Use commutative/associative/distributive/identity properties and even-odd/sign parity rules.
Free, timed SHSAT practice sets on number properties & even/odd rules— every question includes a full worked explanation, and there's no account required.
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Distributive property: multiply the outside number by each term in the parentheses: \(a(b + c) = ab + ac\). It also makes mental math faster: \(6 \times 53 = 6 \times 50 + 6 \times 3 = 300 + 18 = 318\).
Commutative and associative properties: you can change the order or the grouping when you add or multiply. You cannot do this when you subtract or divide: \(8 - 3 \ne 3 - 8\).
Even and odd rules:
For a longer expression, test it with small numbers. If \(m\) is odd and \(n\) is even, try \(m = 3\) and \(n = 4\): \(m \times n + m = 12 + 3 = 15\), which is odd.
Common traps: multiplying only the first term in the parentheses (\(2 \times 9 + 3\)), and thinking odd \(+\) odd is odd.
Distribute 8 to both terms: \(8 \times 39 + 8 \times 8 = 376\). Multiplying only 39 by 8 gives \(320\). Multiplying only 8 by 8 gives \(103\). Adding all three numbers gives \(55\).
The distributive property multiplies 3 by EACH term inside the parentheses: \(3 \times (4 + 6) = 3 \times 4 + 3 \times 6\). \(3 \times 4 + 6\) multiplies only 4 by 3. \(3 \times 6 + 4\) multiplies only 6 by 3. \(3 \times 4 \times 3 \times 6\) multiplies the two products together instead of adding them.
Using a representative pair (even \(m=4\), even \(n=6\)): \(m \times n = 24\), which is even. This follows from the general parity rules (odd+odd=even, even+even=even, odd+even=odd; odd\(\times\)odd=odd, any even factor makes the product even). (Choosing odd comes from a wrong parity rule. Choosing "cannot be determined" misses that these rules work for every odd or even value. Choosing "depends on the value of \(m\) alone" ignores the part that \(n\) plays.)