

(c) There is no greatest or smallest integer.
Solution: (a) True (b) False; Correct Statement: 0 is an integer and it lies between –1 and 1.
(c) True
Example 10: Draw a number line and answer the following.
(a) Which number is 5 units to the right of –3?

(b) Which number is 6 units 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
The number which is 5 units to the right of –3 is 2.
(b)
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
The number which is 6 units to the left of +3 is –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.
Example 11: Write the following integers in ascending order.
–5, 5, 11, –2, 0, 9

Solution: For positive integers, order follows as 5 < 9 < 11.
For negative integers, order follows as –5 < –2.
We know that 0 is greater than every negative integer and smaller than every positive
integer.
Thus, –5 < –2 < 0 < 5 < 9 < 11

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