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प्रश्न
For any integer a, what is (− 1) × a equal to?
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उत्तर
As per the question, three cases will be possible because we can divide the number line among negative integers, 0 and positive integers. So,
In Case 1: When a is any negative integer, that is, −a, then (−1) × (−a) = a
In Case 2: When a is 0, then (−1) × 0 = 0
In Case 3: When a is any positive integer, that is, a, then (−1) × a = −a
Thus, the possible answers are a, 0 and −a
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संबंधित प्रश्न
Starting from (−1) × 5, write various products showing some pattern to show (−1) × (−1) =1.
8 × (−4) = 32
(−12) × (−9) = _______
Say true or false.
The product of two negative integers is a positive integer
Which of the following is the multiplicative identity for an integer a?
______ × (–1) = 47
(–1) is not a multiplicative identity of integers.
Match the following:
| Column I | Column II |
| (a) a × 1 | (i) Additive inverse of a |
| (b) 1 | (ii) Additive identity |
| (c) (–a) ÷ (–b) | (iii) Multiplicative identity |
| (d) a × (–1) | (iv) a ÷ (–b) |
| (e) a × 0 | (v) a ÷ b |
| (f) (–a) ÷ b | (vi) a |
| (g) 0 | (vii) –a |
| (h) a ÷ (–a) | (viii) 0 |
| (i) –a | (ix) –1 |
Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:
u × v = u
x × w = w
u + x = w
- v
- w
- x
Explain your reasoning using the properties of integers.
Determine the integer whose product with (–1) is 0.
