1. Explain integers?
The whole numbers like 0,1,2,3, --- are also called positive numbers.The set of whole numbers along with the negative numbers are called integers.So integers include positive integers,negative integers and zero.The set of integers is denoted by Z or I.
Z = { ... -5, -4, -3, -2,- 1, 0, 1, 2, 3, 4, 5, ... }
2. Arrange the following numbers in ascending order -320 , -226 , -91 , 0 , 72 , 188
Let us put the numbers on the number line
The numbers are in the decreasing order from right to left.So, arranging the numbers in the ascending order we get -320, -226 , -91 , 0 , 72 , 188.
3. Arrange the following numbers in descending order -23, -176 , +8 , +26 , -4 , +100
Let us put the numbers on the number line.
Since the numbers are arranged in descending order from right to left, we can write +100 , + 26 , +8 , -4 , -23 , -176.
4. Add +5 and (-3)
Consider +5 on the number line.The operation between +5 and -3 is addition.But the minus sign for 3 changes the direction of the operation.So the final operation is 5 - 3.Here we move three steps towards left from +5.
Hence ( +5 ) + ( -3 ) is equal to +2.
5. Add (- 4 ) and ( + 2)
Consider -4 on the number line. The operation between (- 4) and ( +2 ) is addition.So addition of +2 is moving in the positive direction, which means moving towards the right of - 4.
Hence ( - 4 ) + ( + 2 ) = -2.
6. Explain absolute value ?
The absolute value of an integer is the distance of that integer from 0 irrespective of the direction , negative or positive.The symbol | | stands for the absolute value of an integer.
7. Solve the problems given below
a) ( - 11 ) + ( + 4 ) b) (- 21 + 32 )
( a ) - 11 + ( + 4 ) = -11 + 4 = -7
( b ) (- 21 + 32 ) = 32 - 21 = 11.
8. Find the solution of the following
a) (- 16 ) - ( - 15 ) b) (- 2 ) + ( -16 )
( a ) (- 16 ) - (- 15) = -16 + 15 = -1
( b ) ( - 2 ) + ( - 16 ) = -2 - 16 = -18 ( Since both have the same sign )
9. Find the product of the following integers
a) (- 7 ) and ( + 9 ) b) (- 6 ) and ( - 12 ) c) 11 and 15
( a ) (- 7 ) × ( +9 ) = -7 × 9 = -63 [(-) × ( + ) = ( - ) ]
( b ) (- 6 ) × (- 12 ) = + 72 [ ( - ) × ( - ) = ( + ) ]
( c ) 11 × 15 = 165 [ ( + ) × ( + ) = ( + ) ]
10. Find the product of the following
a) -16 and 1/256 b) -1/648 and 9
( a ) -16 × 1/256 = 
(Since 256 = 16 ×16 )
= -1/16 (Since ( - ) × ( + ) = ( - ) )
( b ) -1/648 × 9 = 
( Since ( - ) × ( + ) = ( - ) )
11. Find the following
a) -56 × -1/8 b)-4 ×-1/64
( a ) -56 × -1/8 = -7 × 8 × -1/8 = 7 ( ( - ) × ( - ) = ( + ) )
( b ) -4 × 1/64 = 
= -1 × -1/16 = 1/16 [ ( - ) × ( - ) = ( + ) ]
12. Solve the following
a) 16 × 5/4 × -8 b) (-38) × ( + 25 ) × (-2/5 )
( a ) 16 × 5/4 = 4 × 5 = 20
20 × -8 = -160 [ ( + ) ( - ) = ( - ) ]
ie, 16 × 5/4 × -8 = -160
( b ) (- 38 ) × ( + 25 ) × (-2 /5 )
= ( 25 × -2/5 ) × (- 38 )
= (5 × -2 ) × (- 38 )
= -10 × -38
= 380 [ ( - ) × ( - ) = ( + ) ]
13. Divide the following
a) (+350 ) ÷ (+ 35) b) (+ 720 ) ÷ ( +9 )
( a ) ( + 350 ) ÷ ( + 35 ) = 
( b ) ( + 720 ) ÷ ( + 9 ) = 
14. Divide the following
a) -300 ÷ -5 b) -1584 ÷ - 36
( a ) -300 ÷ -5 = 
( b ) - 1584 ÷ - 36 = 
15. Divide the following
a) 0 ÷ 126 b) 0 ÷ -173
( a ) 0 ÷ 126 = 0/126
= 0 [ If we divide zero by any number we get zero as answer ]
( b ) 0 ÷ -173 = 0/-173
= 0 [ If we divide zero by any number we get zero as answer ]
16. Write the absolute value for the following
a ) | -267 | b) | 380 |
( a ) | - 267 | = 267
( B ) | 380 | = 380
17. Solve | -6 + ( - 7 ) | ?
We will solve this problem by applying the BODMAS rule.
Therefore, | -6 + ( - 7 ) | = | -6 + -7 |
= | - 13 | = 13.
18. Solve | 32 - ( 8 ) | ?
| 32 - ( 8 ) | = | 32 - 8 | = | 24 | = 24.
19. Verify whether the following are true
a) | 7 + 5 | = | 7 | + | 5 | b) | 22 + 8 | = | 22 | + | 8 |
( a ) The L.H.S can be calculated as |7 + 5 | = | 12 | = 12
The R.H.S can be calculated as | 7 | + | 5 | = 7 + 5 = 12
ie, | 7 + 5 | = | 7 | + | 5 | is true.
( b ) The L.H.S can be calculated as | 22 + 8 | = | 30 | = 30
The R.H.S can be calculated as | 22 | + | 8 | = 22 + 8 = 30
ie, | 22 + 8 | = | 22 | + | 8 | is true.
20. Check whether the following are true
a ) | - 12 - ( - 4 ) | = | - 12 | - | - 4 | b) | -6 + ( +4 ) | ≠ | -6 | + | 4 |
( a ) The L.H. S can be calculated as
| -12 - ( - 4 ) | = | -12 + 4 | = | - 8 | = 8
The R.H.S can be calculated as
| -12 | - | -4 | = 12 - 4 = 8
ie, | - 12 - ( - 4 ) | = | - 12 | - | - 4 | is true
( b ) The L.H.S can be calculated as
| -6 + ( + 4 ) | = | -6 + 4 | = | -2 | = 2
The R.H.S can be calculated as
| -6 | + | 4 | = 6 + 4 = 10
ie, | -6 + (+4 ) | ≠ | -6 | + | 4 | is true.
