Multiplying Odds and Evens
If _m_ is odd and _n_ is even, which of the following must be odd?
Incorrect.
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If _m_ = 1 and _n_ = 4, then $$\frac{mn}{2}= \frac{4}{2} = 2$$, which is even. Therefore, this expression may be even.
Correct.
The value of _m_ is odd, and, since _n_ is even, _n_ + 1 is odd. Therefore, their product must be odd.
Incorrect.
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If _m_ = 1 and _n_ = 2, then $$(1 + 1) \cdot 2 = 4$$, which is even. Therefore, this expression may be even.
Incorrect.
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If _m_ = 1 and _n_ = 2, then 3_mn_ = 6, which is even. Therefore, this expression may be even.
Incorrect.
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If _m_ = 1, then $$\frac{3m + 1}{2}= \frac{4}{2} = 2$$, which is even. Therefore, this expression may be even.
$$\frac{mn}{2}$$
$$m(n + 1)$$
$$(m + 1)n$$
$$3mn$$
$$\frac{3m + 1}{2}$$
