Parity of Arithmetic Expressions

Transcript

Parity of Arithmetic ExpressionsThe goal of this page is to test if we can identify Odd or even Numbers just by looking at the structure of the math, without actually doing the difficult calculations. Parity rules (Cheat Sheet) Before solving, remember these three simple rules: Addition/Subtraction: Odd ± Odd = Even (e.g., 3 + 5 = 8) Even ± Even = Even (e.g., 2 + 4 = 6) Odd ± Even = Odd (e.g., 3 + 2 = 5) Multiplication: If you multiply any number by an Even number, the result is always Even. Odd × Odd is the only way to get Odd. Powers: An Odd number to any power is Odd. An Even number to any power is Even. Now, let’s do a question Without computing them, find out which of the following arithmetic expressions are even. Let’s look at them one-by-one 43+37 Logic: Odd + Odd. Result: EVEN 672−348 Logic: Even - Even. Result: EVEN 4×347×3 Logic: There is a 𝟒 in the multiplication chain. Since 𝟒 is even, the whole answer must be even. Result: EVEN 708−477 Logic: Even - Odd. (Different parities result in Odd). Result: Odd 809+214 Logic: Odd + Even. Result: Odd 119×303 Logic: Odd × Odd. Result: Odd 543−479 Logic: Odd - Odd. Result: EVEN 513^3 Logic: The base (513) is Odd. An odd number multiplied by itself is always Odd. Result: Odd Answer Summary: The even expressions are 43+37, 672−348, 4×347×3, and 543− 479. Now, let’s look at Algebraic Expressions (with variables)