1. Write the appropriate sign of the product.
(a) (- 3) x (+ 5) = - 15
(b) (+ 8) x (-6) = - 48
(c) (- 15) x (- 3) = + 45
(d) (+ 8) x (- 1) = - 8
(e) (+ 9) x (- 9) = - 81
(f) (- 100) x (- 6) = + 600
(g) (- 11) x (+ 11) = - 121
(h) 1000 x (- 100) = - 100000
2. Find the product of the following
(a) (-5) x 6 = - 30
(b) (-19) x (-3) = + 57
(c) 15 x (-4) = - 60
(d) (- 16) x (- 2) = + 32
(e) (- 5) x 10 x (- 100) = + 5000
(f) (- 25) x 4 x (- 4) = + 400
(g) 7 x (- 4) x (- 12) = +336
(h) (- 1) x (- 1) x (- 1) = - 1
(i) (- 14) x (- 10) x 6 x (- 1) = - 840
(j) (- 19) x 7 x 0 x (- 5) x 2 = 0
3. Find the value of the following
(a) 1234 x 567 - 234 x 567
= 567x (1234 - 234)
= 567x (1000)
Ans = + 567000(b) 739 x 99 - (- 739)
= 739 x 99 + 739
= 739 x 99 + 739 x 1
= 739 x (99 + 1)
= 739 x (100)
Ans = + 739000(c) (- 70) x (10 - 5 - 22 - 83)
= (- 70) x (+ 10 - 110)
= (- 70) x (- 100)
Ans = + 7000(d) 861 x (- 3) + (- 861) x 7
= 861 x (- 3) - 861 x 7
= 861 x (- 3 - 7)
= 861 x (- 10)
Ans = - 8610(e) 326 x (- 108) + 326 x 8
= 326 x (- 108) + 326 x 8
= 326 x (- 108 + 8)
= 326 x (- 100)
Ans = - 32600(f) 242 x (- 95) + 242 x (- 4) - 242
= 242 x (- 95) + 242 x (- 4) - 242 x 1
= 242 x (- 95 + (- 4) - 1)
= 242 x (- 95 - 4 - 1)
= 242 x (- 100)
Ans = - 242004. Write the integer which when multiplied by (- 1) gives
(a) -3
+ 3 x (- 1) = - 3
Ans = + 3(b) 19
(- 19) x (- 1) = + 19
Ans = - 19(c) 0
0 x (- 1) = 0
Ans = 0(d) 74
- 74 x (- 1) = + 74
Ans = - 74(e) - 69
+ 69 x (- 1) = - 69
Ans = + 69(f) - 100
+ 100 x (- 1) = - 100
Ans = + 1005. Compare the following:
(a) (7 + 6) x 10> 7 + 6 x 10
| (7 + 6) x 10 | 7 + 6 x 10 |
|---|---|
| = (13) x 10 | = 7 + 60 |
| = 130 | = 67 |
(b) (11 - 9) x 8> 11 - 9 x 8
| (11 - 9) x 8 | 11 - 9 x 8 |
|---|---|
| = 2 x 8 | = 11 - 72 |
| = 16 | = - 61 |
6. What will be the sign of the product of the following
(a) 7 negative and 3 positive integers.
= (-1) x (-1) x (-1) x (-1) x (-1) x (-1) x (-1) x (+1) x (+1) x (+1)
= - 1
Ans = - (Negative Sign)Note: If there are ODD number of negative integers the answer will be a negative integer. If there are EVEN number of negative integers the answer will be a positive integer.
In this question we have 7 negative integers. 7 is an odd number so the final solution will also ba a negative integer.
(b) 26 negative and 10 positive integers.
In this question we have 26 negative integers. 26 is an even number so the final solution will be a positive integer.
Ans = + (Positive Sign)(c) 11 negative and 11 positive integers.
In this question we have 11 negative integers. 11 is an odd number so the final solution will be a negative integer.
Ans = - (Negative Sign)(d) (-4) x (-5) x (-6) x....x (-13)
= (-4) x (-5) x (-6) x (-7) x (-8) x (-9) x (-10) x (-11) x (-12) x (-13)
In this question we have 10 negative integers. 10 is an even number so the final solution will be a positive integer.
Ans = + (Positive Sign)(e) (-4) x (-5) x (-6) x....x (-13)
= (-4) x (-5) x (-6) x (-7) x (-8) x (-9) x (-10) x (-11) x (-12) x (-13)
In this question we have 10 negative integers. 10 is an even number so the final solution will be a positive integer.
Ans = + (Positive Sign)7. Write True or False
(a) The product of two integers is always an integer.
= (-2) x (3)
= - 6
When we multiply any two integers we always get an integer.
Ans = True(b) The product of two integers with opposite sign is positive.
(- 2) x (+ 3) = - 6
(+ 4) x (- 5) = - 20
The product of two integers with opposite sign is always Negative.
Ans = False(c) The identity element of multiplication is 0.
2 x 0 = 0
(-2) x 0 = 0
2 x 1 = 2
(-2) x 1 = -2
The identity element of multiplication is 1.
Ans = False(d) Of the two integers if one is negative, the product must be negative.
(-2) x 4 = - 8
(-2) x (-4) = + 8
Of the two integers if one is negative, the product can be negative or positive.
Ans = False