Integers - Exercise 1(A)

Write all integers between:

(i) -9 and -3

(ii) -33 and -26

(iii) -5 and 2

(iv) -1 and 6

Answer

(i) All integers between -9 and -3 are:

-8, -7, -6, -5, -4

(ii) All integers between -33 and -26 are:

-32, -31, -30, -29, -28, -27

(iii) All integers between -5 and 2 are:

-4, -3, -2, -1, 0, 1

(iv) All integers between -1 and 6 are:

0, 1, 2, 3, 4, 5

Compare the integers :

(i) -16 and -61

(ii) -39 and 13

(iii) -236 and -362

(iv) -2 and 0

Answer

(i) -16 and -61

(16 < 61) ⇒ (–16 > –61) $\quad$ [∵ a < b ⇒ -a > -b]

(ii) -39 and 13

We know that every negative integer is less than every positive integer.

∴ –39 < 13

(iii) -236 and -362

(236 < 362) ⇒ (–236 > –362) $\quad$ [∵ a < b ⇒ -a > -b]

(iv) -2 and 0

We know that every negative integer is less than 0.

∴ –2 < 0

Evaluate :

(i) 20 - | -11 |

(ii) | -23 | - | -16 |

(iii) | -137 | + | 13 |

(iv) 6 - | -4 |

Answer

(i)

We have

20 - | -11 |

= 20 - 11

= 9 $\quad$ [∵ |-11| = 11]

(ii)

We have

| -23 | - | -16 |

= 23 - 16

= 7 $\quad$ [∵ |-23| = 23 and |-16| = 16]

(iii)

We have

| -137 | + | 13 |

= 137 + 13

= 150 $\quad$ [∵ |-137| = 137 and |13| = 13]

(iv)

We have

6 - |-4|

= 6 - 4

= 2 $\quad$ [∵ |-4| = 4 ]

Arrange the following integers in ascending order :

-9, 11, -23, 41, -37, 0, -5

Answer

Given negative integers are −9, −23, −37, −5.
In ascending order they are −37 < −23 < −9 < −5.

Given positive integers are 11, 41, 0.
In ascending order they are 0 < 11 < 41.

Hence, all the given integers in ascending order are:
−37 < −23 < −9 < −5 < 0 < 11 < 41.

i.e., −37, −23, −9, −5, 0, 11, 41.

Arrange the following integers in ascending order :

-31, 19, -50, -8, -23, 3, 8

Answer

Given negative integers are −31, −50, −8, −23.
In ascending order they are −50 < −31 < −23 < −8.

Given positive integers are 19, 3, 8.
In ascending order they are 3 < 8 < 19.

Hence, all the given integers in ascending order are:
−50 < −31 < −23 < −8 < 3 < 8 < 19.

i.e., −50, −31, −23, −8, 3, 8, 19.

Arrange the following integers in ascending order :

-2, 12, -43, 31, 7, -35, -10

Answer

Given negative integers are −2, −43, −35, −10.
In ascending order they are −43 < −35 < −10 < −2.

Given positive integers are 12, 31, 7.
In ascending order they are 7 < 12 < 31.

Hence, all the given integers in ascending order are:
−43 < −35 < −10 < −2 < 7 < 12 < 31.

i.e., −43, −35, −10, −2, 7, 12, 31.

Arrange the following integers in descending order:

-24, 16, -40, -5, -13, 6, -1

Answer

Given positive integers are 16, 6.
In descending order they are 16 > 6.

Given negative integers are −24, −40, −5, −13, −1.
In descending order they are −1 > −5 > −13 > −24 > −40.

Hence, all the given integers in descending order are:
16 > 6 > −1 > −5 > −13 > −24 > −40.

i.e., 16, 6, −1, −5, −13, −24, −40.

Arrange the following integers in descending order:

0, -7, 19, -23, -3, 8, 46

Answer

Given positive integers are 19, 8, 46.
In descending order they are 46 > 19 > 8.

Given negative integers are −7, −23, −3.
In descending order they are −3 > −7 > −23.

Also, 0 is less than positive integers and greater than negative integers.

Hence, all the given integers in descending order are:
46 > 19 > 8 > 0 > −3 > −7 > −23.

i.e., 46, 19, 8, 0, −3, −7, −23.

Arrange the following integers in descending order:

-31, -13, -49, 4, 37, -9, -52

Answer

Given positive integers are 4, 37.
In descending order they are 37 > 4.

Given negative integers are −31, −13, −49, −9, −52.
In descending order they are −9 > −13 > −31 > −49 > −52.

Hence, all the given integers in descending order are:
37 > 4 > −9 > −13 > −31 > −49 > −52.

i.e., 37, 4, −9, −13, −31, −49, −52.

Fill in the blanks:

(i) 0 is greater than every ............... integer.

(ii) Every negative integer is less than every ............... integer .

(iii) For any two positive integers a and b, if a < b, then -a ............... -b .

(iv) Modulus of a negative integer is always ............... .

(v) The largest negative integer is ............... .

(vi) The smallest positive integer is ............... .

Answer

(i) 0 is greater than every negative integer.

(ii) Every negative integer is less than every positive integer.

(iii) For any two positive integers a and b, if a < b, then −a > −b.

(iv) Modulus of a negative integer is always positive.

(v) The largest negative integer is −1.

(vi) The smallest positive integer is 1.