Question

(i) For any integer a, what is (–1) × a equal to?
(ii) Determine the integer whose product with (–1) is
(a) –22
(b) 37
(c) 0

Answer 1

(i) (-1) × a = -a
(ii) (-1) × 0 = 0 [∵ a × 0 = 0] Hence (c) 0 is the required integer.

Answer 2

i) For any integer a, multiplying by −1 results in the negation of a:
\((-1) \times a = -a \quad (\text{where } a \text{ is any integer})\)

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ii) Solve the following equations to find the required integer a:

(a) \( ?×(−1)=−22\)
Let a be the required integer:
\(a \times (-1) = -22\)
\(−a=−22\)
\(a=22\)
Substituting a back into the equation:
\(22 \times (-1) = -22\)
Thus, the required integer is 22.

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(b)\(? \times (-1) = 37\)

Let a be the required integer:
\(a \times (-1) = 37\)
\(−a=37\)
\(a=−37\)
Substituting a back into the equation:
\(-37 \times (-1) = 37\)
Thus, the required integer is -37.

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(c) \( ? \times (-1) = 0\)
Let a be the required integer:
\(a \times (-1) = 0\)
\(−a=0\)
\(a=0\)
Substituting a back into the equation:
\(0 \times (-1) = 0\)
Multiplying any number by 0 results in 0.
Thus, the required integer is 0.